Consistency and stability of boundary conditions for a two-velocities lattice Boltzmann scheme
<|reference_start|>Consistency and stability of boundary conditions for a two-velocities lattice Boltzmann scheme: We theoretically explore boundary conditions for lattice Boltzmann methods, focusing on a toy two-velocities scheme. By mapping lattice Boltzmann schemes to Finite Difference schemes, we facilitate rigorous consistency and stability analyses. We develop kinetic boundary conditions for inflows and outflows, highlighting the trade-off between accuracy and stability, which we successfully overcome. Consistency analysis relies on modified equations, whereas stability is assessed using GKS (Gustafsson, Kreiss, and Sundstr{\"o}m) theory and -- when this approach fails on coarse meshes -- spectral and pseudo-spectral analyses of the scheme's matrix that explain effects germane to low resolutions.<|reference_end|>
@article{bellotti2024consistency,
    title={Consistency and stability of boundary conditions for a two-velocities
  lattice Boltzmann scheme},
    author={Thomas Bellotti (IRMA)},
    journal={arXiv preprint arXiv:2407.02009},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.02009},
    primaryClass={math.NA cs.NA}
}