High order numerical methods for networks of hyperbolic conservation laws coupled with ODEs and lumped parameter models

JOURNAL OF COMPUTATIONAL PHYSICS

卷:327

Article

Borsche, Raul¹  Kall, Jochen¹ 

[1] TU Kaiserslautern, Erwin Schrodinger Str,Bldg 48, D-67663 Kaiserslautern, Germany

关键词: Networks;    Hyperbolic conservation laws;    Generalized Riemann problem;    Coupling conditions;    ODE;    ADER;    Lumped parameter models;   

DOI  :  10.1016/j.jcp.2016.10.003

来源: Elsevier

【 摘 要 】

In this paper we construct high order finite volume schemes on networks of hyperbolic conservation laws with coupling conditions involving ODEs. We consider two generalized Riemann solvers at the junction, one of Toro-Castro type and a solver of Harten, Enquist, Osher, Chakravarthy type. The ODE is treated with a Taylor method or an explicit Runge-Kutta scheme, respectively. Both resulting high order methods conserve quantities exactly if the conservation is part of the coupling conditions. Furthermore we present a technique to incorporate lumped parameter models, which arise from simplifying parts of a network. The high order convergence and the robust capturing of shocks are investigated numerically in several test cases. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free