Domain Decomposition for Kinetic Problems with Nonequilibrium States
Axel Klar · 1994
A nonequilibrium situation governed by kinetic equations with different Knudsen numbers in different subdomains is discussed. We consider a domain decomposition problem for Boltzmann- and Euler equations, establish the correct coupling conditions and prove the validity of the obtained coupled solution. Moreover numerical examples comparing different types of coupling conditions are presented. 1 Introduction The Boltzmann equation and the more classical gas dynamics equations (such as Euler or Navier-Stokes equations) are used to model hypersonic gas flows. Numerical simulations of such flows are useful for example in the design of space vehicles, in particular in understanding the behavior of the early phases of reentry flights. Such flows are usually far from any kind of local equilibrium states. This means that variants of the Boltzmann equation have to be used as first principle equations instead of the Euler or Navier-Stokes equations. However, when the mean free path of molecules...