Kinetic and Related Models (KRM)

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

Pages: 231 - 250, Volume 2, Issue 1, March 2009      doi:10.3934/krm.2009.2.231

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Giovanni Russo - Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6, 95125 Catania, Italy (email)
Francis Filbet - Université de Lyon, UL1, INSAL, ECL, CNRS, UMR5208, Institut Camille Jordan, 43 boulevard 11 novembre 1918, F-69622 Villeurbanne cedex, France (email)

Abstract: 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:  Rarefied gas flows, Boltzmann equation, Lagrangian methods, Numerical methods for time dependent statistical mechanics.
Mathematics Subject Classification:  Primary: 76P05, 76M20; Secondary: 82C80.

Received: November 2008;      Revised: December 2008;      Available Online: January 2009.