Numerical schemes for coupled systems of nonconservative hyperbolic equations

arXiv (Cornell University)

Abstract

A new linear relaxation system for nonconservative hyperbolic systems is introduced, in which a nonlocal source term accounts for the nonconservative product of the original system. Using an asymptotic analysis the relaxation limit and its stability are investigated. It is shown that the path-conservative Lax-Friedrichs scheme arises from a discrete limit of an implicit-explicit scheme for the relaxation system. The relaxation approach is further employed to couple two nonconservative systems at a static interface. A coupling strategy motivated from conservative Kirchhoff conditions is introduced and a corresponding Riemann solver provided. A fully discrete scheme for coupled nonconservative products is derived and studied in terms of path-conservation. Numerical experiments applying the approach to a coupled model of vascular blood flow are presented.

Authors 3

1. Niklas Kolbe Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

2. Michaël Herty Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

3. Siegfried Müller Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen