Boundary conditions for regularized 13-moment-equations for micro-channel-flows

Authors:
Manuel Torrilhon;Henning Struchtrup
Affiliations:
Seminar for Applied Mathematics, ETH Zurich, Switzerland;Department of Mechanical Engineering, University of Victoria, Canada and Institute of Polymer Physics, ETH Zurich, Switzerland
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

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's equation with boundary conditions obtained from Maxwell's kinetic accommodation model. While for the linear case these kinetic boundary conditions suffice, we need additional conditions in the non-linear case. These are provided by the bulk solutions obtained after properly transforming the equations while keeping their asymptotic accuracy with respect to Boltzmann's equation. After finding a suitable set of boundary conditions and equations, a numerical method for generic shear flow problems is formulated. Several test simulations demonstrate the stable and oscillation-free performance of the new approach.