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March  2009, 2(1): 231-250. doi: 10.3934/krm.2009.2.231

Semilagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics

Giovanni Russo 1, and  Francis Filbet 2,

1. 

Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6, 95125 Catania, Italy
2. 

Université de Lyon, UL1, INSAL, ECL, CNRS, UMR5208, Institut Camille Jordan, 43 boulevard 11 novembre 1918, F-69622 Villeurbanne cedex, France

Received  November 2008 Revised  December 2008 Published  January 2009

In this paper we present a new semilagrangian scheme for the numerical solution of the BGK model of rarefied gas dynamics, in a domain with moving boundaries, in view of applications to Micro Electro Mechanical Systems (MEMS). The source term is treated implicitly, which makes the scheme Asymptotic Preserving in the limit of small Knudsen number. Because of its Lagrangian nature, no stability restriction is posed on the CFL number, which is determined only by accuracy requirements. The method is tested on a one dimensional piston problem. The solution for small Knudsen number is compared with the results obtained by the numerical solution of the Euler equation of gas dynamics.
Keywords: Boltzmann equation, Rarefied gas flows, Lagrangian methods, Numerical methods for time dependent statistical mechanics..
Mathematics Subject Classification: Primary: 76P05, 76M20; Secondary: 82C8.
Citation: Giovanni Russo, Francis Filbet. Semilagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics. Kinetic & Related Models, 2009, 2 (1) : 231-250. doi: 10.3934/krm.2009.2.231
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