We propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime. The typical example we discuss is the derivation of the Euler system from the BGK equation. The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.
This paper is devoted to hydrodynamic models intended to describe charging phenomena the spacecrafts evolving in Low Earth Orbits (LEO) are subject to. The models we are interested in couple the stationary Euler equations to the Poisson equation which defines the electric potential. Furthermore, the charging dynamics is embodied into the boundary conditions where the time derivative of the potential appears. We point out the main mathematical difficulties by restricting to a 1D caricature model for which we present rigorous existence results and numerical simulations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.