Semilagrangian schemes applied to moving boundary problems
for the BGK model of rarefied gas dynamics
Giovanni Russo - Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6, 95125 Catania, Italy (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.
Received: November 2008; Revised: December 2008; Published: January 2009.
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