Méthodes Lattice Boltzmann pour les écoulements compressibles (Thèse 2019 - 2022)
Activités
LBM,
Ecoulements Compressibles,
CFD,
High Mach,
High Reynolds
Publications scientifiques au M2P2
2022
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, American Institute of Physics, 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, American Institute of Physics, 2022, 34 (4), pp.046102. ⟨10.1063/5.0083377⟩. ⟨hal-03627520⟩
T. Coratger, G. Farag, S. Zhao, Pierre Boivin, P. Sagaut. Large-eddy lattice-Boltzmann modeling of transonic flows. Physics of Fluids, American Institute of Physics, 2021, 33 (11), pp.115112. ⟨10.1063/5.0064944⟩. ⟨hal-03424286⟩ Plus de détails...
T. Coratger, G. Farag, S. Zhao, Pierre Boivin, P. Sagaut. Large-eddy lattice-Boltzmann modeling of transonic flows. Physics of Fluids, American Institute of Physics, 2021, 33 (11), pp.115112. ⟨10.1063/5.0064944⟩. ⟨hal-03424286⟩
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, American Institute of Physics, 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, American Institute of Physics, 2021, 33 (8), pp.086101. ⟨10.1063/5.0057407⟩. ⟨hal-03324229⟩
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, American Institute of Physics, 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, American Institute of Physics, 2020, 32 (6), pp.066106. ⟨10.1063/5.0011839⟩. ⟨hal-02885427⟩
Amaury Bannier, Éric Garnier, Pierre Sagaut. Riblet Flow Model Based on an Extended FIK Identity. Flow, Turbulence and Combustion, Springer Verlag (Germany), 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, Springer Verlag (Germany), 2015, 95 (2-3), pp.351-376. ⟨10.1007/s10494-015-9624-2⟩. ⟨hal-01276488⟩