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PreprintCC BY-NC-ND 4.0HAL

NUMERICAL ANALYSIS OF A LAX-WENDROFF TYPE LATTICE BOLTZMANN SCHEME FOR THE ADVECTION EQUATION

  • Thomas Bellotti
  • Filipa Caetano
  • François Dubois
  • Benjamin Graille
Open at sourcePDFDOICite

Abstract

A linear monodimensional lattice Boltzmann scheme with three velocities tackling the advection equation is investigated. We prove that it is second-order accurate and provide necessary and sufficient stability conditions through an explicit formula involving the two relaxation parameters. Relying on existing results for finite difference schemes, we prove convergence for smooth initial data with initialization of the non-conserved moments at equilibrium. Several numerical simulations illustrate these theoretical findings.

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Cite

BibTeXRIS
BibTeX
@misc{bellotti2026numerical,
  title = {{NUMERICAL ANALYSIS OF A LAX-WENDROFF TYPE LATTICE BOLTZMANN SCHEME FOR THE ADVECTION EQUATION}},
  author = {Thomas Bellotti and Filipa Caetano and François Dubois and Benjamin Graille},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23390934},
  eprint = {2610.32810},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05836006v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - NUMERICAL ANALYSIS OF A LAX-WENDROFF TYPE LATTICE BOLTZMANN SCHEME FOR THE ADVECTION EQUATION
AU  - Thomas Bellotti
AU  - Filipa Caetano
AU  - François Dubois
AU  - Benjamin Graille
PY  - 2026
DA  - 2026/10/20
PB  - HAL
DO  - 10.5281/zenodo.23390934
UR  - https://hal.science/hal-05836006v1
AB  - A linear monodimensional lattice Boltzmann scheme with three velocities tackling the advection equation is investigated. We prove that it is second-order accurate and provide necessary and sufficient stability conditions through an explicit formula involving the two relaxation parameters. Relying on existing results for finite difference schemes, we prove convergence for smooth initial data with initialization of the non-conserved moments at equilibrium. Several numerical simulations illustrate these theoretical findings.
ER  -