Lattice Boltzmann Method for solids: high-performance 3D elastodynamics solver using NVIDIA Warp
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The Lattice Boltzmann Method (LBM) has recently been developed to solve problems in solid mechanics, starting with linear elastostatics and continuing with linear elastodynamics in two dimensions. Based on these works, we propose an extension of LBM for linear elastodynamics in three dimensions. Using the asymptotic expansion technique, we prove second-order consistency for periodic, Dirichlet and Neumann boundary conditions for 3D prismatic domains. The scheme is stable under a CFL-like condition. Numerical experiments are conducted to verify our theoretical derivations. Furthermore, we assess the computational performance on a GPU architecture using XLB, an accelerated Lattice Boltzmann library based on the NVIDIA Warp backend. We demonstrate that the proposed LBM approach enables faster simulations than a conventional explicit FEM scheme when applied to large-scale problems.
