Lattice Boltzmann for linear elastodynamics: periodic problems and Dirichlet boundary conditions
<|reference_start|>Lattice Boltzmann for linear elastodynamics: periodic problems and Dirichlet boundary conditions: We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Boltzmann formulation is introduced. The only difference to conventional lattice Boltzmann formulations is the usage of vector-valued populations, so that all computational benefits of the algorithm are preserved. Using the asymptotic expansion technique and the notion of pre-stability structures we further establish second-order consistency as well as analytical stability estimates. Lastly, we introduce a second-order consistent initialization of the populations as well as a boundary formulation for Dirichlet boundary conditions on 2D rectangular domains. All theoretical derivations are numerically verified by convergence studies using manufactured solutions and long-term stability tests.<|reference_end|>
@article{boolakee2024lattice,
    title={Lattice Boltzmann for linear elastodynamics: periodic problems and
  Dirichlet boundary conditions},
    author={Oliver Boolakee, Martin Geier, Laura De Lorenzis},
    journal={arXiv preprint arXiv:2408.01081},
    year={2024},
    doi={10.1016/j.cma.2024.117469},
    archivePrefix={arXiv},
    eprint={2408.01081},
    primaryClass={math.NA cs.NA}
}