A spectral approach to interface layers on networks for the linearized kinetic BGK equation with hyperbolic scaling

Kinetic and Related Models, vol. 24, pp. 51–74

Abstract

We consider in this paper a velocity discretized version of the full linear kinetic BGK model and the corresponding limit for small Knudsen number, the linearized Euler or acoustic system. Considering these equations on networks, coupling conditions for the macroscopic equations are derived from the kinetic conditions via an asymptotic analysis near the nodes of the network. Here, a degeneracy in the limit equations requires not only the investigation of kinetic layers, but also the discussion of viscous layers. Using the kinetic coupling conditions at the junction and coupling kinetic and viscous layers to the outer problems on the edges, one obtains coupled kinetic half-space problems at each node. A spectral method is developed to solve these coupled kinetic half-space problems. This allows us to obtain a detailed picture of the various interface layers near the nodes and to determine the relevant coefficients in the kinetic derived coupling conditions for the macroscopic equations. Numerical results show the accuracy and efficiency of the approach.

Authors 4

1. Raul Borsche

   University of Kaiserslautern · Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

   Affiliation as printed

   RPTU Kaiserslautern , Department of Mathematics , Germany

2. Tobias Damm

   University of Kaiserslautern · Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

   Affiliation as printed

   RPTU Kaiserslautern, Department of Mathematics, Germany

3. Axel Klar corresponding

   University of Kaiserslautern · Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

   Affiliation as printed

   RPTU Kaiserslautern, Department of Mathematics, Germany

4. Yizhou Zhou Aachen Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen, Department of Mathematics, Germany