INTERFACE LAYERS AND COUPLING CONDITIONS ON NETWORKS FOR LINEARIZED KINETIC BGK EQUATION

We consider a linearized kinetic BGK equation and the associated acoustic system on a network. 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 fixpoint problem involving the solutions of kinetic half-space problems. This work extends the procedure developed in [15], where coupling conditions for a simplified BGK model have been derived. Numerical comparisons between different coupling conditions confirm the accuracy of the proposed approximation.