高阶数值方法用于耦合ODEs和 lumped参数模型的守恒律网络
High order numerical methods for networks of hyperbolic conservation laws coupled with ODEs and lumped parameter models
AI总结：
本文提出高阶有限体积方案，用于求解耦合ODEs的守恒律网络，采用两种广义Riemann求解器并探讨 lumped参数模型的整合方法，通过数值测试验证高阶收敛性和激波捕捉能力。
摘要：
本文构造了用于耦合ODEs的守恒律网络的高阶有限体积方案。我们考虑两种广义Riemann求解器，一种为Toro-Castro型，另一种为Harten、Enquist、Osher、Chakravarthy型。ODE通过泰勒方法或显式龙格-库塔方案处理。若守恒是耦合条件的一部分，则所得高阶方法能精确守恒量。此外，我们提出一种整合lumped参数模型的技术，这些模型源于网络简化。通过多个测试案例数值研究高阶收敛性和稳健的激波捕捉能力。
英文摘要：
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 is investigated numerically in several test cases.
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