Semilagrangian Schemes for the BGK Model of the Boltzmann Equation

Giovanni Russo
Università di Catania

In this talk we present a new semilagrangian scheme for the numerical solution of the BGK model of rarefied gas dynamics. The scheme is based on solving the BGK equation in characteristic form. The source term is treated implicitly, which makes the scheme Asymptotic Preserving in the limit of small Knudsen number, although a loss of accuracy is observed close to such regime. Because of its Lagrangian nature, no stability restriction is posed on the CFL number, which is determined only by accuracy requirements.
High resolution in space is obtained by suitable high order reconstruction, while high order in time is obtained by suitable use of Runge-Kutta implicit-explicit schemes. A modified version of the scheme is capable of solving the equation in a domain with moving boundaries, in view of applications to Micro Electro Mechanical Systems (MEMS). 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.

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