Lattice-boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-stokes equations

Mapundi Banda, Axel Klar, Lorenzo Pareschi, Mohammed Seaïd

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A relaxation system based on a Lattice-Boltzmann type discrete velocity model is considered in the low Mach number limit. A third order relaxation scheme is developed working uniformly for all ranges of the mean free path and Mach number. In the incompressible Navier-Stokes limit the scheme reduces to an explicit high order finite difference scheme for the incompressible Navier-Stokes equations based on nonoscillatory upwind discretization. Numerical results and comparisons with other approaches are presented for several test cases in one and two space dimensions.

Original languageEnglish
Pages (from-to)943-965
Number of pages23
JournalMathematics of Computation
Volume77
Issue number262
DOIs
StatePublished - Apr 2008
Externally publishedYes

Keywords

  • High order upwind schemes
  • Incompressible Navier-Stokes equations
  • Lattice-Boltzmann method
  • Low Mach number limit
  • Relaxation schemes
  • Runge-Kutta methods
  • Stiff equations

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