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Semilagrangian schemes applied to moving boundary problemsfor the BGK model of rarefied gas dynamics. (English) Zbl 1372.76090
Summary: 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.

MSC:
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
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