Isabelle Cheylan, Guillaume Fritz, Denis Ricot, Pierre Sagaut. Shape Optimization Using the Adjoint Lattice Boltzmann Method for Aerodynamic Applications. AIAA Journal, 2019, 57 (7), pp.2758-2773. ⟨10.2514/1.J057955⟩. ⟨hal-02468051⟩ Plus de détails...
The present work focuses on shape optimization using the lattice Boltzmann method applied to aerodynamic cases. The adjoint method is used to calculate the sensitivities of the drag force with respect to the shape of an object. The main advantage of the adjoint method is its cost, because it is independent from the number of optimization parameters. The approach used consists in developing a continuous adjoint of the primal problem discretized in space, time, and velocities. An adjoint lattice Boltzmann equation is thus found, which is solved using the same algorithms as in the primal problem. The test cases investigate new features compared to what exists in the literature, such as the derivation of the grid refinement models in the primal problem to obtain their adjoint counterparts, but also the derivation of a double-relaxation-time algorithm and the Ginzburg et al. interpolation at the wall ("Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization, Velocity, Pressure and Mixed Boundary Conditions," Communications in Computational Physics, Vol. 3, No. 2, 2008, pp. 427-478). Regarding the unsteadiness of the primal problem, two methods differing in accuracy and computational effort are compared using a two-dimensional unsteady case. Finally, this first-of-a-kind adjoint solver is applied to a large-scale threedimensional turbulent case (the flow of air around a car at a speed of 130 km/h), which shows its usefulness in the industry.
Isabelle Cheylan, Guillaume Fritz, Denis Ricot, Pierre Sagaut. Shape Optimization Using the Adjoint Lattice Boltzmann Method for Aerodynamic Applications. AIAA Journal, 2019, 57 (7), pp.2758-2773. ⟨10.2514/1.J057955⟩. ⟨hal-02468051⟩
Vincent Mons, Jean-Camille Chassaing, Thomas Gomez, Pierre Sagaut. Reconstruction of unsteady viscous flows using data assimilation schemes. Journal of Computational Physics, 2016, 316, pp.255-280. ⟨10.1016/j.jcp.2016.04.022⟩. ⟨hal-01333881⟩ Plus de détails...
This paper investigates the use of various data assimilation (DA) approaches for the reconstruction of the unsteady flow past a cylinder in the presence of incident coherent gusts. Variational, ensemble Kalman filter-based and ensemble-based variational DA techniques are deployed along with a 2D compressible Navier–Stokes flow solver, which is also used to generate synthetic observations of a reference flow. The performance of these DA schemes is thoroughly analyzed for various types of observations ranging from the global aerodynamic coefficients of the cylinder to the full 2D flow field. Moreover, different reconstruction scenarios are investigated in order to assess the robustness of these methods for large scale DA problems with up to 105 control variables. In particular, we show how an iterative procedure can be used within the framework of ensemble-based methods to deal with both non-uniform unsteady boundary conditions and initial field reconstruction. The different methodologies developed and assessed in this work give a review of what can be done with DA schemes in computational fluid dynamics (CFD) paradigm. In the same time, this work also provides useful information which can also turn out to be rational arguments in the DA scheme choice dedicated to a specific CFD application.
Vincent Mons, Jean-Camille Chassaing, Thomas Gomez, Pierre Sagaut. Reconstruction of unsteady viscous flows using data assimilation schemes. Journal of Computational Physics, 2016, 316, pp.255-280. ⟨10.1016/j.jcp.2016.04.022⟩. ⟨hal-01333881⟩
Seung-Bu Park, Pierre Gentine, Kai Schneider, Marie Farge. Coherent Structures in the Boundary and Cloud Layers: Role of Updrafts, Subsiding Shells, and Environmental Subsidence. Journal of the Atmospheric Sciences, 2016, 73 (4), pp.1789-1814. ⟨10.1175/JAS-D-15-0240.1⟩. ⟨hal-01461782⟩ Plus de détails...
Coherent structures, such as updrafts, downdrafts/shells, and environmental subsidence in the boundary and cloud layers of shallow convection, are investigated using a new classification method. Using large-eddy simulation data, the new method first filters out background turbulence and small-scale gravity waves from the coherent part of the flow, composed of turbulent coherent structures and large-scale transporting gravity waves. Then the algorithm divides this coherent flow into ``updrafts,'' ``downdrafts/shells,'' ``subsidence,'' ``ascendance,'' and four other flow structures using an octant analysis. The novel method can systematically track structures from the cloud-free boundary layer to the cloud layer, thus allowing systematic analysis of the fate of updrafts and downdrafts. The frequency and contribution of the coherent structures to the vertical mass flux and transport of heat and moisture can then be investigated for the first time. Updrafts, subsidence, and downdrafts/subsiding shells-to a lesser extent-are shown to be the most frequent and dominant contributors to the vertical transport of heat and moisture in the boundary layer. Contrary to previous perspective, environmental subsidence transport is shown to be weak in the cloud layer. Instead, downdrafts/shells are the main downward transport contributors, especially in the trade inversion layer. The newly developed method in this study can be used to better evaluate the entrainment and detrainment of individual-or an ensemble of-coherent structures from the unsaturated boundary layer to the cloud layer.
Seung-Bu Park, Pierre Gentine, Kai Schneider, Marie Farge. Coherent Structures in the Boundary and Cloud Layers: Role of Updrafts, Subsiding Shells, and Environmental Subsidence. Journal of the Atmospheric Sciences, 2016, 73 (4), pp.1789-1814. ⟨10.1175/JAS-D-15-0240.1⟩. ⟨hal-01461782⟩
Seung-Bu Park, Pierre Gentine, Kai Schneider, Marie Farge. Coherent Structures in the Boundary and Cloud Layers: Role of Updrafts, Subsiding Shells, and Environmental Subsidence. Journal of the Atmospheric Sciences, American Meteorological Society, 2016, 73 (4), pp.1789-1814. ⟨10.1175/JAS-D-15-0240.1⟩. ⟨hal-01461782⟩ Plus de détails...
Coherent structures, such as updrafts, downdrafts/shells, and environmental subsidence in the boundary and cloud layers of shallow convection, are investigated using a new classification method. Using large-eddy simulation data, the new method first filters out background turbulence and small-scale gravity waves from the coherent part of the flow, composed of turbulent coherent structures and large-scale transporting gravity waves. Then the algorithm divides this coherent flow into ``updrafts,'' ``downdrafts/shells,'' ``subsidence,'' ``ascendance,'' and four other flow structures using an octant analysis. The novel method can systematically track structures from the cloud-free boundary layer to the cloud layer, thus allowing systematic analysis of the fate of updrafts and downdrafts. The frequency and contribution of the coherent structures to the vertical mass flux and transport of heat and moisture can then be investigated for the first time. Updrafts, subsidence, and downdrafts/subsiding shells-to a lesser extent-are shown to be the most frequent and dominant contributors to the vertical transport of heat and moisture in the boundary layer. Contrary to previous perspective, environmental subsidence transport is shown to be weak in the cloud layer. Instead, downdrafts/shells are the main downward transport contributors, especially in the trade inversion layer. The newly developed method in this study can be used to better evaluate the entrainment and detrainment of individual-or an ensemble of-coherent structures from the unsaturated boundary layer to the cloud layer.
Seung-Bu Park, Pierre Gentine, Kai Schneider, Marie Farge. Coherent Structures in the Boundary and Cloud Layers: Role of Updrafts, Subsiding Shells, and Environmental Subsidence. Journal of the Atmospheric Sciences, American Meteorological Society, 2016, 73 (4), pp.1789-1814. ⟨10.1175/JAS-D-15-0240.1⟩. ⟨hal-01461782⟩
Aerodynamic ground effect in flapping-wing insect flight is of importance to comparative morphologies and of interest to the micro-air-vehicle (MAV) community. Recent studies, however, show apparently contradictory results of either some significant extra lift or power savings, or zero ground effect. Here we present a numerical study of fruitfly sized insect takeoff with a specific focus on the significance of leg thrust and wing kinematics. Flapping-wing takeoff is studied using numerical modelling and high performance computing. The aerodynamic forces are calculated using a three-dimensional Navier--Stokes solver based on a pseudo-spectral method with volume penalization. It is coupled with a flight dynamics solver that accounts for the body weight, inertia and the leg thrust, while only having two degrees of freedom: the vertical and the longitudinal horizontal displacement. The natural voluntary takeoff of a fruitfly is considered as reference. The parameters of the model are then varied to explore possible effects of interaction between the flapping-wing model and the ground plane. These modified takeoffs include cases with decreased leg thrust parameter, and/or with periodic wing kinematics, constant body pitch angle. The results show that the ground effect during natural voluntary takeoff is negligible. In the modified takeoffs, when the rate of climb is slow, the difference in the aerodynamic forces due to the interaction with the ground is up to 6%. Surprisingly, depending on the kinematics, the difference is either positive or negative, in contrast to the intuition based on the helicopter theory, which suggests positive excess lift. This effect is attributed to unsteady wing-wake interactions. A similar effect is found during hovering.
Dmitry Kolomenskiy, Masateru Maeda, Thomas Engels, Hao Liu, Kai Schneider, et al.. Aerodynamic Ground Effect in Fruitfly Sized Insect Takeoff. PLoS ONE, 2016, 11 (3), pp.e0152072. ⟨10.1371/journal.pone.0152072⟩. ⟨hal-01299261⟩
Dmitry Kolomenskiy, Jean-Christophe Nave, Kai Schneider. Adaptive gradient-augmented level set method with multiresolution error estimation. Journal of Scientific Computing, 2016, 66 (1), pp.116-140. ⟨10.1007/s10915-015-0014-7⟩. ⟨hal-01146954⟩ Plus de détails...
A space–time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quadtree data structures. For adaptive time integration, an embedded Runge–Kutta method is employed. The precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported.
Dmitry Kolomenskiy, Jean-Christophe Nave, Kai Schneider. Adaptive gradient-augmented level set method with multiresolution error estimation. Journal of Scientific Computing, 2016, 66 (1), pp.116-140. ⟨10.1007/s10915-015-0014-7⟩. ⟨hal-01146954⟩
Frank G. Jacobitz, Kai Schneider, Wouter J.T. Bos, Marie Farge. Structure of sheared and rotating turbulence: Multiscale statistics of Lagrangian and Eulerian accelerations and passive scalar dynamics. Physical Review E , 2016, 93 (1), pp.013113. ⟨10.1103/PhysRevE.93.013113⟩. ⟨hal-01299256⟩ Plus de détails...
The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar dependence on the rotation to shear ratio. The variance and flatness of both accelerations are analyzed and the extreme values of the Eulerian acceleration are observed to be above those of the Lagrangian acceleration. For strong rotation it is observed that flatness yields values close to three, corresponding to Gaussian-like behavior, and for moderate and vanishing rotation the flatness increases. Furthermore, the Lagrangian and Eulerian accelerations are shown to be strongly correlated for strong rotation due to a reduced nonlinear term in this case. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian acceleration is even more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. Moreover, the dynamics of a passive scalar with gradient production in the direction of the mean velocity gradient is analyzed and the influence of the rotation to shear ratio is studied. Concerning the concentration of a passive scalar spread by the flow, the pdf of its Eulerian time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the Eulerian time rate of change of scalar concentration is mainly due to advection, while its Lagrangian counterpart is only due to gradient production and viscous dissipation.
Frank G. Jacobitz, Kai Schneider, Wouter J.T. Bos, Marie Farge. Structure of sheared and rotating turbulence: Multiscale statistics of Lagrangian and Eulerian accelerations and passive scalar dynamics. Physical Review E , 2016, 93 (1), pp.013113. ⟨10.1103/PhysRevE.93.013113⟩. ⟨hal-01299256⟩
Dmitry Kolomenskiy, Jean-Christophe Nave, Kai Schneider. Adaptive gradient-augmented level set method with multiresolution error estimation. Journal of Scientific Computing, 2016, 66, pp.116-140. ⟨10.1007/s10915-015-0014-7⟩. ⟨hal-01146954⟩ Plus de détails...
A space–time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quadtree data structures. For adaptive time integration, an embedded Runge–Kutta method is employed. The precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported.
Dmitry Kolomenskiy, Jean-Christophe Nave, Kai Schneider. Adaptive gradient-augmented level set method with multiresolution error estimation. Journal of Scientific Computing, 2016, 66, pp.116-140. ⟨10.1007/s10915-015-0014-7⟩. ⟨hal-01146954⟩
T. Engels, D. Kolomenskiy, Kai Schneider, F.-O. Lehmann, J. Sesterhenn. Bumblebee Flight in Heavy Turbulence. Physical Review Letters, 2016, 116 (2), pp.028103. ⟨10.1103/PhysRevLett.116.028103⟩. ⟨hal-01299332⟩ Plus de détails...
High-resolution numerical simulations of a tethered model bumblebee in forward flight are performed superimposing homogeneous isotropic turbulent fluctuations to the uniform inflow. Despite tremendous variation in turbulence intensity, between 17% and 99% with respect to the mean flow, we do not find significant changes in cycle-averaged aerodynamic forces, moments or flight power when averaged over realizations, compared to laminar inflow conditions. The variance of aerodynamic measures, however, significantly increases with increasing turbulence intensity, which may explain flight instabilities observed in freely flying bees.
T. Engels, D. Kolomenskiy, Kai Schneider, F.-O. Lehmann, J. Sesterhenn. Bumblebee Flight in Heavy Turbulence. Physical Review Letters, 2016, 116 (2), pp.028103. ⟨10.1103/PhysRevLett.116.028103⟩. ⟨hal-01299332⟩
Benjamin Kadoch, Thorsten Reimann, Kai Schneider, Michael Schäfer. Comparison of a spectral method with volume penalization and a finite volume method with body fitted grids for turbulent flows. Computers and Fluids, 2016, 133, pp.140-150. ⟨10.1016/j.compfluid.2016.04.028⟩. ⟨hal-01455110⟩ Plus de détails...
We consider a turbulent flow past periodic hills at Reynolds number 1400 and compare two numerical methods: A Fourier pseudo–spectral scheme with volume penalization to model the no-slip boundary conditions and a finite volume method with body fitted grids. A detailed comparison of the results is presented for mean velocity profiles and Reynolds stress and confronted with those obtained by Breuer et al. [1]. In addition higher order statistics are performed and their scale-dependence is analyzed using orthogonal wavelets. Moreover, for the Fourier pseudo-spectral scheme, the influence of the Reynolds number is investigated.
Benjamin Kadoch, Thorsten Reimann, Kai Schneider, Michael Schäfer. Comparison of a spectral method with volume penalization and a finite volume method with body fitted grids for turbulent flows. Computers and Fluids, 2016, 133, pp.140-150. ⟨10.1016/j.compfluid.2016.04.028⟩. ⟨hal-01455110⟩
Marie Farge, Kai Schneider. Wavelet transforms and their applications to MHD and plasma turbulence: a review. Journal of Plasma Physics, 2015, 81 (06), pp.435810602. ⟨10.1017/S0022377815001075⟩. ⟨hal-01299264⟩ Plus de détails...
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented.
Marie Farge, Kai Schneider. Wavelet transforms and their applications to MHD and plasma turbulence: a review. Journal of Plasma Physics, 2015, 81 (06), pp.435810602. ⟨10.1017/S0022377815001075⟩. ⟨hal-01299264⟩
Kai Schneider. Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review. Journal of Plasma Physics, 2015, 81 (06), pp.435810601. ⟨10.1017/S0022377815000598⟩. ⟨hal-01299254⟩ Plus de détails...
Immersed boundary methods for computing confined fluid and plasma flows in complex geometries are reviewed. The mathematical principle of the volume penalization technique is described and simple examples for imposing Dirichlet and Neumann boundary conditions in one dimension are given. Applications for fluid and plasma turbulence in two and three space dimensions illustrate the applicability and the efficiency of the method in computing flows in complex geometries, for example in toroidal geometries with asymmetric poloidal cross-sections.
Kai Schneider. Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review. Journal of Plasma Physics, 2015, 81 (06), pp.435810601. ⟨10.1017/S0022377815000598⟩. ⟨hal-01299254⟩
Dmitry Kolomenskiy, Romain Nguyen van Yen, Kai Schneider. Analysis and discretization of the volume penalized Laplace operator with Neumann boundary conditions. Applied Numerical Analysis and Computational Mathematics, 2015, 95, pp.238-249. ⟨10.1016/j.apnum.2014.02.003⟩. ⟨hal-01299247⟩ Plus de détails...
We study the properties of an approximation of the Laplace operator with Neumann boundary conditions using volume penalization. For the one-dimensional Poisson equation we compute explicitly the exact solution of the penalized equation and quantify the penalization error. Numerical simulations using finite differences allow then to assess the discretization and penalization errors. The eigenvalue problem of the penalized Laplace operator with Neumann boundary conditions is also studied. As examples in two space dimensions, we consider a Poisson equation with Neumann boundary conditions in rectangular and circular domains.
Dmitry Kolomenskiy, Romain Nguyen van Yen, Kai Schneider. Analysis and discretization of the volume penalized Laplace operator with Neumann boundary conditions. Applied Numerical Analysis and Computational Mathematics, 2015, 95, pp.238-249. ⟨10.1016/j.apnum.2014.02.003⟩. ⟨hal-01299247⟩
Journal: Applied Numerical Analysis and Computational Mathematics
Anna Karina Fontes Gomes, Margarete Oliveira Domingues, Kai Schneider, Odim Mendes, Ralf Deiterding. An adaptive multiresolution method for ideal magnetohydrodynamics using divergence cleaning with parabolic–hyperbolic correction. Applied Numerical Analysis and Computational Mathematics, 2015, 95 (4), pp.199-213. ⟨10.1016/j.apnum.2015.01.007⟩. ⟨hal-01299252⟩ Plus de détails...
We present an adaptive multiresolution method for the numerical simulation of ideal magnetohydrodynamics in two space dimensions. The discretization uses a finite volume scheme based on a Cartesian mesh and an explicit compact Runge–Kutta scheme for time integration. Harten's cell average multiresolution allows to introduce a locally refined spatial mesh while controlling the error. The incompressibility of the magnetic field is controlled by using a Generalized Lagrangian Multiplier (GLM) approach with a mixed hyperbolic–parabolic correction. Different applications to two-dimensional problems illustrate the properties of the method. For each application CPU time and memory savings are reported and numerical aspects of the method are discussed. The accuracy of the adaptive computations is assessed by comparison with reference solutions computed on a regular fine mesh.
Anna Karina Fontes Gomes, Margarete Oliveira Domingues, Kai Schneider, Odim Mendes, Ralf Deiterding. An adaptive multiresolution method for ideal magnetohydrodynamics using divergence cleaning with parabolic–hyperbolic correction. Applied Numerical Analysis and Computational Mathematics, 2015, 95 (4), pp.199-213. ⟨10.1016/j.apnum.2015.01.007⟩. ⟨hal-01299252⟩
Journal: Applied Numerical Analysis and Computational Mathematics
Wouter J.T. Bos, Benjamin Kadoch, Kai Schneider. Angular statistics of Lagrangian trajectories in turbulence. Physical Review Letters, 2015, 114, pp.214502. ⟨10.1103/PhysRevLett.114.214502⟩. ⟨hal-01085070⟩ Plus de détails...
The angle between subsequent particle displacement increments is evaluated as a function of the timelag in isotropic turbulence. It is shown that the evolution of this angle contains two well-defined power-laws, reflecting the multi-scale dynamics of high-Reynolds number turbulence. The proba-bility density function of the directional change is shown to be self-similar and well approximated by an analytically derived model assuming Gaussianity and independence of the velocity and the Lagrangian acceleration.
Wouter J.T. Bos, Benjamin Kadoch, Kai Schneider. Angular statistics of Lagrangian trajectories in turbulence. Physical Review Letters, 2015, 114, pp.214502. ⟨10.1103/PhysRevLett.114.214502⟩. ⟨hal-01085070⟩
Jorge A. Morales, Wouter J.T. Bos, Kai Schneider, David C. Montgomery. Magnetohydrodynamically generated velocities in confined plasma. Physics of Plasmas, 2015, 22 (4), pp.042515. ⟨10.1063/1.4918774⟩. ⟨hal-00849742⟩ Plus de détails...
We investigate by numerical simulation the rotational flows in a toroid confining a conducting magnetofluid in which a current is driven by the application of externally supported electric and magnetic fields. The computation involves no microscopic instabilities and is purely magnetohydrodynamic (MHD). We show how the properties and intensity of the rotations are regulated by dimensionless numbers (Lundquist and viscous Lundquist) that contain the resistivity and viscosity of the magnetofluid. At the magnetohydrodynamic level (uniform mass density and incompressible magnetofluids), rotational flows appear in toroidal, driven MHD. The evolution of these flows with the transport coefficients, geometry, and safety factor are described.
Jorge A. Morales, Wouter J.T. Bos, Kai Schneider, David C. Montgomery. Magnetohydrodynamically generated velocities in confined plasma. Physics of Plasmas, 2015, 22 (4), pp.042515. ⟨10.1063/1.4918774⟩. ⟨hal-00849742⟩
Olivier Roussel, Kai Schneider. Adaptive multiresolution computations applied to detonations. Zeitschrift für Physikalische Chemie, 2015, 229 (6), pp.931-953. ⟨hal-01118153⟩ Plus de détails...
A space-time adaptive method is presented for the reactive Euler equations describing chemically reacting gas flow where a two species model is used for the chemistry. The governing equations are discretized with a finite volume method and dynamic space adaptivity is introduced using multiresolution analysis. A time splitting method of Strang is applied to be able to consider stiff problems while keeping the method explicit. For time adaptivity an improved Runge--Kutta--Fehlberg scheme is used. Applications deal with detonation problems in one and two space dimensions. A comparison of the adaptive scheme with reference computations on a regular grid allow to assess the accuracy and the computational efficiency, in terms of CPU time and memory requirements.
Olivier Roussel, Kai Schneider. Adaptive multiresolution computations applied to detonations. Zeitschrift für Physikalische Chemie, 2015, 229 (6), pp.931-953. ⟨hal-01118153⟩
Seyed Amin Ghaffari, Stéphane Viazzo, Kai Schneider, Patrick Bontoux. Simulation of forced deformable bodies interacting with two-dimensional incompressible flows: Application to fish-like swimming. International Journal of Heat and Fluid Flow, 2015, Theme special issue celebrating the 75th birthdays of Brian Launder and Kemo Hanjalic, 51, pp.88-109. ⟨10.1016/j.ijheatfluidflow.2014.10.023⟩. ⟨hal-00967077v2⟩ Plus de détails...
We present an efficient algorithm for simulation of deformable bodies interacting with two-dimensional incompressible flows. The temporal and spatial discretizations of the Navier-Stokes equations in vorticity stream-function formulation are based on classical fourth-order Runge-Kutta and compact finite differences, respectively. Using a uniform Cartesian grid we benefit from the advantage of a new fourth-order direct solver for the Poisson equation to ensure the incompressibility constraint down to machine zero. For introducing a deformable body in fluid flow, the volume penalization method is used. A Lagrangian structured grid with prescribed motion covers the deformable body interacting with the surrounding fluid due to the hydrodynamic forces and moment calculated on the Eulerian reference grid. An efficient law for curvature control of an anguilliform fish, swimming to a prescribed goal, is proposed. Validation of the developed method shows the efficiency and expected accuracy of the algorithm for fish-like swimming and also for a variety of fluid/solid interaction problems.
Seyed Amin Ghaffari, Stéphane Viazzo, Kai Schneider, Patrick Bontoux. Simulation of forced deformable bodies interacting with two-dimensional incompressible flows: Application to fish-like swimming. International Journal of Heat and Fluid Flow, 2015, Theme special issue celebrating the 75th birthdays of Brian Launder and Kemo Hanjalic, 51, pp.88-109. ⟨10.1016/j.ijheatfluidflow.2014.10.023⟩. ⟨hal-00967077v2⟩
Journal: International Journal of Heat and Fluid Flow
Thomas Engels, Dmitry Kolomenskiy, Kai Schneider, Jörn Sesterhenn. Numerical simulation of fluid–structure interaction with the volume penalization method. Journal of Computational Physics, 2015, 281, pp.96-115. ⟨10.1016/j.jcp.2014.10.005⟩. ⟨hal-01299253⟩ Plus de détails...
We present a novel scheme for the numerical simulation of fluid–structure interaction problems. It extends the volume penalization method, a member of the family of immersed boundary methods, to take into account flexible obstacles. We show how the introduction of a smoothing layer, physically interpreted as surface roughness, allows for arbitrary motion of the deformable obstacle. The approach is carefully validated and good agreement with various results in the literature is found. A simple one-dimensional solid model is derived, capable of modeling arbitrarily large deformations and imposed motion at the leading edge, as it is required for the simulation of simplified models for insect flight. The model error is shown to be small, while the one-dimensional character of the model features a reasonably easy implementation. The coupled fluid–solid interaction solver is shown not to introduce artificial energy in the numerical coupling, and validated using a widely used benchmark. We conclude with the application of our method to models for insect flight and study the propulsive efficiency of one and two wing sections.
Thomas Engels, Dmitry Kolomenskiy, Kai Schneider, Jörn Sesterhenn. Numerical simulation of fluid–structure interaction with the volume penalization method. Journal of Computational Physics, 2015, 281, pp.96-115. ⟨10.1016/j.jcp.2014.10.005⟩. ⟨hal-01299253⟩
Thomas Engels, Dmitry Kolomenskiy, Kai Schneider, Jörn Sesterhenn. Numerical simulation of fluid–structure interaction with the volume penalization method. Journal of Computational Physics, 2015, 281, pp.96-115. ⟨10.1016/j.jcp.2014.10.005⟩. ⟨hal-01299253⟩ Plus de détails...
We present a novel scheme for the numerical simulation of fluid–structure interaction problems. It extends the volume penalization method, a member of the family of immersed boundary methods, to take into account flexible obstacles. We show how the introduction of a smoothing layer, physically interpreted as surface roughness, allows for arbitrary motion of the deformable obstacle. The approach is carefully validated and good agreement with various results in the literature is found. A simple one-dimensional solid model is derived, capable of modeling arbitrarily large deformations and imposed motion at the leading edge, as it is required for the simulation of simplified models for insect flight. The model error is shown to be small, while the one-dimensional character of the model features a reasonably easy implementation. The coupled fluid–solid interaction solver is shown not to introduce artificial energy in the numerical coupling, and validated using a widely used benchmark. We conclude with the application of our method to models for insect flight and study the propulsive efficiency of one and two wing sections.
Thomas Engels, Dmitry Kolomenskiy, Kai Schneider, Jörn Sesterhenn. Numerical simulation of fluid–structure interaction with the volume penalization method. Journal of Computational Physics, 2015, 281, pp.96-115. ⟨10.1016/j.jcp.2014.10.005⟩. ⟨hal-01299253⟩
The dynamics of a magnetically forced conducting fluid in confined geometries is studied. A pseudospectral method with volume penalisation is used to solve the resistive magnetohydrodynamic (MHD) equations. A helical magnetic field is imposed via boundary conditions, which generates a response in the velocity field for large enough magnitudes. Different helical structures are observed in the flow depending on the magnitude and direction of the forcing and the cross-sectional geometry of the fluid domain. A computational technique for finding a solenoidal vector field which can be used in complex geometries is also proposed.
Romain Nguyen Van Yen, Dmitry Kolomenskiy, Kai Schneider. Approximation of the Laplace and Stokes operators with Dirichlet ă boundary conditions through volume penalization: a spectral viewpoint. Numerische Mathematik, 2014, 128 (2), pp.301-338. ⟨10.1007/s00211-014-0610-8⟩. ⟨hal-01464705⟩ Plus de détails...
We report the results of a study on the spectral properties of Laplace ă and Stokes operators modified with a volume penalization term designed ă to approximate Dirichlet conditions in the limit when a penalization ă parameter, , tends to zero. The eigenvalues and eigenfunctions are ă determined either analytically or numerically as functions of , both in ă the continuous case and after applying Fourier or finite difference ă discretization schemes. For fixed , we find that only the part of the ă spectrum corresponding to eigenvalues approaches Dirichlet boundary ă conditions, while the remainder of the spectrum is made of uncontrolled, ă spurious wall modes. The penalization error for the controlled ă eigenfunctions is estimated as a function of and . Surprisingly, in the ă Stokes case, we show that the eigenfunctions approximately satisfy, with ă a precision , Navier slip boundary conditions with slip length equal to ă . Moreover, for a given discretization, we show that there exists a ă value of , corresponding to a balance between penalization and ă discretization errors, below which no further gain in precision is ă achieved. These results shed light on the behavior of volume ă penalization schemes when solving the Navier-Stokes equations, outline ă the limitations of the method, and give indications on how to choose the ă penalization parameter in practical cases.
Romain Nguyen Van Yen, Dmitry Kolomenskiy, Kai Schneider. Approximation of the Laplace and Stokes operators with Dirichlet ă boundary conditions through volume penalization: a spectral viewpoint. Numerische Mathematik, 2014, 128 (2), pp.301-338. ⟨10.1007/s00211-014-0610-8⟩. ⟨hal-01464705⟩
Jorge A. Morales, Wouter J.T. Bos, Kai Schneider, David Montgomery. The effect of toroidicity on Reversed Field Pinch dynamics. Plasma Physics and Controlled Fusion, 2014, 56, pp.095024 ⟨10.1088/0741-3335/56/9/095024⟩. ⟨hal-01026354⟩ Plus de détails...
The influence of the curvature of the imposed magnetic field on Reversed Field Pinch dynamics is investigated by comparing the flow of a magnetofluid in a torus with aspect ratio 1.83, with the flow in a periodic cylinder. It is found that an axisymmetric toroidal mode is always present in the toroidal, but absent in the cylindrical configuration. In particular, in contrast to the cylinder, the toroidal case presents a double poloidal recirculation cell with a shear localized at the plasma edge. Quasi-single-helicity states are found to be more persistent in toroidal than in periodic cylinder geometry.
Jorge A. Morales, Wouter J.T. Bos, Kai Schneider, David Montgomery. The effect of toroidicity on Reversed Field Pinch dynamics. Plasma Physics and Controlled Fusion, 2014, 56, pp.095024 ⟨10.1088/0741-3335/56/9/095024⟩. ⟨hal-01026354⟩
A. Salhi, Frank G. Jacobitz, Kai Schneider, Claude Cambon. Nonlinear dynamics and anisotropic structure of rotating sheared turbulence. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 89, pp.013020. ⟨10.1103/PhysRevE.89.013020⟩. ⟨hal-01048730⟩ Plus de détails...
Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations
A. Salhi, Frank G. Jacobitz, Kai Schneider, Claude Cambon. Nonlinear dynamics and anisotropic structure of rotating sheared turbulence. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 89, pp.013020. ⟨10.1103/PhysRevE.89.013020⟩. ⟨hal-01048730⟩
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
The paper presents a numerical investigation of the leading-edge vortices generated by rotating triangular wings at Reynolds number Re=250. A series of three-dimensional numerical simulations have been carried out using a Fourier pseudo-spectral method with volume penalization. The transition from stable attachment of the leading-edge vortex to periodic vortex shedding is explored, as a function of the wing aspect ratio and the angle of attack. It is found that, in a stable configuration, the spanwise flow in the recirculation bubble past the wing is due to the centrifugal force, incompressibility and viscous stresses. For the flow outside of the bubble, an inviscid model of spanwise flow is presented.
Romain Nguyen van Yen, Dmitry Kolomenskiy, Kai Schneider. Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint. Numerische Mathematik, 2014, 128 (2), pp.301-338. ⟨10.1007/s00211-014-0610-8⟩. ⟨hal-00830110⟩ Plus de détails...
We report the results of a detailed study of the spectral properties of Laplace and Stokes operators, modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, $\eta$, tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of $\eta$, both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed $\eta$, we find that only the part of the spectrum corresponding to eigenvalues $\lambda \lesssim \eta^{-1}$ approaches Dirichlet boundary conditions, while the remainder of the spectrum is made of uncontrolled, spurious wall modes. The penalization error for the controlled eigenfunctions is estimated as a function of $\eta$ and $\lambda$. Surprisingly, in the Stokes case, we show that the eigenfunctions approximately satisfy, with a precision $O(\eta)$, Navier slip boundary conditions with slip length equal to $\sqrt{\eta}$. Moreover, for a given discretization, we show that there exists a value of $\eta$, corresponding to a balance between penalization and discretization errors, below which no further gain in precision is achieved. These results shed light on the behavior of volume penalization schemes when solving the Navier-Stokes equations, outline the limitations of the method, and give indications on how to choose the penalization parameter in practical cases.
Romain Nguyen van Yen, Dmitry Kolomenskiy, Kai Schneider. Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint. Numerische Mathematik, 2014, 128 (2), pp.301-338. ⟨10.1007/s00211-014-0610-8⟩. ⟨hal-00830110⟩
Naoya Okamoto, Katsunori Yoshimatsu, Kai Schneider, Marie Farge. Small-scale anisotropic intermittency in magnetohydrodynamic turbulence at low magnetic Reynolds numbers. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 89 (3), pp.033013. ⟨10.1103/physreve.89.033013⟩. ⟨hal-01087726⟩ Plus de détails...
Small-scale anisotropic intermittency is examined in three-dimensional incompressible magnetohydrodynamic turbulence subjected to a uniformly imposed magnetic field. Orthonormal wavelet analyses are applied to direct numerical simulation data at moderate Reynolds number and for different interaction parameters. The magnetic Reynolds number is sufficiently low such that the quasistatic approximation can be applied. Scale-dependent statistical measures are introduced to quantify anisotropy in terms of the flow components, either parallel or perpendicular to the imposed magnetic field, and in terms of the different directions. Moreover, the flow intermittency is shown to increase with increasing values of the interaction parameter, which is reflected in strongly growing flatness values when the scale decreases. The scale-dependent anisotropy of energy is found to be independent of scale for all considered values of the interaction parameter. The strength of the imposed magnetic field does amplify the anisotropy of the flow.
Naoya Okamoto, Katsunori Yoshimatsu, Kai Schneider, Marie Farge. Small-scale anisotropic intermittency in magnetohydrodynamic turbulence at low magnetic Reynolds numbers. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 89 (3), pp.033013. ⟨10.1103/physreve.89.033013⟩. ⟨hal-01087726⟩
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Anthony Randriamampianina, Emilia Crespo del Arco. High resolution method for direct numerical simulation of the instability and transition in a baroclinic cavity. Thomas von Larcher, Paul D. Williams. Modelling atmospheric and oceanic flows: insights from laboratory experiments and numerical simulations, Wiley, chapter V.2, 2014, American Geophysical Union Series, 978-1-118-85593-5. ⟨hal-00993357⟩ Plus de détails...
Anthony Randriamampianina, Emilia Crespo del Arco. High resolution method for direct numerical simulation of the instability and transition in a baroclinic cavity. Thomas von Larcher, Paul D. Williams. Modelling atmospheric and oceanic flows: insights from laboratory experiments and numerical simulations, Wiley, chapter V.2, 2014, American Geophysical Union Series, 978-1-118-85593-5. ⟨hal-00993357⟩
Naoya Okamoto, Katsunori Yoshimatsu, Kai Schneider, Marie Farge. Small-scale anisotropic intermittency in magnetohydrodynamic turbulence at low magnetic Reynolds numbers. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2014, 89 (3), pp.033013. ⟨10.1103/physreve.89.033013⟩. ⟨hal-01087726⟩ Plus de détails...
Small-scale anisotropic intermittency is examined in three-dimensional incompressible magnetohydrodynamic turbulence subjected to a uniformly imposed magnetic field. Orthonormal wavelet analyses are applied to direct numerical simulation data at moderate Reynolds number and for different interaction parameters. The magnetic Reynolds number is sufficiently low such that the quasistatic approximation can be applied. Scale-dependent statistical measures are introduced to quantify anisotropy in terms of the flow components, either parallel or perpendicular to the imposed magnetic field, and in terms of the different directions. Moreover, the flow intermittency is shown to increase with increasing values of the interaction parameter, which is reflected in strongly growing flatness values when the scale decreases. The scale-dependent anisotropy of energy is found to be independent of scale for all considered values of the interaction parameter. The strength of the imposed magnetic field does amplify the anisotropy of the flow.
Naoya Okamoto, Katsunori Yoshimatsu, Kai Schneider, Marie Farge. Small-scale anisotropic intermittency in magnetohydrodynamic turbulence at low magnetic Reynolds numbers. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2014, 89 (3), pp.033013. ⟨10.1103/physreve.89.033013⟩. ⟨hal-01087726⟩
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Marie Farge, H. Keith Moffatt, Kai Schneider. FOREWORD: Turbulence Colloquium Marseille 2011. Journal of Turbulence, 2013, 14 (9), pp.39-42. ⟨10.1080/14685248.2013.851836⟩. ⟨hal-01300038⟩ Plus de détails...
Marie Farge, H. Keith Moffatt, Kai Schneider. FOREWORD: Turbulence Colloquium Marseille 2011. Journal of Turbulence, 2013, 14 (9), pp.39-42. ⟨10.1080/14685248.2013.851836⟩. ⟨hal-01300038⟩
Thomas Engels, Dmitry Kolomenskiy, Kai Schneider, Jörn Sesterhenn. Two-dimensional simulation of the fluttering instability using a pseudospectral method with volume penalization. Computers & Structures, 2013, 122, pp. 101-112 ⟨10.1016/j.compstruc.2012.12.007⟩. ⟨hal-01299992⟩ Plus de détails...
We present a new numerical scheme for the simulation of deformable objects immersed in a viscous incompressible fluid. The two-dimensional Navier-Stokes equations are discretized with an efficient Fourier pseudo-spectral scheme. Using the volume penalization method arbitrary inflow conditions can be enforced, together with the no-slip conditions at the boundary of the immersed flexible object. With respect to Kolomenskiy and Schneider (2009) [1], where rigid moving obstacles have been considered, the present work extends the volume penalization method to account for moving deformable objects while avoiding numerical oscillations in the hydrodynamic forces. For the solid part, a simple and accurate one-dimensional model, the non-linear beam equation, is employed. The coupling between the fluid and solid parts is realized with a fast explicit staggered scheme. The method is applied to the fluttering instability of a slender structure immersed in a free stream. This coupled non-linear system can enter three distinct states: stability of the initial condition or maintenance of an either periodic or chaotic fluttering motion. We present a detailed parameter study for different Reynolds numbers and reduced free-stream velocities. The dynamics of the transition from a periodic to a chaotic state is investigated. The results are compared with those obtained by an inviscid vortex shedding method [2] and by a viscous linear stability analysis [3], yielding for both satisfactory agreement. New results concerning the transition to chaos are presented.
Thomas Engels, Dmitry Kolomenskiy, Kai Schneider, Jörn Sesterhenn. Two-dimensional simulation of the fluttering instability using a pseudospectral method with volume penalization. Computers & Structures, 2013, 122, pp. 101-112 ⟨10.1016/j.compstruc.2012.12.007⟩. ⟨hal-01299992⟩
Rodrigo M. Pereira, Romain Nguyen-Van-Yen, Marie Farge, Kai Schneider. Wavelet methods to eliminate resonances in the Galerkin-truncated Burgers and Euler equations. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2013, 87 (3), pp.033017. ⟨10.1103/PhysRevE.87.033017⟩. ⟨hal-00830421⟩ Plus de détails...
It is well known that solutions to the Fourier-Galerkin truncation of the inviscid Burgers equation (and other hyperbolic conservation laws) do not converge to the physically relevant entropy solution after the formation of the first shock. This loss of convergence was recently studied in detail in [S. S. Ray et al., Phys. Rev. E 84, 016301 (2011)], and traced back to the appearance of a spatially localized resonance phenomenon perturbing the solution. In this work, we propose a way to remove this resonance by filtering a wavelet representation of the Galerkin-truncated equations. A method previously developed with a complex-valued wavelet frame is applied and expanded to embrace the use of real-valued orthogonal wavelet basis, which we show to yield satisfactory results only under the condition of adding a safety zone in wavelet space. We also apply the complex-valued wavelet based method to the 2D Euler equation problem, showing that it is able to filter the resonances in this case as well.
Rodrigo M. Pereira, Romain Nguyen-Van-Yen, Marie Farge, Kai Schneider. Wavelet methods to eliminate resonances in the Galerkin-truncated Burgers and Euler equations. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2013, 87 (3), pp.033017. ⟨10.1103/PhysRevE.87.033017⟩. ⟨hal-00830421⟩
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
M. Farge, K. Schneider, Olivier Pannekoucke, R. Nguyen Van Yen. Multiscale representations: fractals, self-similar random processes and wavelets. H.J. Fernando. Handbook of Environmental Fluid Dynamics, II, Taylor and Francis, pp.311-332, 2013. ⟨hal-01313530⟩ Plus de détails...
M. Farge, K. Schneider, Olivier Pannekoucke, R. Nguyen Van Yen. Multiscale representations: fractals, self-similar random processes and wavelets. H.J. Fernando. Handbook of Environmental Fluid Dynamics, II, Taylor and Francis, pp.311-332, 2013. ⟨hal-01313530⟩
Rodrigo M. Pereira, Romain Nguyen-Van-Yen, Marie Farge, Kai Schneider. Wavelet methods to eliminate resonances in the Galerkin-truncated Burgers and Euler equations. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2013, 87 (3), pp.033017. ⟨10.1103/PhysRevE.87.033017⟩. ⟨hal-00830421⟩ Plus de détails...
It is well known that solutions to the Fourier-Galerkin truncation of the inviscid Burgers equation (and other hyperbolic conservation laws) do not converge to the physically relevant entropy solution after the formation of the first shock. This loss of convergence was recently studied in detail in [S. S. Ray et al., Phys. Rev. E 84, 016301 (2011)], and traced back to the appearance of a spatially localized resonance phenomenon perturbing the solution. In this work, we propose a way to remove this resonance by filtering a wavelet representation of the Galerkin-truncated equations. A method previously developed with a complex-valued wavelet frame is applied and expanded to embrace the use of real-valued orthogonal wavelet basis, which we show to yield satisfactory results only under the condition of adding a safety zone in wavelet space. We also apply the complex-valued wavelet based method to the 2D Euler equation problem, showing that it is able to filter the resonances in this case as well.
Rodrigo M. Pereira, Romain Nguyen-Van-Yen, Marie Farge, Kai Schneider. Wavelet methods to eliminate resonances in the Galerkin-truncated Burgers and Euler equations. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2013, 87 (3), pp.033017. ⟨10.1103/PhysRevE.87.033017⟩. ⟨hal-00830421⟩
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Dmitry Kolomenskiy, Thomas Engels, Kai Schneider. Numerical Modelling of Flexible Heaving Foils. Journal of Aero Aqua Bio-mechanisms, 2013, 3 (1), pp. 22-28 ⟨10.5226/jabmech.3.22⟩. ⟨hal-01299235⟩ Plus de détails...
We consider the effects of chordwise flexibility on the aerodynamic performance of flapping wings using numerical simulation. The two-dimensional Navier-Stokes equations are solved using a Fourier pseudo-spectral method with no-slip boundary conditions imposed by the volume penalization method. The flexible wing is modelled with a non-linear beam equation. Our numerical simulations of heaving plates show that the maximum thrust is achieved at a stroke frequency lower than resonant, which is in agreement with experiments. The oscillatory part of the force only increases in amplitude when the frequency increases. We also consider aerodynamic interactions between two heaving foils.
Dmitry Kolomenskiy, Thomas Engels, Kai Schneider. Numerical Modelling of Flexible Heaving Foils. Journal of Aero Aqua Bio-mechanisms, 2013, 3 (1), pp. 22-28 ⟨10.5226/jabmech.3.22⟩. ⟨hal-01299235⟩
Katsunori Yoshimatsu, Naoya Okamoto, Yasuhiro Kawahara, Kai Schneider, Marie Farge. Coherent vorticity and current density simulation of three-dimensional magnetohydrodynamic turbulence using orthogonal wavelets. Geophysical and Astrophysical Fluid Dynamics, 2013, 107 (1-2), pp.73-92. ⟨10.1080/03091929.2012.654790⟩. ⟨hal-01032369⟩ Plus de détails...
A simulation method to track the time evolution of coherent vorticity and current density, called coherent vorticity and current density simulation (CVCS), is developed for three-dimensional (3D) incompressible magnetohydrodynamic (MHD) turbulence. The vorticity and current density fields are, respectively, decomposed at each time step into two orthogonal components, the coherent and incoherent fields, using an orthogonal wavelet representation. Each of the coherent fields is reconstructed from the wavelet coefficients whose modulus is larger than a threshold, while their incoherent counterparts are obtained from the remaining coefficients. The two threshold values depend on the instantaneous kinetic and magnetic enstrophies. The induced coherent velocity and magnetic fields are computed from the coherent vorticity and current density using the Biot-Savart kernel. In order to compute the flow evolution, one should retain not only the coherent wavelet coefficients but also their neighbors in wavelet space, and the set of those additional coefficients is called the safety zone. CVCS is performed for 3D forced incompressible homogeneous MHD turbulence without mean magnetic field for a magnetic Prandtl number equal to unity and with 256^3 grid points. The quality of CVCS is assessed by comparing the results with a direct numerical simulation. It is found that CVCS with the safety zone well preserves the statistical predictability of the turbulent flow with a reduced number of degrees of freedom. CVCS is also compared with a Fourier truncated simulation using a spectral cutoff filter where the number of retained Fourier modes is similar to the number of the wavelet coefficients retained by CVCS. It is shown that the wavelet representation is more suitable than the Fourier representation, especially concerning the probability density functions of vorticity and current density.
Katsunori Yoshimatsu, Naoya Okamoto, Yasuhiro Kawahara, Kai Schneider, Marie Farge. Coherent vorticity and current density simulation of three-dimensional magnetohydrodynamic turbulence using orthogonal wavelets. Geophysical and Astrophysical Fluid Dynamics, 2013, 107 (1-2), pp.73-92. ⟨10.1080/03091929.2012.654790⟩. ⟨hal-01032369⟩
Journal: Geophysical and Astrophysical Fluid Dynamics
The spatiotemporal self-organization of viscoresistive magnetohydrodynamics (MHD) in a toroidal geometry is studied. Curl-free toroidal magnetic and electric fields are imposed. It is observed in our simulations that a flow is generated, which evolves from dominantly poloidal to toroidal when the Lundquist numbers are increased. It is shown that this toroidal organization of the flow is consistent with the tendency of the velocity field to align with the magnetic field. Up-down asymmetry of the geometry causes the generation of a non-zero toroidal angular momentum.
Jorge Morales, Wouter J.T. Bos, Kai Schneider, David Montgomery. Intrinsic rotation of toroidally confined magnetohydrodynamics. Physical Review Letters, 2012, 109 (175002), pp.175002. ⟨10.1103/PhysRevLett.109.175002⟩. ⟨hal-00733093⟩
Raimund Buerger, Ricardo Ruiz-Baier, Kai Schneider, Ă Hector Torres. A MULTIRESOLUTION METHOD FOR THE SIMULATION OF SEDIMENTATION IN INCLINED ă CHANNELS. International Journal of Numerical Analysis and Modeling, 2012, 9 (3), pp.479-504. ⟨hal-01464735⟩ Plus de détails...
An adaptive multiresolution scheme is proposed for the numerical ă solution of a spatially two-dimensional model of sedimentation of ă suspensions of small solid particles dispersed in a viscous fluid. This ă model consists in a version of the Stokes equations for incompressible ă fluid flow coupled with a hyperbolic conservation law for the local ă solids concentration. We study the process in an inclined, rectangular ă closed vessel, a configuration that gives rise a well-known increase of ă settling rates (compared with a vertical vessel) known as the ``Boycott ă effect''. Sharp fronts and discontinuities in the concentration field ă are typical features of sedimentation phenomena. This solution behavior ă calls for locally refined meshes to concentrate computational effort on ă zones of strong variation. The spatial discretization presented herein ă is naturally based on a finite volume (FV) formulation for the Stokes ă problem including a pressure stabilization technique, while a ă Godunov-type scheme endowed with a fully adaptive multiresolution (MR) ă technique is applied to capture the evolution of the concentration ă field, which in addition induces an important speed-up of CPU time and ă savings in memory requirements. Numerical simulations illustrate that ă the proposed scheme is robust and allows for substantial reductions in ă computational effort while the computations remain accurate and stable.
Raimund Buerger, Ricardo Ruiz-Baier, Kai Schneider, Ă Hector Torres. A MULTIRESOLUTION METHOD FOR THE SIMULATION OF SEDIMENTATION IN INCLINED ă CHANNELS. International Journal of Numerical Analysis and Modeling, 2012, 9 (3), pp.479-504. ⟨hal-01464735⟩
Journal: International Journal of Numerical Analysis and Modeling
Romain Nguyen van Yen, Nicolas Fedorczak, F. Brochard, Gildas Bonhomme, Kai Schneider, et al.. Tomographic reconstruction of tokamak plasma light emission from single image using wavelet-vaguelette decomposition. Nuclear Fusion, 2012, 52 (1), pp.013005. ⟨10.1088/0029-5515/52/1/013005⟩. ⟨hal-01032416⟩ Plus de détails...
Images acquired by cameras installed in tokamaks are difficult to interpret because the three-dimensional structure of the plasma is flattened in a non-trivial way. Nevertheless, taking advantage of the slow variation of the fluctuations along magnetic field lines, the optical transformation may be approximated by a generalized Abel transform, for which we propose an inversion technique based on the wavelet-vaguelette decomposition. After validation of the new method using an academic test case and numerical data obtained with the Tokam 2D code, we present an application to an experimental movie obtained in the tokamak Tore Supra. A comparison with a classical regularization technique for ill-posed inverse problems, the singular value decomposition, allows us to assess the efficiency. The superiority of the wavelet-vaguelette technique is reflected in preserving local features, such as blobs and fronts, in the denoised emissivity map.
Romain Nguyen van Yen, Nicolas Fedorczak, F. Brochard, Gildas Bonhomme, Kai Schneider, et al.. Tomographic reconstruction of tokamak plasma light emission from single image using wavelet-vaguelette decomposition. Nuclear Fusion, 2012, 52 (1), pp.013005. ⟨10.1088/0029-5515/52/1/013005⟩. ⟨hal-01032416⟩
Romain Nguyen van Yen, Marie Farge, Kai Schneider. Scale-wise coherent vorticity extraction for conditional statistical modeling of homogeneous isotropic two-dimensional turbulence. Physica D: Nonlinear Phenomena, 2012, 241 (3), pp.186-201. ⟨10.1016/j.physd.2011.05.022⟩. ⟨hal-01115481⟩ Plus de détails...
Classical statistical theories of turbulence have shown their limitations, in that they cannot predict much more than the energy spectrum in an idealized setting of statistical homogeneity and stationarity. We explore the applicability of a conditional statistical modeling approach: can we sort out what part of the information should be kept, and what part should be modeled statistically, or, in other words, "dissipated"? Our mathematical framework is the initial value problem for the two-dimensional (2D) Euler equations, which we approximate numerically by solving the 2D Navier-Stokes equations in the vanishing viscosity limit. In order to obtain a good approximation of the inviscid dynamics, we use a spectral method and a resolution going up to 8192(2). We introduce a macroscopic concept of dissipation, relying on a split of the flow between coherent and incoherent contributions: the coherent flow is constructed from the large wavelet coefficients of the vorticity field, and the incoherent flow from the small ones. In previous work, a unique threshold was applied to all wavelet coefficients, while here we also consider the effect of a scale by scale thresholding algorithm, called scale-wise coherent vorticity extraction. We study the statistical properties of the coherent and incoherent vorticity fields, and the transfers of enstrophy between them, and then use these results to propose, within a maximum entropy framework, a simple model for the incoherent vorticity. In the framework of this model, we show that the flow velocity can be predicted accurately in the L-2 norm for about 10 eddy turnover times. (C) 2011 Elsevier B.V. All rights reserved.
Romain Nguyen van Yen, Marie Farge, Kai Schneider. Scale-wise coherent vorticity extraction for conditional statistical modeling of homogeneous isotropic two-dimensional turbulence. Physica D: Nonlinear Phenomena, 2012, 241 (3), pp.186-201. ⟨10.1016/j.physd.2011.05.022⟩. ⟨hal-01115481⟩
Benjamin Kadoch, Dmitry Kolomenskiy, Philippe Angot, Kai Schneider. A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles. Journal of Computational Physics, 2012, 231 (12), pp.4365-4383. ⟨10.1016/j.jcp.2012.01.036⟩. ⟨hal-01032208⟩ Plus de détails...
A volume penalization method for imposing homogeneous Neumann boundary conditions in advection-diffusion equations is presented. Thus complex geometries which even may vary in time can be treated efficiently using discretizations on a Cartesian grid. A mathematical analysis of the method is conducted first for the one-dimensional heat equation which yields estimates of the penalization error. The results are then confirmed numerically in one and two space dimensions. Simulations of two-dimensional incompressible flows with passive scalars using a classical Fourier pseudo-spectral method validate the approach for moving obstacles. The potential of the method for real world applications is illustrated by simulating a simplified dynamical mixer where for the fluid flow and the scalar transport no-slip and no-flux boundary conditions are imposed, respectively.
Benjamin Kadoch, Dmitry Kolomenskiy, Philippe Angot, Kai Schneider. A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles. Journal of Computational Physics, 2012, 231 (12), pp.4365-4383. ⟨10.1016/j.jcp.2012.01.036⟩. ⟨hal-01032208⟩
Raimund Burger, Ricardo Ruiz-Baier, Kai Schneider, Hector Torres. A multiresolution method for the simulation of sedimentation in inclined channels. International Journal of Numerical Analysis and Modeling, 2012, 9 (3), pp.479-504. ⟨hal-01032442⟩ Plus de détails...
An adaptive multiresolution scheme is proposed for the numerical solution of a spatially two-dimensional model of sedimentation of suspensions of small solid particles dispersed in a viscous fluid. This model consists in a version of the Stokes equations for incompressible fluid flow coupled with a hyperbolic conservation law for the local solids concentration. We study the process in an inclined, rectangular closed vessel, a configuration that gives rise a well-known increase of settling rates (compared with a vertical vessel) known as the "Boycott effect". Sharp fronts and discontinuities in the concentration field are typical features of sedimentation phenomena. This solution behavior calls for locally refined meshes to concentrate computational effort on zones of strong variation. The spatial discretization presented herein is naturally based on a finite volume (FV) formulation for the Stokes problem including a pressure stabilization technique, while a Godunov-type scheme endowed with a fully adaptive multiresolution (MR) technique is applied to capture the evolution of the concentration field, which in addition induces an important speed-up of CPU time and savings in memory requirements. Numerical simulations illustrate that the proposed scheme is robust and allows for substantial reductions in computational effort while the computations remain accurate and stable.
Raimund Burger, Ricardo Ruiz-Baier, Kai Schneider, Hector Torres. A multiresolution method for the simulation of sedimentation in inclined channels. International Journal of Numerical Analysis and Modeling, 2012, 9 (3), pp.479-504. ⟨hal-01032442⟩
Journal: International Journal of Numerical Analysis and Modeling
J. X. Sheng, A. Ysasi, Dmitry Kolomenskiy, E. Kanso, M. Nitsche, et al.. Simulating vortex wakes of flapping plates. Childress S. and all. Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding, Springer Science+Business Media, pp.255-262, 2012, The IMA Volumes in Mathematics and its Applications, 978-1-4614-3996-7. ⟨10.1007/978-1-4614-3997-4_21⟩. ⟨hal-01032453⟩ Plus de détails...
We compare different models to simulate two-dimensional vortex wakes behind oscillating plates. In particular, we compare solutions using a vortex sheet model and the simpler Brown-Michael model to solutions of the full Navier-Stokes equations obtained using a penalization method. The goal is to determine whether simpler models can be used to obtain good approximations to the form of the wake and the induced forces on the body.
J. X. Sheng, A. Ysasi, Dmitry Kolomenskiy, E. Kanso, M. Nitsche, et al.. Simulating vortex wakes of flapping plates. Childress S. and all. Natural Locomotion in Fluids and on Surfaces: Swimming, Flying, and Sliding, Springer Science+Business Media, pp.255-262, 2012, The IMA Volumes in Mathematics and its Applications, 978-1-4614-3996-7. ⟨10.1007/978-1-4614-3997-4_21⟩. ⟨hal-01032453⟩
Michael Wilczek, Benjamin Kadoch, Kai Schneider, Rudolf Friedrich, Marie Farge. Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence. Physics of Fluids, 2012, 24 (3), pp.035108. ⟨10.1063/1.3694807⟩. ⟨hal-01455124⟩ Plus de détails...
We investigate the conditional vorticity budget of fully developed three-dimensional homogeneous isotropic turbulence with respect to coherent and incoherent flow contributions. The coherent vorticity extraction based on orthogonal wavelets allows to decompose the vorticity field into coherent and incoherent contributions, of which the latter are noise-like. The impact of the vortex structures observed in fully developed turbulence on statistical balance equations is quantified considering the conditional vorticity budget. The connection between the basic structures present in the flow and their statistical implications is thereby assessed. The results are compared to those obtained for large-and small-scale contributions using a Fourier decomposition , which reveals pronounced differences.
Michael Wilczek, Benjamin Kadoch, Kai Schneider, Rudolf Friedrich, Marie Farge. Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence. Physics of Fluids, 2012, 24 (3), pp.035108. ⟨10.1063/1.3694807⟩. ⟨hal-01455124⟩
Frank G. Jacobitz, Kai Schneider, Wouter J.T. Bos, Marie Farge. On helical multiscale characterization of homogeneous turbulence. Journal of Turbulence, 2012, 13, pp.N35. ⟨10.1080/14685248.2012.711476⟩. ⟨hal-00780153⟩ Plus de détails...
Frank G. Jacobitz, Kai Schneider, Wouter J.T. Bos, Marie Farge. On helical multiscale characterization of homogeneous turbulence. Journal of Turbulence, 2012, 13, pp.N35. ⟨10.1080/14685248.2012.711476⟩. ⟨hal-00780153⟩
Benjamin Kadoch, D Del-Castillo-Negrete, W Bos, K. Schneider. Influence of flow topology on Lagrangian statistics in two-dimensional turbulence. Journal of Physics: Conference Series, 2011, 318 (5), pp.052032. ⟨10.1088/1742-6596/318/5/052032⟩. ⟨hal-02535093⟩ Plus de détails...
Benjamin Kadoch, D Del-Castillo-Negrete, W Bos, K. Schneider. Influence of flow topology on Lagrangian statistics in two-dimensional turbulence. Journal of Physics: Conference Series, 2011, 318 (5), pp.052032. ⟨10.1088/1742-6596/318/5/052032⟩. ⟨hal-02535093⟩
M Wilczek, Benjamin Kadoch, K. Schneider, R. Friedrich, M. Farge. Wavelet Analysis of the Conditional Vorticity Budget in Fully Developed Homogeneous Isotropic Turbulence. Journal of Physics: Conference Series, 2011, 318 (6), pp.062024. ⟨10.1088/1742-6596/318/6/062024⟩. ⟨hal-02535213⟩ Plus de détails...
M Wilczek, Benjamin Kadoch, K. Schneider, R. Friedrich, M. Farge. Wavelet Analysis of the Conditional Vorticity Budget in Fully Developed Homogeneous Isotropic Turbulence. Journal of Physics: Conference Series, 2011, 318 (6), pp.062024. ⟨10.1088/1742-6596/318/6/062024⟩. ⟨hal-02535213⟩
Romain Nguyen van Yen, Benjamin Kadoch, Vivek Kumar, Benjamin Ménétrier, Marie Farge, et al.. Influence of waves on Lagrangian acceleration in two-dimensional turbulent flows. ESAIM: Proceedings, 2011, 32, pp.231-241. ⟨10.1051/proc/2011023⟩. ⟨hal-02535109⟩ Plus de détails...
Romain Nguyen van Yen, Benjamin Kadoch, Vivek Kumar, Benjamin Ménétrier, Marie Farge, et al.. Influence of waves on Lagrangian acceleration in two-dimensional turbulent flows. ESAIM: Proceedings, 2011, 32, pp.231-241. ⟨10.1051/proc/2011023⟩. ⟨hal-02535109⟩
Benjamin Kadoch, Diego del Castillo Negrete, Wouter J.T. Bos, Kai Schneider. Lagrangian statistics and flow topology in forced two-dimensional turbulence. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2011, 83, pp.036314. ⟨10.1103/PhysRevE.83.036314⟩. ⟨hal-00647805⟩ Plus de détails...
A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.
Benjamin Kadoch, Diego del Castillo Negrete, Wouter J.T. Bos, Kai Schneider. Lagrangian statistics and flow topology in forced two-dimensional turbulence. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2011, 83, pp.036314. ⟨10.1103/PhysRevE.83.036314⟩. ⟨hal-00647805⟩
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Shinpei Futatani, Wouter J.T. Bos, Diego del Castillo Negrete, Kai Schneider, Sadruddin Benkadda, et al.. Coherent vorticity extraction in resistive drift-wave turbulence: Comparison of orthogonal wavelets versus proper orthogonal decomposition. Comptes Rendus. Physique, 2011, 12, pp.123-131. ⟨10.1016/j.crhy.2010.12.004⟩. ⟨hal-00647820⟩ Plus de détails...
We assess two techniques for extracting coherent vortices out of turbulent flows: the wavelet based Coherent Vorticity Extraction (CVE) and the Proper Orthogonal Decomposition (POD). The former decomposes the flow field into an orthogonal wavelet representation and subsequent thresholding of the coefficients allows one to split the flow into organized coherent vortices with non-Gaussian statistics and an incoherent random part which is structureless. POD is based on the singular value decomposition and decomposes the flow into basis functions which are optimal with respect to the retained energy for the ensemble average. Both techniques are applied to direct numerical simulation data of two-dimensional drift-wave turbulence governed by Hasegawa-Wakatani equation, considering two limit cases: the quasi-hydrodynamic and the quasi-adiabatic regimes. The results are compared in terms of compression rate, retained energy, retained enstrophy and retained radial flux, together with the enstrophy spectrum and higher order statistics.
Shinpei Futatani, Wouter J.T. Bos, Diego del Castillo Negrete, Kai Schneider, Sadruddin Benkadda, et al.. Coherent vorticity extraction in resistive drift-wave turbulence: Comparison of orthogonal wavelets versus proper orthogonal decomposition. Comptes Rendus. Physique, 2011, 12, pp.123-131. ⟨10.1016/j.crhy.2010.12.004⟩. ⟨hal-00647820⟩
Kai Schneider, Salah Neffaa, Wouter J.T. Bos. A pseudo-spectral method with volume penalisation for magnetohydrodynamic turbulence in confined domains. Computer Physics Communications, 2011, 182 (1), pp.2-7. ⟨10.1016/j.cpc.2010.05.019⟩. ⟨hal-00647827⟩ Plus de détails...
We present a Fourier pseudo-spectral method for solving the resistive magnetohydrodynamic equations of incompressible flow in confined domains. A volume penalisation method allows to take into account boundary conditions and the geometry of the domain. A code validation is presented for the z-pinch test case. Numerical simulations of decaying MHD turbulence in two space dimensions show spontaneous spin-up of the flow in non-axisymmetric geometries, which is reflected by the generation of angular momentum. First results of decaying MHD turbulence in a cylinder illustrate the potential of the new method for three-dimensional simulations.
Kai Schneider, Salah Neffaa, Wouter J.T. Bos. A pseudo-spectral method with volume penalisation for magnetohydrodynamic turbulence in confined domains. Computer Physics Communications, 2011, 182 (1), pp.2-7. ⟨10.1016/j.cpc.2010.05.019⟩. ⟨hal-00647827⟩
Dmitry Kolomenskiy, H.K. Moffatt, Marie Farge, Kai Schneider. Two- and three-dimensional numerical simulations of the clap-fling-sweep of hovering insects. Journal of Fluids and Structures, 2011, 27 (5-6), pp.784-791. ⟨10.1016/j.jfluidstructs.2011.05.002⟩. ⟨hal-01022662⟩ Plus de détails...
The importance of three-dimensional effects for flapping wings is addressed by means of numerical simulation. In particular, the clap-fling-sweep mechanism is examined. The flow at the beginning of the downstroke is shown to be in reasonable agreement with the two-dimensional approximation. After the wings move farther than one chord length apart, three-dimensional effects become essential. Two values of the Reynolds number are considered. At Re=128, the spanwise flow from the wing roots to the wing tips is driven by the centrifugal forces acting on the mass of the fluid trapped in the recirculation bubble behind the wings. It removes the excess of vorticity and delays the periodic vortex shedding. At Re=1400, vortex breakdown occurs past the outer portion of the wings, and multiple vortex filaments are shed into the wake.
Dmitry Kolomenskiy, H.K. Moffatt, Marie Farge, Kai Schneider. Two- and three-dimensional numerical simulations of the clap-fling-sweep of hovering insects. Journal of Fluids and Structures, 2011, 27 (5-6), pp.784-791. ⟨10.1016/j.jfluidstructs.2011.05.002⟩. ⟨hal-01022662⟩
Coherent vorticity simulation (CVS) is a multiscale method to compute incompressible turbulent flows based on the wavelet filtered Navier-Stokes equations. At each time step the vorticity field is decomposed into two orthogonal components using an orthogonal wavelet basis: the coherent vorticity, corresponding to the coefficients whose modulus is larger than a threshold, and the remaining incoherent vorticity. The threshold value only depends on the total enstrophy, which evolves in time, and on the maximal resolution, which remains constant. The induced coherent velocity is computed from the coherent vorticity using the Biot-Savart kernel. To compute the flow evolution one only retains the coherent wavelet coefficients and some of their neighbors in space, scale, and direction, which define the safety zone. Two different strategies are studied to minimize at each time step the number of degrees of freedom to be computed, either by increasing the threshold value or by reducing the width of the safety zone. Their efficiency is compared for a three-dimensional forced homogeneous isotropic turbulent flow at initial Taylor microscale Reynolds number Rλ=153. The quality of the results is assessed in comparison to a direct numerical simulation of the same flow. It is found that, as long as a safety zone is present, CVS well preserves the statistical predictability of the turbulent flow (even the vorticity and velocity probability distribution functions) with a reduced number of degrees of freedom.
Naoya Okamoto, Katsunori Yoshimatsu, Kai Schneider, Marie Farge, Yukio Kaneda. Coherent vorticity simulation of three-dimensional forced homogeneous isotropic turbulence. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2011, 9 (3), pp.1144-1161. ⟨10.1137/10079598X⟩. ⟨hal-01022690⟩
Journal: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Dmitry Kolomenskiy, H.K. Moffatt, Marie Farge, Kai Schneider. The Lighthill-Weis-Fogh clap-fling-sweep mechanism revisited. Journal of Fluid Mechanics, 2011, 676, pp.572-606. ⟨10.1017/jfm.2011.83⟩. ⟨hal-01022736⟩ Plus de détails...
The Lighthill-Weis-Fogh 'clap-fling-sweep' mechanism for lift generation in insect flight is re-examined. The novelty of this mechanism lies in the change of topology (the 'break') that occurs at a critical instant tc when two wings separate at their 'hinge' point as 'fling' gives way to 'sweep', and the appearance of equal and opposite circulations around the wings at this critical instant. Our primary aim is to elucidate the behaviour near the hinge point as time t passes through tc. First, Lighthill's inviscid potential flow theory is reconsidered. It is argued that provided the linear and angular accelerations of the wings are continuous, the velocity field varies continuously through the break, although the pressure field jumps instantaneously at t = tc. Then, effects of viscosity are considered. Near the hinge, the local Reynolds number is very small and local similarity solutions imply a logarithmic (integrable) singularity of the pressure jump across the hinge just before separation, in contrast to the 'negligible pressure jump' of inviscid theory invoked by Lighthill. We also present numerical simulations of the flow using a volume penalization technique to represent the motion of the wings. For Reynolds number equal to unity (based on wing chord), the results are in good agreement with the analytical solution. At a realistic Reynolds number of about 20, the flow near the hinge is influenced by leading-edge vortices, but local effects still persist. The lift coefficient is found to be much greater than that in the corresponding inviscid flow.
Dmitry Kolomenskiy, H.K. Moffatt, Marie Farge, Kai Schneider. The Lighthill-Weis-Fogh clap-fling-sweep mechanism revisited. Journal of Fluid Mechanics, 2011, 676, pp.572-606. ⟨10.1017/jfm.2011.83⟩. ⟨hal-01022736⟩
Romain Nguyen van Yen, Marie Farge, Kai Schneider. Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity. Physical Review Letters, 2011, 106, pp.184502. ⟨10.1103/PhysRevLett.106.184502⟩. ⟨hal-01022604⟩ Plus de détails...
We perform numerical experiments of a dipole crashing into a wall, a generic event in two-dimensional incompressible flows with solid boundaries. The Reynolds number (Re) is varied from 985 to 7880, and no-slip boundary conditions are approximated by Navier boundary conditions with a slip length proportional to Re(-1). Energy dissipation is shown to first set up within a vorticity sheet of thickness proportional to Re(-1) in the neighborhood of the wall, and to continue as this sheet rolls up into a spiral and detaches from the wall. The energy dissipation rate integrated over these regions appears to converge towards Re-independent values, indicating the existence of energy dissipating structures that persist in the vanishing viscosity limit.
Romain Nguyen van Yen, Marie Farge, Kai Schneider. Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity. Physical Review Letters, 2011, 106, pp.184502. ⟨10.1103/PhysRevLett.106.184502⟩. ⟨hal-01022604⟩
Romain Nguyen van Yen, Marie Farge, Kai Schneider. Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity. Physical Review Letters, American Physical Society, 2011, 106, pp.184502. ⟨10.1103/PhysRevLett.106.184502⟩. ⟨hal-01022604⟩ Plus de détails...
We perform numerical experiments of a dipole crashing into a wall, a generic event in two-dimensional incompressible flows with solid boundaries. The Reynolds number (Re) is varied from 985 to 7880, and no-slip boundary conditions are approximated by Navier boundary conditions with a slip length proportional to Re(-1). Energy dissipation is shown to first set up within a vorticity sheet of thickness proportional to Re(-1) in the neighborhood of the wall, and to continue as this sheet rolls up into a spiral and detaches from the wall. The energy dissipation rate integrated over these regions appears to converge towards Re-independent values, indicating the existence of energy dissipating structures that persist in the vanishing viscosity limit.
Romain Nguyen van Yen, Marie Farge, Kai Schneider. Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity. Physical Review Letters, American Physical Society, 2011, 106, pp.184502. ⟨10.1103/PhysRevLett.106.184502⟩. ⟨hal-01022604⟩
Benjamin Kadoch, K. Iyer, D. Donzis, Kai Schneider, Marie Farge, et al.. On the role of vortical structures for turbulent mixing using direct numerical simulation and wavelet-based coherent vorticity extraction. Journal of Turbulence, 2011, 12 (20), pp.1-17. ⟨10.1080/14685248.2011.562511⟩. ⟨hal-01022715⟩ Plus de détails...
The influence of vortical structures on the transport and mixing of passive scalars is investigated. Initial conditions are taken from a direct numerical simulation database of forced homogeneous isotropic turbulence, with passive scalar fluctuations, driven by a uniform mean gradient, are performed for Taylor microscale Reynolds numbers (R λ) of 140 and 240, and Schmidt numbers 1/8 and 1. For each R λ, after reaching a fully developed turbulent regime, which is statistically steady, the Coherent Vorticity Extraction is applied to the flow. It is shown that the coherent part is able to preserve the vortical structures with only less than 4% of wavelet coefficients while retaining 99.9% of energy. In contrast, the incoherent part is structureless and contains negligible energy. By taking the total, coherent and incoherent velocity fields in turn as initial conditions, new simulations were performed without forcing while the uniform mean scalar gradient is maintained. It is found that the results from simulations with total and coherent velocity fields as initial conditions are very similar. In contrast, the time integration of the incoherent flow exhibits its primarily dissipative nature. The evolutions of passive scalars at Schmidt numbers 1/8 and 1 advected by the total, coherent or incoherent velocity suggest that the vortical structures retained in the coherent part play a dominant role in turbulent transport and mixing. Indeed, the total and coherent flows give almost the same time evolution of the scalar variance, scalar flux and mean scalar dissipation, while the incoherent flow only gives rise to weak scalar diffusion.
Benjamin Kadoch, K. Iyer, D. Donzis, Kai Schneider, Marie Farge, et al.. On the role of vortical structures for turbulent mixing using direct numerical simulation and wavelet-based coherent vorticity extraction. Journal of Turbulence, 2011, 12 (20), pp.1-17. ⟨10.1080/14685248.2011.562511⟩. ⟨hal-01022715⟩
Katsunori Yoshimatsu, Kai Schneider, Naoya Okamoto, Yasuhiro Kawahara, Marie Farge. Intermittency and geometrical statistics of three-dimensional homogeneous magnetohydrodynamic turbulence: a wavelet viewpoint. Physics of Plasmas, 2011, 18 (9), pp.092304. ⟨10.1063/1.3628637⟩. ⟨hal-01022645⟩ Plus de détails...
Scale-dependent and geometrical statistics of three-dimensional incompressible homogeneous magnetohydrodynamicturbulence without mean magnetic field are examined by means of the orthogonal wavelet decomposition. The flow is computed by direct numerical simulation with a Fourier spectral method at resolution 5123 and a unit magnetic Prandtl number. Scale-dependent second and higher order statistics of the velocity and magnetic fields allow to quantify their intermittency in terms of spatial fluctuations of the energy spectra, the flatness, and the probability distribution functions at different scales. Different scale-dependent relative helicities, e.g., kinetic, cross, and magnetic relative helicities, yield geometrical information on alignment between the different scale-dependent fields. At each scale, the alignment between the velocity and magnetic field is found to be more pronounced than the other alignments considered here, i.e., the scale-dependent alignment between the velocity and vorticity, the scale-dependent alignment between the magnetic field and its vector potential, and the scale-dependent alignment between the magnetic field and the current density. Finally, statistical scale-dependent analyses of both Eulerian and Lagrangian accelerations and the corresponding time-derivatives of the magnetic field are performed. It is found that the Lagrangian acceleration does not exhibit substantially stronger intermittency compared to the Eulerian acceleration, in contrast to hydrodynamic turbulence where the Lagrangian acceleration shows much stronger intermittency than the Eulerian acceleration. The Eulerian time-derivative of the magnetic field is more intermittent than the Lagrangian time-derivative of the magnetic field.
Katsunori Yoshimatsu, Kai Schneider, Naoya Okamoto, Yasuhiro Kawahara, Marie Farge. Intermittency and geometrical statistics of three-dimensional homogeneous magnetohydrodynamic turbulence: a wavelet viewpoint. Physics of Plasmas, 2011, 18 (9), pp.092304. ⟨10.1063/1.3628637⟩. ⟨hal-01022645⟩
Kai Schneider, Salah Neffaa, Wouter J.T. Bos. A pseudo-spectral method with volume penalisation for magnetohydrodynamic turbulence in confined domains. Computer Physics Communications, Elsevier, 2011, 182 (1), pp.2-7. ⟨10.1016/j.cpc.2010.05.019⟩. ⟨hal-00647827⟩ Plus de détails...
We present a Fourier pseudo-spectral method for solving the resistive magnetohydrodynamic equations of incompressible flow in confined domains. A volume penalisation method allows to take into account boundary conditions and the geometry of the domain. A code validation is presented for the z-pinch test case. Numerical simulations of decaying MHD turbulence in two space dimensions show spontaneous spin-up of the flow in non-axisymmetric geometries, which is reflected by the generation of angular momentum. First results of decaying MHD turbulence in a cylinder illustrate the potential of the new method for three-dimensional simulations.
Kai Schneider, Salah Neffaa, Wouter J.T. Bos. A pseudo-spectral method with volume penalisation for magnetohydrodynamic turbulence in confined domains. Computer Physics Communications, Elsevier, 2011, 182 (1), pp.2-7. ⟨10.1016/j.cpc.2010.05.019⟩. ⟨hal-00647827⟩
Kai Schneider, Oleg V. Vasilyev. Wavelet methods in computational fluid dynamics. Annual Review of Fluid Mechanics, 2010, 42, pp.473-503. ⟨10.1146/annurev-fluid-121108-145637⟩. ⟨hal-01024632⟩ Plus de détails...
This article reviews state-of-the-art adaptive, multiresolution wavelet methodologies for modeling and simulation of turbulent flows with various examples. Different numerical methods for solving the Navier-Stokes equations in adaptive wavelet bases are described. We summarize coherent vortex extraction methodologies, which utilize the efficient wavelet decomposition of turbulent flows into space-scale contributions, and present a hierarchy of wavelet-based turbulence models. Perspectives for modeling and computing industrially relevant flows are also given.
Kai Schneider, Oleg V. Vasilyev. Wavelet methods in computational fluid dynamics. Annual Review of Fluid Mechanics, 2010, 42, pp.473-503. ⟨10.1146/annurev-fluid-121108-145637⟩. ⟨hal-01024632⟩
Dmitry Kolomenskiy, Kai Schneider. Numerical simulations of falling leaves using a pseudo-spectral method with volume penalization. Theoretical and Computational Fluid Dynamics, 2010, 24 (1-4), pp.169-173. ⟨10.1007/s00162-009-0171-0⟩. ⟨hal-01024134⟩ Plus de détails...
The dynamics of falling leaves is studied by means of numerical simulations. The two-dimensional incompressible Navier-Stokes equations, coupled with the equations governing solid body dynamics, are solved using a Fourier pseudo-spectral method with volume penalization to impose no-slip boundary conditions. Comparison with other numerical methods is made. Simulations performed for different values of the Reynolds number show that its decrease stabilizes the free fall motion.
Dmitry Kolomenskiy, Kai Schneider. Numerical simulations of falling leaves using a pseudo-spectral method with volume penalization. Theoretical and Computational Fluid Dynamics, 2010, 24 (1-4), pp.169-173. ⟨10.1007/s00162-009-0171-0⟩. ⟨hal-01024134⟩
Journal: Theoretical and Computational Fluid Dynamics
Raimund Burger, Ricardo Ruiz-Baier, Kai Schneider. Adaptive multiresolution methods for the simulation of waves in excitable media. Journal of Scientific Computing, 2010, 43 (2), pp.261-290. ⟨10.1007/s10915-010-9356-3⟩. ⟨hal-01024084⟩ Plus de détails...
We present fully adaptive multiresolution methods for a class of spatially two-dimensional reaction-diffusion systems which describe excitable media and often give rise to the formation of spiral waves. A novel model ingredient is a strongly degenerate diffusion term that controls the degree of spatial coherence and serves as a mechanism for obtaining sharper wave fronts. The multiresolution method is formulated on the basis of two alternative reference schemes, namely a classical finite volume method, and Barkley's approach (Barkley in Phys. D 49:61-70, 1991), which consists in separating the computation of the nonlinear reaction terms from that of the piecewise linear diffusion. The proposed methods are enhanced with local time stepping to attain local adaptivity both in space and time. The computational efficiency and the numerical precision of our methods are assessed. Results illustrate that the fully adaptive methods provide stable approximations and substantial savings in memory storage and CPU time while preserving the accuracy of the discretizations on the corresponding finest uniform grid.
Raimund Burger, Ricardo Ruiz-Baier, Kai Schneider. Adaptive multiresolution methods for the simulation of waves in excitable media. Journal of Scientific Computing, 2010, 43 (2), pp.261-290. ⟨10.1007/s10915-010-9356-3⟩. ⟨hal-01024084⟩
Romain Nguyen van Yen, Diego Del-Castillo-Negrete, Kai Schneider, Marie Farge, Guangye Chen. Wavelet-based density estimation for noise reduction in plasma simulations using particles. Journal of Computational Physics, 2010, 229 (8), pp.2821-2839. ⟨10.1016/j.jcp.2009.12.010⟩. ⟨hal-00828015⟩ Plus de détails...
For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on wavelet analysis is proposed and tested to reduce this noise. The method, known as wavelet based density estimation (WBDE), was previously introduced in the statistical literature to estimate probability densities given a finite number of independent measurements. Its novel application to plasma simulations can be viewed as a natural extension of the finite size particles (FSP) approach, with the advantage of estimating more accurately distribution functions that have localized sharp features. The proposed method preserves the moments of the particle distribution function to a good level of accuracy, has no constraints on the dimensionality of the system, does not require an a priori selection of a global smoothing scale, and its able to adapt locally to the smoothness of the density based on the given discrete particle data. Most importantly, the computational cost of the denoising stage is of the same order as one time step of a FSP simulation. The method is compared with a recently proposed proper orthogonal decomposition based method, and it is tested with three particle data sets that involve different levels of collisionality and interaction with external and self-consistent fields.
Romain Nguyen van Yen, Diego Del-Castillo-Negrete, Kai Schneider, Marie Farge, Guangye Chen. Wavelet-based density estimation for noise reduction in plasma simulations using particles. Journal of Computational Physics, 2010, 229 (8), pp.2821-2839. ⟨10.1016/j.jcp.2009.12.010⟩. ⟨hal-00828015⟩
Olivier Roussel, Kai Schneider. Coherent Vortex Simulation of weakly compressible turbulent mixing layers using adaptive multiresolution methods. Journal of Computational Physics, 2010, 229 (6), pp.2267-2286. ⟨10.1016/j.jcp.2009.11.034⟩. ⟨hal-01024617⟩ Plus de détails...
An adaptive mulitresolution method based on a second-order finite volume discretization is presented for solving the three-dimensional compressible Navier-Stokes equations in Cartesian geometry. The explicit time discretization is of second-order and for flux evaluation a 2-4 Mac Cormack scheme is used. Coherent Vortex Simulations (CVS) are performed by decomposing the flow variables into coherent and incoherent contributions. The coherent part is computed deterministically on a locally refined grid using the adaptive multiresolution method while the influence of the incoherent part is neglected to model turbulent dissipation. The computational efficiency of this approach in terms of memory and CPU time compression is illustrated for turbulent mixing layers in the weakly compressible regime and for Reynolds numbers based on the mixing layer thickness between 50 and 200. Comparisons with direct numerical simulations allow to assess the precision and efficiency of CVS.
Olivier Roussel, Kai Schneider. Coherent Vortex Simulation of weakly compressible turbulent mixing layers using adaptive multiresolution methods. Journal of Computational Physics, 2010, 229 (6), pp.2267-2286. ⟨10.1016/j.jcp.2009.11.034⟩. ⟨hal-01024617⟩
Benjamin Kadoch, Emmanuel Leriche, Kai Schneider, Marie Farge. On the Role of Coherent Structures in a Lid Driven Cavity Flow. Turbulence and Interactions., pp.207-214, 2010, ⟨10.1007/978-3-642-14139-3_25⟩. ⟨hal-02535124⟩ Plus de détails...
Benjamin Kadoch, Emmanuel Leriche, Kai Schneider, Marie Farge. On the Role of Coherent Structures in a Lid Driven Cavity Flow. Turbulence and Interactions., pp.207-214, 2010, ⟨10.1007/978-3-642-14139-3_25⟩. ⟨hal-02535124⟩
Dmitry Kolomenskiy, H.K. Moffatt, Marie Farge, Kai Schneider. Vorticity generation during the clap-fling-sweep of some hovering insects. Theoretical and Computational Fluid Dynamics, 2010, 24 (1-4), pp.209-215. ⟨10.1007/s00162-009-0137-2⟩. ⟨hal-01024119⟩ Plus de détails...
Numerical simulations of the Lighthill-Weis-Fogh mechanism are performed using a Fourier pseudo-spectral method with volume penalization. Single-winged and double-winged configurations are compared, and the vortex shedding patterns are related to the lift generated in both cases. The computations of the lift coefficient are validated against the results reported previously by Miller and Peskin (J Exp Biol 208:195-212, 2005).
Dmitry Kolomenskiy, H.K. Moffatt, Marie Farge, Kai Schneider. Vorticity generation during the clap-fling-sweep of some hovering insects. Theoretical and Computational Fluid Dynamics, 2010, 24 (1-4), pp.209-215. ⟨10.1007/s00162-009-0137-2⟩. ⟨hal-01024119⟩
Journal: Theoretical and Computational Fluid Dynamics
D. Kolomensky, Benjamin Kadoch, W. Bos, K. Schneider, P. Angot. Scalar mixing in turbulent confined flow. Advances in Turbulence XII, pp.525-528, 2009, ⟨10.1007/978-3-642-03085-7_126⟩. ⟨hal-02535201⟩ Plus de détails...
D. Kolomensky, Benjamin Kadoch, W. Bos, K. Schneider, P. Angot. Scalar mixing in turbulent confined flow. Advances in Turbulence XII, pp.525-528, 2009, ⟨10.1007/978-3-642-03085-7_126⟩. ⟨hal-02535201⟩
K. Schneider, S. Neffaa, Benjamin Kadoch, W. Bos. Lagrangian intermittency and time-correlations in two-dimensional turbulence. dvances in Turbulence XII, pp.737-740, 2009, ⟨10.1007/978-3-642-03085-7_179⟩. ⟨hal-02535186⟩ Plus de détails...
K. Schneider, S. Neffaa, Benjamin Kadoch, W. Bos. Lagrangian intermittency and time-correlations in two-dimensional turbulence. dvances in Turbulence XII, pp.737-740, 2009, ⟨10.1007/978-3-642-03085-7_179⟩. ⟨hal-02535186⟩
Benjamin Kadoch, W. Bos, K. Schneider. Lagrangian statistics of two–dimensional turbulence in a square container. Advances in Turbulence XII, pp.35-38, 2009, ⟨10.1007/978-3-642-03085-7_8⟩. ⟨hal-02535140⟩ Plus de détails...
Benjamin Kadoch, W. Bos, K. Schneider. Lagrangian statistics of two–dimensional turbulence in a square container. Advances in Turbulence XII, pp.35-38, 2009, ⟨10.1007/978-3-642-03085-7_8⟩. ⟨hal-02535140⟩
Benjamin Kadoch, Margarete Oliveira Domingues, Ingmar Broemstrup, Lionel Larchevêque, Kai Schneider, et al.. Coherent Vorticity Extraction in 3D Homogeneous Isotropic Turbulence: Influence of the Reynolds Number and Geometrical Statistics. Brazilian Journal of Physics, 2009, 39. ⟨hal-02081129⟩ Plus de détails...
The coherent vorticity extraction method (CVE) is based on the nonlinear filtering of the vorticity field projected onto an orthonormal wavelet basis made of compactly supported functions. CVE decomposes each turbulent flow realization into two orthogonal components: a coherent and an incoherent random flow. They both contribute to all scales in the inertial range, but exhibit different statistical behavior. We apply CVE to 256 3 subcubes extracted from 3D homogeneous isotropic turbulent flows at different Taylor microscale Reynolds numbers (R λ = 140, 240 and 680), computed by a direct numerical simulation (DNS) at different resolutions (N = 256 3 , 512 3 and 2048 3), respectively. We compare the total, coherent and incoherent vorticity fields obtained by using CVE and show that few wavelets coefficients are sufficient to represent the coherent vortices of the flows. Geometrical statistics in term of helicity are also analyzed and the λ 2 criterion is applied to the filtered flow fields.
Benjamin Kadoch, Margarete Oliveira Domingues, Ingmar Broemstrup, Lionel Larchevêque, Kai Schneider, et al.. Coherent Vorticity Extraction in 3D Homogeneous Isotropic Turbulence: Influence of the Reynolds Number and Geometrical Statistics. Brazilian Journal of Physics, 2009, 39. ⟨hal-02081129⟩
Henning Bockhorn, Jordan Denev, Margarete Domingues, Carlos Falconi, Marie Farge, et al.. Numerical Simulation of Turbulent Flows in Complex Geometries Using the Coherent Vortex Simulation Approach Based on Orthonormal Wavelet Decomposition. Numerical Simulation of Turbulent Flows and Noise Generation, pp.175-200, 2009, ⟨10.1007/978-3-540-89956-3_8⟩. ⟨hal-02535064⟩ Plus de détails...
Henning Bockhorn, Jordan Denev, Margarete Domingues, Carlos Falconi, Marie Farge, et al.. Numerical Simulation of Turbulent Flows in Complex Geometries Using the Coherent Vortex Simulation Approach Based on Orthonormal Wavelet Decomposition. Numerical Simulation of Turbulent Flows and Noise Generation, pp.175-200, 2009, ⟨10.1007/978-3-540-89956-3_8⟩. ⟨hal-02535064⟩
Margarete Domingues, Ingmar Broemstrup, Kai Schneider, Marie Farge, Benjamin Kadoch. Coherent vortex extraction in 3D homogeneous isotropic turbulence using orthogonal wavelets. ESAIM: Proceedings, 2007, 16, pp.164-180. ⟨10.1051/proc:2007005⟩. ⟨hal-02535148⟩ Plus de détails...
Margarete Domingues, Ingmar Broemstrup, Kai Schneider, Marie Farge, Benjamin Kadoch. Coherent vortex extraction in 3D homogeneous isotropic turbulence using orthogonal wavelets. ESAIM: Proceedings, 2007, 16, pp.164-180. ⟨10.1051/proc:2007005⟩. ⟨hal-02535148⟩
K. Schneider, M. Farge. Numerical simulation of the transient flow behaviour in tube bundles using a volume penalization method. Journal of Fluids and Structures, 2005, 20 (4), pp.555-566. ⟨10.1016/j.jfluidstructs.2005.02.006⟩. ⟨hal-01299228⟩ Plus de détails...
We present high resolution numerical simulations of incompressible two-dimensional flows in tube bundles, staggered or in-line, as encountered in heat exchangers or chemical reactors. We study the time evolution of several flows in arrays of cylinders, squares and double-cruciform shaped tubes at a Reynolds number of 200. The numerical scheme is either based on adaptive wavelet or Fourier pseudo-spectral space discretization with adaptive time stepping. A volume penalization method is used to impose no-slip boundary conditions on the tubes. Lift and drag coefficients for the different geometries of tube bundles are compared and perspectives for fluid–structure interaction are given.
K. Schneider, M. Farge. Numerical simulation of the transient flow behaviour in tube bundles using a volume penalization method. Journal of Fluids and Structures, 2005, 20 (4), pp.555-566. ⟨10.1016/j.jfluidstructs.2005.02.006⟩. ⟨hal-01299228⟩