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Poster De Conférence Année : 2022

Lattice Boltzman Method with Adaptative Mesh Refinement strategy to solve the transport equation

Résumé

Introduction The Lattice Boltzmann Method (LBM) is a widely used method for solving the transport equation in media with complex geometry. This popularity stems both from its simplicity of implementation and from its intrinsically parallelizable algorithm, which makes it a highly efficient High-Performance Computing (HPC) numerical method. The main drawback of this method, in its basic form, is the use of a lattice similar to a regular Cartesian mesh, which can lead to use a large number of sites with a level of discretization that is much too high in areas of low interest. We propose here to use an Adaptive Mesh Refinement method for the LBM with the strong objective of not reducing the HPC efficiency of LBM. HPC strategy Our main objective is to develop a high-level language portable simulation tool on different parallel CPU and GPU architectures without having to rewrite it with each new processors technological advance. To do this, we have developed our code in C++ coupled with the Kokkos library that allows us to obtain an executable that runs on several kinds of architectures (as multicores x86 multicores, GPU NVIDIA®, AMD GPU or ARM processor) [1,2]. LBM on non-conformal grids In order to modify a LB numerical scheme to a nonconforming lattice, we choose to use a Lax-Wendroff discretization approach for replacing the streaming step. The LB algorithm then reads (1) for collision step where Ωi is the transport collision operator and (2) for the streaming step. $f^*_i (x,t) = f_i (x,t) - \Omega_i$ (1) $f_i (x, t+\Delta t) = f^*_i (x,t) - \chi(f^*_i (x,t) - f^*_i (x-e_i \Delta x,t)) - 0.5 \chi (1-\chi)(f^*_i (x+e_i \Delta x,t) - 2f^*_i (x,t) + f^*_i (x-e_i \Delta x,t))$ (2)_ This scheme is stable for $\chi<1$, which we impose by choice of Δt on the finest network and thus guarantee stability on all refinement levels. The mesh is organised in blocks of a given number of cells in an octree structure. The communication between neighboring blocks is done via ghost cells. For neighboring blocks of different refinement level, the ghost layers are filled using quadratic interpolation. Adaptive Mesh Refinement criteria In order to compute the transport as accurately as possible, we have chosen to refine as much as possible the high concentration gradient zones and have therefore chosen to use a criterion based on the gradient to refine or to coarsen each block component of the lattice. When the mesh adaptation criteria requires to refine a given block, the values to be assigned to the refined lattice are obtained by projection and when the criterion value asks for coarsening, the value to be assigned is obtained by averaging. References [1] Compatibilities of kokkos library (2020). https://github.com/kokkos/kokkos/wiki/Compiling (Web link accessible on March 8, 2022). [2] Verdier, W., Kestener, P., & Cartalade, A. (2020). Performance portability of lattice Boltzmann methods for two-phase flows with phase change. Computer Methods in Applied Mechanics and Engineering, 370, 113266.
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Dates et versions

cea-04469328 , version 1 (20-02-2024)

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  • HAL Id : cea-04469328 , version 1

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Evangelos Stavropoulos Vasilakis, Pierre Kestener, Alain Cartalade, Alain Genty. Lattice Boltzman Method with Adaptative Mesh Refinement strategy to solve the transport equation. CMWR 2022, Jun 2022, Gdansk, Poland. 2022. ⟨cea-04469328⟩
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