Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Kinetic Layers and Coupling Conditions for Macroscopic Equations on Networks I
The Wave Equation
 SIAM journal on scientific computing 40 (2018), Nr.3, S.A1784A1808 ISSN: 01965204 ISSN: 10648275 ISSN: 08857474 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer ITWM () 
Abstract
We consider kinetic and associated macroscopic equations on networks. The general approach will be explained in this paper for a linear kinetic BGK model and the corresponding limit for a small Knudsen number, which is the wave equation. Coupling conditions for the macroscopic equations are derived from the kinetic conditions via an asymptotic analysis near the nodes of the network. This analysis leads to the consideration of a fixedpoint problem involving the coupled solutions of kinetic half space problems. A new approximate method for the solution of kinetic half space problems is derived and used for the determination of the coupling conditions. Numerical comparisons between the solutions of the macroscopic equation with different coupling conditions and the kinetic solution are presented for the case of tripod and more complicated networks.