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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 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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Additional Information

Mapundi Banda
Affiliation: School of Mathematical Sciences, University of KwaZulu-Natal, Private X01, 3209 Pietermaritzburg, South Africa
Email: bandamk@ukzn.ac.za

Axel Klar
Affiliation: Fachbereich Mathematik, TU Kaiserslautern, Erwin-Schroedinger-Str. 48, D-67663 Kaiserslautern, Germany
Email: klar@mathematik.uni-kl.de

Lorenzo Pareschi
Affiliation: Department of Mathematics, University of Ferrara, Via Machiavelli 35, I-44100 Ferrara, Italy
Email: pareschi@dm.unife.it

Mohammed Seaïd
Affiliation: Fachbereich Mathematik, TU Kaiserslautern, Erwin-Schroedinger-Str. 48, D-67663 Kaiserslautern, Germany
Email: seaid@mathematik.uni-kl.de

DOI: https://doi.org/10.1090/S0025-5718-07-02034-0
Keywords: Lattice-Boltzmann method, relaxation schemes, low Mach number limit, incompressible Navier-Stokes equations, high order upwind schemes, Runge-Kutta methods, stiff equations
Received by editor(s): November 10, 2005
Received by editor(s) in revised form: January 15, 2007
Published electronically: December 17, 2007
Additional Notes: This work was supported by DFG grant KL 1105/9-1 and partially by TMR project “Asymptotic Methods in Kinetic Theory”, Contract Number ERB FMRX CT97 0157.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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