A convergent method for linear half-space kinetic equations
Provides a systematic numerical framework for half-space kinetic equations, which is useful for researchers in kinetic-fluid coupling simulations.
The authors prove well-posedness for a class of linear half-space kinetic equations and develop a convergent Galerkin method with quasi-optimal error control, enabling efficient kinetic-fluid coupling simulations.
We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both analysis and numerics includes three steps: adding damping terms to the original half-space equation, using an inf-sup argument and even-odd decomposition to establish the well-posedness of the damped equation, and then recovering solutions to the original half-space equation. The proposed numerical methods for the damped equation is shown to be quasi-optimal and the numerical error of approximations to the original equation is controlled by that of the damped equation. This efficient solution to the half-space problem is useful for kinetic-fluid coupling simulations.