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Boundary conditions for regularized 13-moment-equations for micro-channel-flows. (English) Zbl 1132.76049

Summary: Boundary conditions are the major obstacle in simulations based on advanced continuum models of rarefied and micro-flows of gases. In this paper, we present a theory how to combine the regularized 13-moment-equations derived from Boltzmann equation with boundary conditions obtained from Maxwell kinetic accommodation model. While for the linear case these kinetic boundary conditions suffice, we need additional conditions in the nonlinear case. These are provided by the bulk solutions obtained after properly transforming the equations while keeping their asymptotic accuracy with respect to Boltzmann equation. After finding a suitable set of boundary conditions and equations, we formulate a numerical method for generic shear flow problems. Several test simulations demonstrate the stable and oscillation-free performance of the new approach.

MSC:

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