Lattice-Boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-Stokes equations

Banda, Mapundi; Klar, Axel; Pareschi, Lorenzo; Seaïd, Mohammed

doi:10.1090/S0025-5718-07-02034-0

Lattice-Boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-Stokes equations

Authors: Mapundi Banda, Axel Klar, Lorenzo Pareschi and Mohammed Seaïd
Journal: Math. Comp. 77 (2008), 943-965
MSC (2000): Primary 76P05, 76D05, 65M06, 35B25
DOI: https://doi.org/10.1090/S0025-5718-07-02034-0
Published electronically: December 17, 2007
MathSciNet review: 2373186
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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.

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