Numerical schemes for coupled systems of nonconservative hyperbolic equations

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-conser...

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Published in:arXiv.org 2023-11
Main Authors: Kolbe, Niklas, Herty, Michael, Müller, Siegfried
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Language:English
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Blood flow
Hyperbolic systems
Riemann solver
Stability analysis
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Müller, Siegfried
description 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.
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subjects Blood flow
Hyperbolic systems
Riemann solver
Stability analysis
title Numerical schemes for coupled systems of nonconservative hyperbolic equations
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