2023/11/06 by Kolbe, Niklas, Herty, Michael, Müller, Siegfried
#35L65 #35R02 #65M08 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2311.03581
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.