Transition from Kinetic theory to macroscopic fluid equations: A problem for domain decomposition and a source for new algorithms

Abstract

In the paper we give a survey on the transition from kinetic theory to macroscopic fluid equations, where the macroscopic equations are defined as asymptotic limits of a kinetic equation. This relation can be used to derive computationally efficient domain decomposition schemes for the simulation of rarefied gas flows close to the continuum limit. Moreover, we present some basic ideas for the derivation of kinetic induced numerical schemes for macroscopic equations, namely kinetic schemes for general conservation laws as well as Lattice—Boltzmann methods for the incompressible Navier—Stokes equations.