TY - JOUR T1 - Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes AU - Besse , Christophe AU - Borghol , Saja AU - Goudon , Thierry AU - Lacroix-Violet , Ingrid AU - Dudon , Jean-Paul JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 519 EP - 561 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.10-m1041 UR - https://global-sci.org/intro/article_detail/aamm/181.html KW - Hydrodynamic regimes, Knudsen layer, finite volume scheme, initial-boundary value problems for conservation laws, Evaporation-condensation problem. AB -

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.