Half-space kinetic equations with general boundary conditions

Li, Qin; Lu, Jianfeng; Sun, Weiran

doi:10.1090/mcom/3155

Half-space kinetic equations with general boundary conditions
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by Qin Li, Jianfeng Lu and Weiran Sun PDF

Math. Comp. 86 (2017), 1269-1301 Request permission

Abstract:

We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various types of reflections, extending our previous work on half-space equations with incoming boundary conditions. As in our previous work, the main technique is a damping adding-removing procedure. We establish the well-posedness of linear (or linearized) half-space equations with general boundary conditions and quasi-optimality of the numerical scheme. The numerical method is validated by examples including a two-species transport equation, a multi-frequency transport equation, and the linearized BGK equation in 2D velocity space.

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