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

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• 作者：Raul Borsche ; ^{borsche@mathematik.uni-kl.de" class="auth_mail" title="E-mail the corresponding author} ; Jochen Kall ^{kall@mathematik.uni-kl.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Networks ; Hyperbolic conservation laws ; Generalized Riemann problem ; Coupling conditions ; ODE ; ADER ; Lumped parameter models
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：327
• 期：Complete
• 页码：678-699
• 全文大小：1736 K

文摘

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.