Après thèse CIFRE réalisée avec le M2P2 : "Evaluation du potentiel de LBM pour applications aérothermiques tournantes hors veine turbomachines incluant des zones de haut MACH"
Activités
Lattice Boltzmann Method
stabilité numérique
théorie cinétique
écoulements compressibles
analyses linéaires
Publications scientifiques au M2P2
2022
Gauthier Wissocq, Pierre Sagaut. Hydrodynamic limits and numerical errors of isothermal lattice Boltzmann schemes. Journal of Computational Physics, 2022, 450, pp.110858. ⟨10.1016/j.jcp.2021.110858⟩. ⟨hal-04064045⟩ Plus de détails...
With the aim of better understanding the numerical properties of the lattice Boltzmann method (LBM), a general methodology is proposed to derive its hydrodynamic limits in the discrete setting. It relies on a Taylor expansion in the limit of low Knudsen numbers. With a single asymptotic analysis, two kinds of deviations with the Navier-Stokes (NS) equations are explicitly evidenced: consistency errors, inherited from the kinetic description of the LBM, and numerical errors attributed to its space and time discretization. The methodology is applied to the Bhatnagar-Gross-Krook (BGK), the regularized and the multiple relaxation time (MRT) collision models in the isothermal framework. Deviation terms are systematically confronted to linear analyses in order to validate their expressions, interpret them and provide explanations for their numerical properties. The low dissipation of the BGK model is then related to a particular pattern of its error terms in the Taylor expansion. Similarly, dissipation properties of the regularized and MRT models are explained by a phenomenon referred to as hyperviscous degeneracy. The latter consists in an unexpected resurgence of high-order Knudsen effects induced by a large numerical prefactor. It is at the origin of over-dissipation and severe instabilities in the low-viscosity regime.
Gauthier Wissocq, Pierre Sagaut. Hydrodynamic limits and numerical errors of isothermal lattice Boltzmann schemes. Journal of Computational Physics, 2022, 450, pp.110858. ⟨10.1016/j.jcp.2021.110858⟩. ⟨hal-04064045⟩
Gauthier Wissocq, Thomas Coratger, Gabriel Farag, Song Zhao, Pierre Boivin, et al.. Restoring the conservativity of characteristic-based segregated models: application to the hybrid lattice Boltzmann method. Physics of Fluids, 2022, 34 (4), pp.046102. ⟨10.1063/5.0083377⟩. ⟨hal-03627520⟩ Plus de détails...
A general methodology is introduced to build conservative numerical models for fluid simulations based on segregated schemes, where mass, momentum and energy equations are solved by different methods. It is here especially designed for developing new numerical discretizations of the total energy equation, adapted to a thermal coupling with the lattice Boltzmann method (LBM). The proposed methodology is based on a linear equivalence with standard discretizations of the entropy equation, which, as a characteristic variable of the Euler system, allows efficiently decoupling the energy equation with the LBM. To this extent, any LBM scheme is equivalently written under a finite-volume formulation involving fluxes, which are further included in the total energy equation as numerical corrections. The viscous heat production is implicitly considered thanks to the knowledge of the LBM momentum flux. Three models are subsequently derived: a first-order upwind, a Lax-Wendroff and a third-order Godunov-type schemes. They are assessed on standard academic test cases: a Couette flow, entropy spot and vortex convections, a Sod shock tube, several two-dimensional Riemann problems and a shock-vortex interaction. Three key features are then exhibited: 1) the models are conservative by construction, recovering correct jump relations across shock waves, 2) the stability and accuracy of entropy modes can be explicitly controlled, 3) the low dissipation of the LBM for isentropic phenomena is preserved.
Gauthier Wissocq, Thomas Coratger, Gabriel Farag, Song Zhao, Pierre Boivin, et al.. Restoring the conservativity of characteristic-based segregated models: application to the hybrid lattice Boltzmann method. Physics of Fluids, 2022, 34 (4), pp.046102. ⟨10.1063/5.0083377⟩. ⟨hal-03627520⟩
Thomas Astoul, Gauthier Wissocq, Jean-François Boussuge, Alois Sengissen, Pierre Sagaut. Lattice Boltzmann method for computational aeroacoustics on non-uniform meshes: A direct grid coupling approach. Journal of Computational Physics, 2021, 447, pp.110667. ⟨10.1016/j.jcp.2021.110667⟩. ⟨hal-03514616⟩ Plus de détails...
The present study proposes an accurate lattice Boltzmann direct coupling algorithm, well suited for industrial purposes, making it highly valuable for aeroacoustic applications. It is indeed known that the convection of vortical structures across a grid refinement interface, where cell size is abruptly doubled, is likely to generate spurious noise that may corrupt the solution over the whole computational domain. This issue becomes critical in the case of aeroacoustic simulations, where accurate pressure estimations are of paramount importance. Consequently, any interfering noise that may pollute the acoustic predictions must be reduced. The proposed grid refinement algorithm differs from conventionally used ones, in which an overlapping mesh layer is considered. Instead, it provides a direct connection allowing a tighter link between fine and coarse grids, especially with the use of a coherent equilibrium function shared by both grids. Moreover, the direct coupling makes the algorithm more local and prevents the duplication of points, which might be detrimental for massive parallelization. This work follows our first study (Astoul et al. 2020 [1]) on the deleterious effect of non-hydrodynamic modes crossing mesh transitions, which can be addressed using an appropriate collision model: the hybrid recursive regularization. The grid coupling algorithm is assessed in the context of computational aeroacoustics and compared to a widely-used cell-vertex algorithm. The validation benchmark includes the simulation of (1) an acoustic pulse, (2) a vortex transport by a mean flow, and finally, (3) a turbulent circular cylinder wake flow at high Reynolds number. In the end, the proposed approach is proven to drastically reduced the spurious noise generated at grid interfaces, hence, paving the way for accurate and efficient aeroacoustic simulations based on lattice Boltzmann methods. (C) 2021 Elsevier Inc. All rights reserved.
Thomas Astoul, Gauthier Wissocq, Jean-François Boussuge, Alois Sengissen, Pierre Sagaut. Lattice Boltzmann method for computational aeroacoustics on non-uniform meshes: A direct grid coupling approach. Journal of Computational Physics, 2021, 447, pp.110667. ⟨10.1016/j.jcp.2021.110667⟩. ⟨hal-03514616⟩
G. Farag, T. Coratger, G. Wissocq, S. Zhao, Pierre Boivin, et al.. A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods. Physics of Fluids, 2021, 33 (8), pp.086101. ⟨10.1063/5.0057407⟩. ⟨hal-03324229⟩ Plus de détails...
A unified expression for high-speed compressible segregated consistent lattice Boltzmann methods, namely, pressure-based and improved density-based methods, is given. It is theoretically proved that in the absence of forcing terms, these approaches are strictly identical and can be recast in a unique form. An important result is that the difference with classical density-based methods lies in the addition of fourth-order term in the equilibrium function. It is also shown that forcing terms used to balance numerical errors in both original pressure-based and improved density-based methods can be written in a generalized way. A hybrid segregated efficient lattice-Boltzmann for compressible flow based on this unified model, equipped with a recursive regularization kernel, is proposed and successfully assessed on a wide set of test cases with and without shock waves.
G. Farag, T. Coratger, G. Wissocq, S. Zhao, Pierre Boivin, et al.. A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods. Physics of Fluids, 2021, 33 (8), pp.086101. ⟨10.1063/5.0057407⟩. ⟨hal-03324229⟩
Amaury Bannier, Éric Garnier, Pierre Sagaut. Riblet Flow Model Based on an Extended FIK Identity. Flow, Turbulence and Combustion, 2015, 95 (2-3), pp.351-376. ⟨10.1007/s10494-015-9624-2⟩. ⟨hal-01276488⟩ Plus de détails...
Large Eddy Simulations of zero-pressure-gradient turbulent boundary layers over riblets have been conducted. All along the controlled domain, riblets maintain a significant 11 % drag reduction with respect to the flat plate at the same R e τ (from 250 to 450). To compare the flows above riblets and a reference smooth wall, an appropriate vertical shift between the two surfaces is required. In the present study, the “vertical origin” is set using the identity of Fukagata, Iwamoto and Kasagi (FIK) in Phys. Fluids, vol. 14, 2002, L73. This identity, which provides a physically meaningful decomposition of the skin friction, has been extended to complex wall surfaces and constitutes the basis for the derivation of a new virtual origin. Using this FIK-based origin, it is shown that the complex interactions between the riblets and the near-wall turbulent structures can be taken into account by a simple shift of the two axes of the mean and turbulent velocity profiles. The appropriate upward shift Δu +, typical for drag reduction, is directly dependent on the skin friction on the riblets and on the reference smooth plate at the same R e τ .
Amaury Bannier, Éric Garnier, Pierre Sagaut. Riblet Flow Model Based on an Extended FIK Identity. Flow, Turbulence and Combustion, 2015, 95 (2-3), pp.351-376. ⟨10.1007/s10494-015-9624-2⟩. ⟨hal-01276488⟩