622 RWTH Publication No: 974382        2023       
TITLE Numerical schemes for coupled systems of nonconservative hyperbolic equations
AUTHORS Niklas Kolbe, Michael Herty, Siegfried Müller
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.
KEYWORDS nonconservative products; relaxation system; finite volume method; hyperbolic systems; coupling conditons; Riemann solvers