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Lattice-Boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-Stokes equations
Authors:Mapundi Banda  Axel Klar  Lorenzo Pareschi  Mohammed Seaï  d
Institution:School of Mathematical Sciences, University of KwaZulu-Natal, Private X01, 3209 Pietermaritzburg, South Africa ; Fachbereich Mathematik, TU Kaiserslautern, Erwin-Schroedinger-Str. 48, D-67663 Kaiserslautern, Germany ; Department of Mathematics, University of Ferrara, Via Machiavelli 35, I-44100 Ferrara, Italy ; Fachbereich Mathematik, TU Kaiserslautern, Erwin-Schroedinger-Str. 48, D-67663 Kaiserslautern, Germany
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:Lattice-Boltzmann method  relaxation schemes  low Mach number limit  incompressible Navier-Stokes equations  high order upwind schemes  Runge-Kutta methods  stiff equations
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