Speaker
Description
The lattice Boltzmann method has recently been developed to solve problems in solid mechanics, starting with linear elastostatics [1, 2] and continuing with linear elastodynamics [3] in two dimensions. Based on these works, we propose an extension of the lattice Boltzmann method for linear elastodynamics in three dimensions. As in the 2D case, we transform the system into an equivalent first-order hyperbolic system of equations, on which the lattice Bolzmann scheme with vector-valued populations is applied. Using the asymptotic expansion technique, we prove second-order consistency for both periodic and Dirichlet boundary conditions for 3D prismatic domains. The scheme is stable under a CFL-like condition. Moreover, we propose a projection of the solution on a 2Drectangular domain, which recovers the solution using a 2D lattice Boltzmann formulation. Finally, we conduct numerical experiments to verify our theoretical derivations.
References:
[1] Boolakee, O., Geier, M. and De Lorenzis, L., A new lattice Boltzmann scheme for linear elasticsolids: periodic problems. Comp. Meth. Appl. Mech. Eng. (2023) 404:115756.
[2] Boolakee, O., Geier, M. and De Lorenzis, L., Dirichlet and Neumann boundary conditions fora lattice Boltzmann scheme for linear elastic solids on arbitrary domains. Comp. Meth. Appl.Mech. Eng. (2023) 415:116225.
[3] Boolakee, O., Geier, M. and De Lorenzis, L., Lattice Boltzmann for linear elastodynamics: pe-riodic problems and Dirichlet boundary conditions. (2024).
https://doi.org/10.48550/arXiv.2408.01081 . Preprint.
