Numerical
modeling of plasma flows in Tokamak configurations
Multilevel
Schemes for Conservation Laws
Penalization
method for compressible flows
Wavelets in Numerical Analysis
Publications scientifiques au M2P2
2021
G. Farag, S. Zhao, G. Chiavassa, Pierre Boivin. Consistency study of Lattice-Boltzmann schemes macroscopic limit. Physics of Fluids, 2021, 33 (3), pp.037101. ⟨10.1063/5.0039490⟩. ⟨hal-03160898⟩ Plus de détails...
Owing to the lack of consensus about the way Chapman-Enskog should be performed, a new Taylor-Expansion of Lattice-Boltzmann models is proposed. Contrarily to the Chapman-Enskog expansion, recalled in this manuscript, the method only assumes an su ciently small time step. Based on the Taylor expansion, the collision kernel is reinterpreted as a closure for the stress-tensor equation. Numerical coupling of Lattice-Boltzmann models with other numerical schemes, also encompassed by the method, are shown to create error terms whose scalings are more complex than those obtained via Chapman-Enskog. An athermal model and two compressible models are carefully analyzed through this new scope, casting a new light on each model's consistency with the Navier-Stokes equations.
G. Farag, S. Zhao, G. Chiavassa, Pierre Boivin. Consistency study of Lattice-Boltzmann schemes macroscopic limit. Physics of Fluids, 2021, 33 (3), pp.037101. ⟨10.1063/5.0039490⟩. ⟨hal-03160898⟩
G. Farag, S. Zhao, T. Coratger, Pierre Boivin, G. Chiavassa, et al.. A pressure-based regularized lattice-Boltzmann method for the simulation of compressible flows. Physics of Fluids, 2020, 32 (6), pp.066106. ⟨10.1063/5.0011839⟩. ⟨hal-02885427⟩ Plus de détails...
A new pressure-based Lattice-Boltzmann method (HRR-p) is proposed for the simulation of flows for Mach numbers ranging from 0 to 1.5. Compatible with nearest neighbor lattices (e.g. D3Q19), the model consists of a predictor step comparable to classical athermal Lattice-Boltzmann methods, appended with a fully local and explicit correction step for the pressure. Energy conservation-for which the Hermi-tian quadrature is not accurate enough on such lattice-is solved via a classical finite volume MUSCL-Hancock scheme based on the entropy equation. The Euler part of the model is then validated for the transport of three canonical modes (vortex, en-tropy, and acoustic propagation), while its diffusive/viscous properties are assessed via thermal Couette flow simulations. All results match the analytical solutions, with very limited dissipation. Lastly, the robustness of the method is tested in a one dimensional shock tube and a two-dimensional shock-vortex interaction.
G. Farag, S. Zhao, T. Coratger, Pierre Boivin, G. Chiavassa, et al.. A pressure-based regularized lattice-Boltzmann method for the simulation of compressible flows. Physics of Fluids, 2020, 32 (6), pp.066106. ⟨10.1063/5.0011839⟩. ⟨hal-02885427⟩
Dan Feng, Laure Malleret, Guillaume Chiavassa, Olivier Boutin, Audrey Soric. Biodegradation capabilities of acclimated activated sludge towards glyphosate: Experimental study and kinetic modeling. Biochemical Engineering Journal, 2020, 161, pp.107643. ⟨10.1016/j.bej.2020.107643⟩. ⟨hal-02960167⟩ Plus de détails...
The acclimation process of activated sludge from a wastewater treatment plant for degradation of glyphosate and its biodegradation kinetics were studied in a batch reactor. The parameters monitored included the concentrations of glyphosate, as well as aminomethylphosphonic acid (AMPA), its main metabolite, total organic carbon (TOC), pH, dissolved oxygen (DO) and biomass concentration. M the end of the acclimation process, glyphosate removal efficiency of the acclimated sludge was compared to the fresh sludge one. The results showed that the acclimation process highly increased degradation efficiency. Complete glyphosate removal has been achieved during kinetics experiments. Glyphosate removal kinetic of the acclimated sludge was modeled by Monod model that accurately fitted the experimental results with a maximum growth rate (mu(max)) of 0.34 h(-1) and half-saturation constant (K-s) of 1600 mg L-1. Finally, a biodegradation pathway of glyphosate used as carbon source was proposed.
Dan Feng, Laure Malleret, Guillaume Chiavassa, Olivier Boutin, Audrey Soric. Biodegradation capabilities of acclimated activated sludge towards glyphosate: Experimental study and kinetic modeling. Biochemical Engineering Journal, 2020, 161, pp.107643. ⟨10.1016/j.bej.2020.107643⟩. ⟨hal-02960167⟩
Harold Berjamin, Bruno Lombard, Guillaume Chiavassa, Nicolas Favrie. Plane-strain waves in nonlinear elastic solids with softening. Wave Motion, 2019, 89, pp.65-78. ⟨hal-02057946⟩ Plus de détails...
Propagation of elastic waves in damaged media (concrete, rocks) is studied theoretically and numerically. Such materials exhibit a nonlinear behavior, with long-time softening and recovery processes (slow dynamics). A constitutive model combining Murnaghan hyperelasticity with the slow dynamics is considered, where the softening is represented by the evolution of a scalar variable. The equations of motion in the Lagrangian framework are detailed. These equations are rewritten as a nonlinear hyperbolic system of balance laws, which is solved numerically using a finite-volume method with flux limiters. Numerical examples illustrate specific features of nonlinear elastic waves, as well as the effect of the material's softening. In particular, the generation of solitary waves in a periodic layered medium is illustrated numerically.
Harold Berjamin, Bruno Lombard, Guillaume Chiavassa, Nicolas Favrie. Plane-strain waves in nonlinear elastic solids with softening. Wave Motion, 2019, 89, pp.65-78. ⟨hal-02057946⟩
H Berjamin, Bruno Lombard, Guillaume Chiavassa, Nicolas Favrie. A Finite-Volume Approach to 1D Nonlinear Elastic Waves: Application to Slow Dynamics. Acta Acustica united with Acustica, 2018, ⟨10.3813/Aaa.919197⟩. ⟨hal-02111888⟩ Plus de détails...
A numerical method for longitudinal wave propagation in nonlinear elastic solids is presented. Here, we consider polynomial stress-strain relationships, which are widely used in nondestructive evaluation. The large-strain and infinitesimal-strain constitutive laws deduced from Murnaghan'sl aw are detailed, and polynomial expressions are obtained. The Lagrangian equations of motion yield ahyperbolic system of conservation laws. The latter is solved numerically using afi nite-volume method with flux limiters based on Roe linearization. The method is tested on the Riemann problem, which yields nonsmooth solutions. The method is then applied to acontinuum model with one scalar internal variable, accounting for the softening of the material (slowdynamics).
H Berjamin, Bruno Lombard, Guillaume Chiavassa, Nicolas Favrie. A Finite-Volume Approach to 1D Nonlinear Elastic Waves: Application to Slow Dynamics. Acta Acustica united with Acustica, 2018, ⟨10.3813/Aaa.919197⟩. ⟨hal-02111888⟩
Harold Berjamin, Bruno Lombard, Guillaume Chiavassa, Nicolas Favrie. A finite-volume approach to 1D nonlinear elastic waves: Application to slow dynamics. Acta Acustica united with Acustica, 2018, 104, pp.561-570. ⟨hal-01806373⟩ Plus de détails...
A numerical method for longitudinal wave propagation in nonlinear elastic solids is presented. Here, we consider polynomial stress-strain relationships, which are widely used in nondestructive evaluation. The large-strain and infinitesimal-strain constitutive laws deduced from Murnaghan's law are detailed , and polynomial expressions are obtained. The Lagrangian equations of motion yield a hyperbolic system of conservation laws. The latter is solved numerically using a finite-volume method with flux limiters based on Roe linearization. The method is tested on the Riemann problem, which yields nonsmooth solutions. The method is then applied to a continuum model with one scalar internal variable, accounting for the softening of the material (slow dynamics).
Harold Berjamin, Bruno Lombard, Guillaume Chiavassa, Nicolas Favrie. A finite-volume approach to 1D nonlinear elastic waves: Application to slow dynamics. Acta Acustica united with Acustica, 2018, 104, pp.561-570. ⟨hal-01806373⟩
Harold Berjamin, Bruno Lombard, Guillaume Chiavassa, Nicolas Favrie. Modeling longitudinal wave propagation in nonlinear viscoelastic solids with softening. International Journal of Solids and Structures, 2018, 141-142, pp.35-44. ⟨10.1016/j.ijsolstr.2018.02.009⟩. ⟨hal-01701624⟩ Plus de détails...
A model for longitudinal wave propagation in rocks and concrete is presented. Such materials are known to soften under a dynamic loading, i.e. the speed of sound diminishes with forcing amplitudes. Also known as slow dynamics, the softening of the material is not instantaneous. Based on continuum mechanics with internal variables of state, a new formulation is proposed, which accounts for nonlinear Zener viscoelasticity and softening. A finite-volume method using Roe linearization is developed for the system of partial differential equations so-obtained. The method is used to carry out resonance simulations, and its performance is assessed in the linear viscoelastic case. Qualitative agreement with experimental results of nonlinear ultrasound spectroscopy (NRUS) and dynamic acousto-elastic testing (DAET) is obtained.
Harold Berjamin, Bruno Lombard, Guillaume Chiavassa, Nicolas Favrie. Modeling longitudinal wave propagation in nonlinear viscoelastic solids with softening. International Journal of Solids and Structures, 2018, 141-142, pp.35-44. ⟨10.1016/j.ijsolstr.2018.02.009⟩. ⟨hal-01701624⟩
Journal: International Journal of Solids and Structures
H Berjamin, Bruno Lombard, Guillaume Chiavassa, N Favrie. Analytical solution to the 1D nonlinear elastodynamics with general constitutive laws. Wave Motion, 2017, 74, pp.35-55. ⟨10.1016/j.wavemoti.2017.06.006⟩. ⟨hal-01350116⟩ Plus de détails...
Under the hypothesis of small deformations, the equations of 1D elastodynamics write as a 2 × 2 hyperbolic system of conservation laws. Here, we study the Riemann problem for convex and nonconvex constitutive laws. In the convex case, the solution can include shock waves or rarefaction waves. In the nonconvex case, compound waves must also be considered. In both convex and nonconvex cases, a new existence criterion for the initial velocity jump is obtained. Also, admissibility regions are determined. Lastly, analytical solutions are completely detailed for various constitutive laws (hyperbola, tanh and polynomial), and reference test cases are proposed.
H Berjamin, Bruno Lombard, Guillaume Chiavassa, N Favrie. Analytical solution to the 1D nonlinear elastodynamics with general constitutive laws. Wave Motion, 2017, 74, pp.35-55. ⟨10.1016/j.wavemoti.2017.06.006⟩. ⟨hal-01350116⟩
H Berjamin, N Favrie, B Lombard, G Chiavassa. Nonlinear waves in solids with slow dynamics: an internal-variable model. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017, 473 (2201), pp.20170024. ⟨10.1098/rspa.2017.0024⟩. ⟨hal-01517335⟩ Plus de détails...
In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease known as " slow dynamics " occurs at time scales larger than the period of the forcing. Also, hysteresis is observed in the steady-state response. The phenomenological model by Vakhnenko et al. is based on a variable that describes the softening of the material [Phys. Rev. E 70-1, 2004]. However, this model is 1D and it is not thermodynamically admissible. In the present article, a 3D model is derived in the framework of the finite strain theory. An internal variable that describes the softening of the material is introduced, as well as an expression of the specific internal energy. A mechanical constitu-tive law is deduced from the Clausius-Duhem inequality. Moreover, a family of evolution equations for the internal variable is proposed. Here, an evolution equation with one relaxation time is chosen. By construction, this new model of continuum is thermodynamically admissible and dissipative (inelas-tic). In the case of small uniaxial deformations, it is shown analytically that the model reproduces qualitatively the main features of real experiments.
H Berjamin, N Favrie, B Lombard, G Chiavassa. Nonlinear waves in solids with slow dynamics: an internal-variable model. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017, 473 (2201), pp.20170024. ⟨10.1098/rspa.2017.0024⟩. ⟨hal-01517335⟩
Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Guillaume Chiavassa, Maria Carmen Martí, Pep Mulet. Hybrid WENO schemes for polydisperse sedimentation models. International Journal of Computer Mathematics, 2015, 93 (11), pp.1-17. ⟨10.1080/00207160.2015.1075985⟩. ⟨hal-01297719⟩ Plus de détails...
Polydisperse sedimentation models can be described by a strongly coupled system of conservation laws for the concentration of each species of solids. Typical solutions for the sedimentation model considered for batch settling in a column include stationary kinematic shocks separating layers of sediment of different composition. This phenomenon, known as segregation of species, is a specially demanding task for numerical simulation due to the need of accurate numerical simulations. Very high-order accurate solutions can be constructed by incorporating characteristic information, available due to the hyperbolicity analysis made in Donat and Mulet [A secular equation for the Jacobian matrix of certain multispecies kinematic flow models, Numer. Methods Partial Differential Equations 26 (2010), pp. 159–175.] But characteristic-based schemes, see Bürger et al. [On the implementation of WENO schemes for a class of polydisperse sedimentation models, J. Comput. Phys. 230 (2011), pp. 2322–2344], are very expensive in terms of computational time, since characteristic information is not readily available, and they are not really necessary in constant areas, where a less complex method can obtain similar results. With this idea in mind, in this paper we develop a hybrid finite difference WENO scheme that only uses the characteristic information of the Jacobian matrix of the system in those regions where singularities exist or are starting to develop, while it uses a component-wise approximation of the scheme in smooth regions. We perform some experiments showing the computational gains that can be achieved by this strategy.
Guillaume Chiavassa, Maria Carmen Martí, Pep Mulet. Hybrid WENO schemes for polydisperse sedimentation models. International Journal of Computer Mathematics, 2015, 93 (11), pp.1-17. ⟨10.1080/00207160.2015.1075985⟩. ⟨hal-01297719⟩
Journal: International Journal of Computer Mathematics
Bouchra Bensiali, Guillaume Chiavassa, Jacques Liandrat. Penalization of Robin boundary conditions. Applied Numerical Mathematics: an IMACS journal, 2015, 96, pp.134-152. ⟨hal-01266091⟩ Plus de détails...
This paper is devoted to the mathematical analysis of a method based on fictitious domain approach. Boundary conditions of Robin type (also known as Fourier boundary conditions) are enforced using a penalization method. A complete description of the method and a full analysis are provided for univariate elliptic and parabolic problems using finite difference approximation. Numerical evidence of the predicted estimations is provided as well as numerical results for a nonlinear problem and a first extension of the method in the bivariate situation is proposed.
Bouchra Bensiali, Guillaume Chiavassa, Jacques Liandrat. Penalization of Robin boundary conditions. Applied Numerical Mathematics: an IMACS journal, 2015, 96, pp.134-152. ⟨hal-01266091⟩
Journal: Applied Numerical Mathematics: an IMACS journal
Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. Wave simulation in 2D heterogeneous transversely isotropic porous media ă with fractional attenuation: A Cartesian grid approach. Journal of Computational Physics, 2014, 275, pp.118-142. ⟨10.1016/j.jcp.2014.07.002⟩. ⟨hal-01464704⟩ Plus de détails...
A time-domain numerical modeling of transversely isotropic Biot ă poroelastic waves is proposed in two dimensions. The viscous dissipation ă occurring in the pores is described using the dynamic permeability model ă developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in ă the Biot-JKD model are proportional to the square root of the frequency. ă In the time-domain, these coefficients introduce shifted fractional ă derivatives of order 1/2, involving a convolution product. Based on a ă diffusive representation, the convolution kernel is replaced by a finite ă number of memory variables that satisfy local-in-time ordinary ă differential equations, resulting in the Biot-DA (diffusive ă approximation) model. The properties of both the Biot-JKD and the ă Biot-DA models are analyzed: hyperbolicity, decrease of energy, ă dispersion. To determine the coefficients of the diffusive ă approximation, two approaches are analyzed: Gaussian quadratures and ă optimization methods in the frequency range of interest. The nonlinear ă optimization is shown to be the better way of determination. A splitting ă strategy is then applied to approximate numerically the Biot-DA ă equations. The propagative part is discretized using a fourth-order ADER ă scheme on a Cartesian grid, whereas the diffusive part is solved ă exactly. An immersed interface method is implemented to take into ă account heterogeneous media on a Cartesian grid and to discretize the ă jump conditions at interfaces. Numerical experiments are presented. ă Comparisons with analytical solutions show the efficiency and the ă accuracy of the approach, and some numerical experiments are performed ă to investigate wave phenomena in complex media, such as multiple ă scattering across a set of random scatterers. (C) 2014 Elsevier Inc. All ă rights reserved.
Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. Wave simulation in 2D heterogeneous transversely isotropic porous media ă with fractional attenuation: A Cartesian grid approach. Journal of Computational Physics, 2014, 275, pp.118-142. ⟨10.1016/j.jcp.2014.07.002⟩. ⟨hal-01464704⟩
Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. Wave simulation in 2D heterogeneous transversely isotropic porous media with fractional attenuation: a Cartesian grid approach. Journal of Computational Physics, 2014, 275, pp.118-142. ⟨hal-00949686v2⟩ Plus de détails...
A time-domain numerical modeling of transversely isotropic Biot poroelastic waves is proposed in two dimensions. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency. In the time-domain, these coefficients introduce shifted fractional derivatives of order 1/21/2, involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations, resulting in the Biot-DA (diffusive approximation) model. The properties of both the Biot-JKD and the Biot-DA model are analyzed: hyperbolicity, decrease of energy, dispersion. To determine the coefficients of the diffusive approximation, two approaches are analyzed: Gaussian quadratures and optimization methods in the frequency range of interest. The nonlinear optimization is shown to be the better way of determination. A splitting strategy is then applied to approximate numerically the Biot-DA equations. The propagative part is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. An immersed interface method is implemented to take into account heterogeneous media on a Cartesian grid and to discretize the jump conditions at interfaces. Numerical experiments are presented. Comparisons with analytical solutions show the efficiency and the accuracy of the approach, and some numerical experiments are performed to investigate wave phenomena in complex media, such as multiple scattering across a set of random scatterers.
Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. Wave simulation in 2D heterogeneous transversely isotropic porous media with fractional attenuation: a Cartesian grid approach. Journal of Computational Physics, 2014, 275, pp.118-142. ⟨hal-00949686v2⟩
Philippe Ghendrih, Thomas Auphan, B. Bensiali, Marco Bilanceri, K. Bodi, et al.. Divertor imbalance and divertor density regimes for ballooned cross-field turbulence. Journal of Nuclear Materials, 2013, 438, pp.S368-S371. ⟨10.1016/j.jnucmat.2013.01.070⟩. ⟨hal-00920748⟩ Plus de détails...
The ballooned nature of cross-field transport is shown to govern the steady state divertor imbalance of the energy flux leading to a factor 10 between the low field side and high field energy flux. An even stronger ratio is found for the divertor temperatures. Conversely the particle flux is expected to be a factor 10 larger on the high field side than on the low field side. The transition to detachment, close to divertor thermal collapse, exhibits several constraints to maintain steady state solutions. These constraints, related in particular to a large drop of the divertor density upon detachment, are shown to strongly correlate the pressure and particle flux variation along the field line and consequently the various loss channels. This delicate balance between different mechanisms is a possible understanding of the difficulty reported in detached plasma operation and simulation.
Philippe Ghendrih, Thomas Auphan, B. Bensiali, Marco Bilanceri, K. Bodi, et al.. Divertor imbalance and divertor density regimes for ballooned cross-field turbulence. Journal of Nuclear Materials, 2013, 438, pp.S368-S371. ⟨10.1016/j.jnucmat.2013.01.070⟩. ⟨hal-00920748⟩
Guillaume Chiavassa, Bruno Lombard. Wave propagation across acoustic / Biot's media: a finite-difference method. Communications in Computational Physics, 2013, 13 (4), pp.985-1012. ⟨10.4208/cicp.140911.050412a⟩. ⟨hal-00623627v2⟩ Plus de détails...
Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect pores. Well-possedness of the initial-boundary value problem is proven. Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context: a fourth-order ADER scheme with Strang splitting for time-marching; a space-time mesh-refinement to capture the slow compressional wave predicted by Biot's theory; and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution. Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions, demonstrating the accuracy of the approach.
Guillaume Chiavassa, Bruno Lombard. Wave propagation across acoustic / Biot's media: a finite-difference method. Communications in Computational Physics, 2013, 13 (4), pp.985-1012. ⟨10.4208/cicp.140911.050412a⟩. ⟨hal-00623627v2⟩
Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. A time-domain numerical modeling of two-dimensional wave propagation in porous media with frequency-dependent dynamic permeability. Journal of the Acoustical Society of America, 2013, 134 (6), pp.4610-4623. ⟨10.1121/1.4824832⟩. ⟨hal-00736757⟩ Plus de détails...
An explicit finite-difference scheme is presented for solving the two-dimensional Biot equations of poroelasticity across the full range of frequencies. The key difficulty is to discretize the Johnson-Koplik-Dashen (JKD) model which describes the viscous dissipations in the pores. Indeed, the time-domain version of Biot-JKD model involves order 1/2 fractional derivatives which amounts to a time convolution product. To avoid storing the past values of the solution, a diffusive representation of fractional derivatives is used: the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. The coefficients of the diffusive representation follow from an optimization procedure of the dispersion relation. Then, various methods of scientific computing are applied: the propagative part of the equations is discretized using a fourth-order finite-difference scheme, whereas the diffusive part is solved exactly. An immersed interface method is implemented to discretize the geometry on a Cartesian grid, and also to discretize the jump conditions at interfaces. Numerical experiments are proposed in various realistic configurations.
Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. A time-domain numerical modeling of two-dimensional wave propagation in porous media with frequency-dependent dynamic permeability. Journal of the Acoustical Society of America, 2013, 134 (6), pp.4610-4623. ⟨10.1121/1.4824832⟩. ⟨hal-00736757⟩
Journal: Journal of the Acoustical Society of America
Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. Biot-JKD model: simulation of 1D transient poroelastic waves with fractional derivatives. Journal of Computational Physics, 2013, 237, pp.1-20. ⟨10.1016/j.jcp.2012.12.003⟩. ⟨hal-00713127v2⟩ Plus de détails...
A time-domain numerical modeling of Biot poroelastic waves is presented. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency: in the time-domain, these coefficients introduce order 1/2 shifted fractional derivatives involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. Thanks to the dispersion relation, the coefficients in the diffusive representation are obtained by performing an optimization procedure in the frequency range of interest. A splitting strategy is then applied numerically: the propagative part of Biot-JKD equations is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. Comparisons with analytical solutions show the efficiency and the accuracy of this approach.
Emilie Blanc, Guillaume Chiavassa, Bruno Lombard. Biot-JKD model: simulation of 1D transient poroelastic waves with fractional derivatives. Journal of Computational Physics, 2013, 237, pp.1-20. ⟨10.1016/j.jcp.2012.12.003⟩. ⟨hal-00713127v2⟩
Wave propagation in a stratified fluid / porous medium is studied here using analytical and numerical methods. The semi-analytical method is based on an exact stiffness matrix method coupled with a matrix conditioning procedure, preventing the occurrence of poorly conditioned numerical systems. Special attention is paid to calculating the Fourier integrals. The numerical method is based on a high order finite-difference time-domain scheme. Mesh refinement is applied near the interfaces to discretize the slow compressional diffusive wave predicted by Biot's theory. Lastly, an immersed interface method is used to discretize the boundary conditions. The numerical benchmarks are based on realistic soil parameters and on various degrees of hydraulic contact at the fluid / porous boundary. The time evolution of the acoustic pressure and the porous velocity is plotted in the case of one and four interfaces. The excellent level of agreement found to exist between the two approaches confirms the validity of both methods, which cross-checks them and provides useful tools for future researches.
Gaëlle Lefeuve-Mesgouez, Arnaud Mesgouez, Guillaume Chiavassa, Bruno Lombard. Semi-analytical and numerical methods for computing transient waves in 2D acoustic / poroelastic stratified media. Wave Motion, 2012, 49-7 (7), pp.667-680. ⟨10.1016/j.wavemoti.2012.04.006⟩. ⟨hal-00667795v2⟩
Philippe Ghendrih, K. Bodi, Hugo Bufferand, Guillaume Chiavassa, Guido Ciraolo, et al.. Transition to supersonic flows in the edge plasma. Plasma Physics and Controlled Fusion, 2011, 53 (5), pp.054019. ⟨10.1088/0741-3335/53/5/054019⟩. ⟨hal-00848545⟩ Plus de détails...
With a proper choice of a single dimensionless control parameter one describes the transition between subsonic and supersonic flows as a bifurcation. The bifurcation point is characterized by specific properties of the control parameter: the control parameter has a vanishing derivative in space and takes the maximum possible value equal to 1. This method is then applied to the sheath plasma with constant temperatures, allowing one to recover the Bohm boundary condition as well as the location of the point where the bifurcation takes place. This analysis is extended to fronts, rarefaction waves and divertor plasmas. Two cases are found, those where departure from quasineutrality is mandatory to generate a maximum in the variation of the control parameter (sheath and fronts) and those where the physics of the quasineutral plasma can generate such a maximum (rarefaction waves and supersonic flow in divertors). The conditions that are required to recover the Bohm condition, when modelling the wall using the penalization technique, are also addressed and generalized.
Philippe Ghendrih, K. Bodi, Hugo Bufferand, Guillaume Chiavassa, Guido Ciraolo, et al.. Transition to supersonic flows in the edge plasma. Plasma Physics and Controlled Fusion, 2011, 53 (5), pp.054019. ⟨10.1088/0741-3335/53/5/054019⟩. ⟨hal-00848545⟩
Guilhem Dif-Pradalier, J Gunn, Guido Ciraolo, C S Chang, Guillaume Chiavassa, et al.. The Mistral base case to validate kinetic and fluid turbulence transport codes of the edge and SOL plasmas. Journal of Nuclear Materials, 2011, 415, ⟨10.1016/j.jnucmat.2010.12.035⟩. ⟨cea-01468372⟩ Plus de détails...
Experimental data from the Tore Supra experiments are extrapolated in the SOL and edge to investigate the Kelvin–Helmholtz instability. The linear analysis indicates that a large part of the SOL is rather unstable. The effort is part of the setup of the Mistral base case that is organised to validate the codes and address new issues on turbulent edges, including the comparison of kinetic and fluid modelling in the edge plasma.
Guilhem Dif-Pradalier, J Gunn, Guido Ciraolo, C S Chang, Guillaume Chiavassa, et al.. The Mistral base case to validate kinetic and fluid turbulence transport codes of the edge and SOL plasmas. Journal of Nuclear Materials, 2011, 415, ⟨10.1016/j.jnucmat.2010.12.035⟩. ⟨cea-01468372⟩
Frédéric Schwander, Guillaume Chiavassa, Guido Ciraolo, Philippe Ghendrih, Livia Isoardi, et al.. Parallel shear flow instability in the tokamak edge. Journal of Nuclear Materials, 2011, 415 (1), pp.S601-S604. ⟨10.1016/j.jnucmat.2010.10.073⟩. ⟨hal-00848536⟩ Plus de détails...
The transition between the core and scrape-off layer of a tokamak corresponds to a marked momentum shear layer, owing to sheath acceleration on limiters which drives near-sonic flows along the plasma magnetic field in the scrape-off layer, and a parallel shear flow instability can possibly be triggered. The possibility of this instability driven by the velocity gradient is investigated numerically, using a minimum model of particle and parallel momentum transport in the edge of a tokamak, in a computational domain modelling a limiter plasma with background turbulence modelled as an effective diffusion. It is found that unstable regions can exist in the vicinity of a limiter, in agreement with experimental findings, when momentum radial transport - and therefore coupling between SOL and core flows - is sufficiently weak. Instability is reinforced by core rotation, and is found to be maximum downstream of the limiter (with respect to the core plasma flow).
Frédéric Schwander, Guillaume Chiavassa, Guido Ciraolo, Philippe Ghendrih, Livia Isoardi, et al.. Parallel shear flow instability in the tokamak edge. Journal of Nuclear Materials, 2011, 415 (1), pp.S601-S604. ⟨10.1016/j.jnucmat.2010.10.073⟩. ⟨hal-00848536⟩
Guillaume Chiavassa, Bruno Lombard. Time domain numerical modeling of wave propagation in 2D heterogeneous porous media. Journal of Computational Physics, 2011, 230 (13), pp.5288-5309. ⟨10.1016/j.jcp.2011.03.030⟩. ⟨hal-00547008v2⟩ Plus de détails...
This paper deals with the numerical modeling of wave propagation in porous media described by Biot's theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot's system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space-time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering.
Guillaume Chiavassa, Bruno Lombard. Time domain numerical modeling of wave propagation in 2D heterogeneous porous media. Journal of Computational Physics, 2011, 230 (13), pp.5288-5309. ⟨10.1016/j.jcp.2011.03.030⟩. ⟨hal-00547008v2⟩
Livia Isoardi, Hugo Bufferand, Guillaume Chiavassa, Guido Ciraolo, Frédéric Schwander, et al.. 2D modelling of electron and ion temperature in the plasma edge and SOL. Journal of Nuclear Materials, 2011, 415 (1), pp.S574-S578. ⟨10.1016/j.jnucmat.2010.12.318⟩. ⟨hal-00848528⟩ Plus de détails...
We are interested here in modelling the electron and ion temperature fields, Te and Ti respectively, in order to understand the main trends that govern the ratio Ti/Te that is being better documented in the SOL with RFA probes and . The experimental evidence gathered from several devices indicates that this temperature ratio significantly exceeds unity in most data sets that have been analysed, including measurements in the SOL of limiter devices like Tore Supra. Several issues of interest have been addressed with this version of the SOLEDGE-2D code. First, we have analysed the width of the SOL heat channels to the wall components and compared these values to analytical expressions. The key control mechanism of the width of the SOL heat channel is given by a balance between the sheath boundary conditions and the transverse transport. More advanced simulations address the interplay between the edge and SOL plasma allowing one to recover regimes with Ti/Te > 1.
Livia Isoardi, Hugo Bufferand, Guillaume Chiavassa, Guido Ciraolo, Frédéric Schwander, et al.. 2D modelling of electron and ion temperature in the plasma edge and SOL. Journal of Nuclear Materials, 2011, 415 (1), pp.S574-S578. ⟨10.1016/j.jnucmat.2010.12.318⟩. ⟨hal-00848528⟩
Hugo Bufferand, Guido Ciraolo, Livia Isoardi, Guillaume Chiavassa, Frédéric Schwander, et al.. Applications of SOLEDGE-2D code to complex SOL configurations and analysis of Mach probe measurements. Journal of Nuclear Materials, 2011, 415 (1), pp.S589-S592. ⟨10.1016/j.jnucmat.2010.11.037⟩. ⟨hal-00848483⟩ Plus de détails...
A series of experiments dedicated to the determination of the ballooning nature of the edge and SOL transport has been achieved on Tore Supra and , proposing a quantitative characterization of the radial flux that enters the SOL. The aim of this paper is to back up the interpretation of these probe flow measurements making use of SOLEDGE-2D code. In particular, this fluid code allows one to study density and parallel momentum transport in a 2D geometry including edge and SOL region. Moreover, thanks to an appropriate numerical technique recently proposed and , SOLEDGE-2D code is also able to deal with a complex geometry of plasma facing components including main and secondary limiters.
Hugo Bufferand, Guido Ciraolo, Livia Isoardi, Guillaume Chiavassa, Frédéric Schwander, et al.. Applications of SOLEDGE-2D code to complex SOL configurations and analysis of Mach probe measurements. Journal of Nuclear Materials, 2011, 415 (1), pp.S589-S592. ⟨10.1016/j.jnucmat.2010.11.037⟩. ⟨hal-00848483⟩
A. Paredes, Eric Serre, Livia Isoardi, Guillaume Chiavassa, Guido Ciraolo, et al.. Boundary conditions at the limiter surface obtained in the modelling of plasma wall interaction with a penalization technique. Journal of Nuclear Materials, 2011, 415 (1), pp.S579-S583. ⟨10.1016/j.jnucmat.2010.12.247⟩. ⟨hal-00848532⟩ Plus de détails...
Isoardi et al. [1] recently proposed a penalization technique to model solid plasma facing components that treats a solid obstacle as a sink region corresponding to the strong plasma recombination in the solid state material. A major advantage of this approach is that it produces a system that can be solved in an obstacle free domain, thus allowing the use of powerful numerical algorithms. Such a technique implemented in a minimal transport model for ionic density and parallel momentum appeared to exhibit a Mach-1 transition at the boundary layer between the plasma presheath and the limiter region. In this paper, we reconsider this result by analysing the physics of detached plasmas that are governed both by strong recombination and plasma pressure decrease, as imposed by the penalization technique within the limiter region. The analysis provides a unique control parameter A=Γcsmi/ΠA=Γcsmi/Π (Γ being the parallel particles flux, cs the sound speed, mi the ionic mass and Π the total plasma pressure) that allows one to understand the results of the penalization technique for the Mach-1 transition.
A. Paredes, Eric Serre, Livia Isoardi, Guillaume Chiavassa, Guido Ciraolo, et al.. Boundary conditions at the limiter surface obtained in the modelling of plasma wall interaction with a penalization technique. Journal of Nuclear Materials, 2011, 415 (1), pp.S579-S583. ⟨10.1016/j.jnucmat.2010.12.247⟩. ⟨hal-00848532⟩
Guillaume Chiavassa, Hugo Bufferand, Guido Ciraolo, Philippe Ghendrih, Hervé Guillard, et al.. Parallel expansion of density bursts. Journal of Nuclear Materials, 2011, 415 (1), pp.S613-S616. ⟨10.1016/j.jnucmat.2010.10.086⟩. ⟨hal-00848522⟩ Plus de détails...
Evidence of poloidally localized cross-field transport in experiments and theoretical analysis of turbulence transport governs the onset of parallel transport towards equilibrium. When cross-field transport appears in bursts, both for ELM relaxation events and microturbulence, the parallel transport of particles is shown to generate fronts that propagate with supersonic velocities. It is shown that after a short transient the density structure is no longer monotonic and that the two fronts (one co, the other counter the magnetic field) are independent. Furthermore, the time trace of the particle flux at a given location is characterized by a sharp rise followed by a longer time scale relaxation. Comparing the time delay and magnitude of the density burst at two locations allows to estimate the magnitude and the location of the generation of the front.
Guillaume Chiavassa, Hugo Bufferand, Guido Ciraolo, Philippe Ghendrih, Hervé Guillard, et al.. Parallel expansion of density bursts. Journal of Nuclear Materials, 2011, 415 (1), pp.S613-S616. ⟨10.1016/j.jnucmat.2010.10.086⟩. ⟨hal-00848522⟩
Pierre Haldenwang, Pierrette Guichardon, Guillaume Chiavassa, N. Ibaseta. Exact solution to mass transfer in Berman flow: application to concentration polarization combined with osmosis in crossflow membrane filtration. International Journal of Heat and Mass Transfer, 2010, 53 (19-20), pp.3898-3904. ⟨10.1016/j.ijheatmasstransfer.2010.05.008⟩. ⟨hal-00907275⟩ Plus de détails...
Concentration polarization affects numerous systems of membrane separation, and combined with osmosis, it can cause substantial reductions in permeation. We establish an exact solution to the conservation law of a solute advected by Berman flow. This flow is characteristic of reverse osmosis or nanofiltration. The resulting concentration polarization is then combined with the osmosis (counter-) effect. For large Péclet number of permeation, it yields a rigorous support to the semi-empirical "film" model, and accounts for the limit flux phenomenon. The main results are summarized in a simple diagram that relates three different Péclet numbers, and show that polarization combined with osmosis can withstand operating pressure almost totally.
Pierre Haldenwang, Pierrette Guichardon, Guillaume Chiavassa, N. Ibaseta. Exact solution to mass transfer in Berman flow: application to concentration polarization combined with osmosis in crossflow membrane filtration. International Journal of Heat and Mass Transfer, 2010, 53 (19-20), pp.3898-3904. ⟨10.1016/j.ijheatmasstransfer.2010.05.008⟩. ⟨hal-00907275⟩
Journal: International Journal of Heat and Mass Transfer
Livia Isoardi, Guido Ciraolo, Guillaume Chiavassa, Pierre Haldenwang, Eric Serre, et al.. Modelling SOL flow pattern spreading in the edge plasma. Journal of Nuclear Materials, 2009, 390-391, pp.388-391. ⟨10.1016/j.jnucmat.2009.01.088⟩. ⟨hal-00848559⟩ Plus de détails...
The transition region between closed and open magnetic flux surfaces plays a crucial role for tokamak performances. Appropriate understanding of the edge region remains a major challenge owing to several open issues as momentum transport, turbulence overshoot or neutral penetration. We consider here a transport model system to investigate the propagation of parallel momentum from the SOL into the core plasma and vice-versa. The numerical results show that for small values of the radial diffusion coefficient, the density profile decays exponentially from the core to the SOL as predicted by 1D analytical solution. A spreading of the parallel momentum from the SOL to the core is observed, with the presence of non-zero velocities also in the regions far from the SOL. The effect of an imposed rotation of the core plasma is investigated as well as the dynamics of an overdensity imposed in the core plasma.
Livia Isoardi, Guido Ciraolo, Guillaume Chiavassa, Pierre Haldenwang, Eric Serre, et al.. Modelling SOL flow pattern spreading in the edge plasma. Journal of Nuclear Materials, 2009, 390-391, pp.388-391. ⟨10.1016/j.jnucmat.2009.01.088⟩. ⟨hal-00848559⟩
