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

Mapundi Banda; Axel Klar; Lorenzo Pareschi; Mohammed Seaïd

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

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 journal › Article › peer-review

5 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 language	English
Pages (from-to)	943-965
Number of pages	23
Journal	Mathematics of Computation
Volume	77
Issue number	262
DOIs	https://doi.org/10.1090/S0025-5718-07-02034-0
State	Published - Apr 2008
Externally published	Yes

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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10.1090/S0025-5718-07-02034-0

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

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.",

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

author = "Mapundi Banda and Axel Klar and Lorenzo Pareschi and Mohammed Sea{\"i}d",

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T1 - Lattice-boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-stokes equations

AU - Banda, Mapundi

AU - Klar, Axel

AU - Pareschi, Lorenzo

AU - Seaïd, Mohammed

PY - 2008/4

Y1 - 2008/4

N2 - 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.

AB - 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.

KW - High order upwind schemes

KW - Incompressible Navier-Stokes equations

KW - Lattice-Boltzmann method

KW - Low Mach number limit

KW - Relaxation schemes

KW - Runge-Kutta methods

KW - Stiff equations

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U2 - 10.1090/S0025-5718-07-02034-0

DO - 10.1090/S0025-5718-07-02034-0

M3 - Article

AN - SCOPUS:42349116799

SN - 0025-5718

VL - 77

SP - 943

EP - 965

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 262

ER -

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

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Keywords

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