Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations
<|reference_start|>Numerical approximations of a lattice Boltzmann scheme with a family of partial differential equations: In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We first derive a family of equivalent partial differential equations at various orders, and we compare the lattice Boltzmann experimental results with a spectral approximation of the differential equations. For an unsteady situation, we show that the initialization scheme at a sufficiently high order of the microscopic moments plays a crucial role to observe an asymptotic error consistent with the orderof approximation. For a stationary long-time limit, we observe that the measured asymptotic error converges with a reduced order of precision compared to the one suggested by asymptotic analysis.<|reference_end|>
@article{boghosian2024numerical,
    title={Numerical approximations of a lattice Boltzmann scheme with a family of
  partial differential equations},
    author={Bruce M Boghosian, Franc{c}ois Dubois (LMO, LMSSC), Pierre Lallemand
  (CSRC)},
    journal={arXiv preprint arXiv:2403.19231},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.19231},
    primaryClass={math.NA cs.NA}
}