Half-space Kinetic Equations with General Boundary Conditions
For researchers in kinetic theory and numerical analysis, this provides a rigorous framework for half-space equations with general boundary conditions, but it is an incremental extension of prior work.
This work extends previous results on half-space kinetic equations to include general boundary conditions with reflections, proving well-posedness and quasi-optimality of a numerical scheme, validated on multi-species and multi-frequency transport equations and the linearized BGK equation.
We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary conditions. As in [LLS14], 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.