Numerical Schemes for Coupled Systems of Nonconservative Hyperbolic Equations

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-09-11 DOI:10.1137/23m1615176

Niklas Kolbe, Michael Herty, Siegfried Müller

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引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2143-2171, October 2024.
Abstract. The coupling of nonconservative hyperbolic systems at a static interface has been a delicate issue as common approaches rely on the Lax-curves of the systems, which are not always available. To address this a new linear relaxation system 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 in the uncoupled setting. It is shown that the path-conservative Lax–Friedrichs scheme arises from a discrete limit of an implicit-explicit scheme for the relaxation system. Employing the relaxation approach, a novel technique to couple two nonconservative systems under a large class of coupling conditions is established. A particular 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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非守恒双曲方程耦合系统的数值方案

SIAM 数值分析期刊》第 62 卷第 5 期第 2143-2171 页，2024 年 10 月。摘要。非守恒双曲系统在静态界面上的耦合一直是一个棘手的问题，因为常见的方法依赖于系统的拉克斯曲线，而拉克斯曲线并不总是可用的。为了解决这个问题，我们引入了一个新的线性松弛系统，其中一个非局部源项解释了原始系统的非保守乘积。通过渐近分析，研究了非耦合情况下的松弛极限及其稳定性。结果表明，路径保守的 Lax-Friedrichs 方案来自松弛系统的隐式-显式方案的离散极限。利用松弛方法，建立了一种在大量耦合条件下耦合两个非保守系统的新技术。介绍了一种基于保守基尔霍夫条件的特殊耦合策略，并提供了相应的黎曼求解器。从路径守恒的角度推导并研究了耦合非守恒产品的完全离散方案。介绍了将该方法应用于血管血流耦合模型的数值实验。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.