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Lattice-Boltzmann type relaxation systems and high order relaxation schemes for the incompressible Navier-Stokes equations |
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| Authors: | Mapundi Banda Axel Klar Lorenzo Pareschi Mohammed Seaï d. |
| Affiliation: | 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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