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Numerical properties of high order discrete velocity solutions to the BGK kinetic equation. (English) Zbl 1366.76080

Summary: A high order numerical method for the solution of model kinetic equations is proposed. The new method employs discontinuous Galerkin (DG) discretizations in the spatial and velocity variables and Runge-Kutta discretizations in the temporal variable. The method is implemented for the one-dimensional Bhatnagar-Gross-Krook equation. Convergence of the numerical solution and accuracy of the evaluation of macroparameters are studied for different orders of velocity discretization. Synthetic model problems are proposed and implemented to test accuracy of discretizations in the free molecular regime. The method is applied to the solution of the normal shock wave problem and the one-dimensional heat transfer problem.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs

Software:

WENO
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Full Text: DOI

References:

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