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A linearization of Mieussens’s discrete velocity model for kinetic equations. (English) Zbl 1160.82341

Summary: A linearization is developed for Mieussens’s discrete velocity model [see, e.g., L. Mieussens, J. Comput. Phys. 162, No. 2, 429–466 (2000; Zbl 0984.76070)] for kinetic equations. The basic idea is to use a linearized expression of the reference distribution function in the kinetic equation, instead of its exact expression, in the numerical scheme. This modified scheme is applied to various kinetic models, which include the BGK model, the ES-BGK model, the BGK model with velocity-dependent collision frequency, and the recently proposed ES-BGK model with velocity-dependent collision frequency. One-dimensional stationary shock waves and stationary planar Couette flow, which are two benchmark problems for rarefied gas flows, are chosen as test examples. Molecules are modeled as Maxwell molecules and hard sphere molecules. It is found that results from the modified scheme are very similar to results from the original Mieussens’s numerical scheme for various kinetic equations in almost all tests we did, while, depending on the test case, 20–40 percent of computational time can be saved. The application of the method is not affected by the Knudsen number and molecular models, but is restricted to lower Mach numbers for the BGK (or the ES-BGK) model with velocity-dependent collision frequency.

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics

Citations:

Zbl 0984.76070
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References:

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