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Rarefied flow computations using nonlinear model Boltzmann equations. (English) Zbl 0845.76064

High resolution finite difference schemes for solving nonlinear model Boltzmann equations are presented for computations of rarefied gas flows. The discrete ordinate method is first applied to describe the velocity space dependence of the distribution function caused by the model Boltzmann equation in phase space by a set of hyperbolic conservation laws with source terms in physical space. Then a high order essentially nonoscillatory method due to Harten is adapted and extended to solve the above hyperbolic system. Explicit methods using operator splitting, and implicit methods using the lower-upper factorization are described to treat the multidimensional problems. The methods are tested on both steady and unsteady rarefied gas flows to illustrate their potential use.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics

Software:

HLLE
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