Riemann Solvers with Runge–Kutta Discontinuous Galerkin Schemes for the 1D Shallow Water Equations
Riemann Solvers with Runge–Kutta Discontinuous Galerkin Schemes for the 1D Shallow Water Equations
复制标题
一维浅水方程的带有龙格-库塔不连续伽辽金格式的黎曼求解器
DOI：
10.1061/(asce)0733-9429(2008)134:2(243
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发表时间：
2008
影响因子：
2.4
通讯作者：
R. Mosé
中科院分区：
文献类型：
--
作者：
G. Kesserwani;R. Ghostine;J. Vazquez;A. Ghenaim;R. Mosé
本调查的频谱打开一些杰出的黎曼解算器（或所谓的解算器）的评价，浅水方程，当采用高阶龙格-库塔间断伽辽金（RKDG）方法。基于以下假设：数值方法的精度阶数越高，黎曼解算器的选择就越不重要;实际文献中使用Lax-Friedrich解算器，因为它简单且成本较低，而许多其他解算器也可以应用，如Goddom，Roe，Osher，HLL，HLLC和HLLE。在实际应用中，流动可以由几何形状控制，并且必须考虑摩擦效应。为了得到一个合适的高阶RKDG方法的黎曼解函数的选择，进行了一维数值研究。用这一系列求解器与高阶RKDG方法相结合计算了三个传统的水力学问题。最后，对这两种求解器的性能进行了比较。
The spectrum of this survey turns on the evaluation of some eminent Riemann solvers (or the so-called solver), for the shallow water equations, when employed with high-order Runge–Kutta discontinuous Galerkin (RKDG) methods. Based on the assumption that: The higher is the accuracy order of a numerical method, the less crucial is the choice of Riemann solver; actual literature rather use the Lax-Friedrich solver as it is easy and less costly, whereas many others could be also applied such as the Godunov, Roe, Osher, HLL, HLLC, and HLLE. In practical applications, the flow can be dominated by geometry, and friction effects have to be taken into consideration. With the intention of obtaining a suitable choice of the Riemann solver function for high-order RKDG methods, a one-dimensional numerical investigation was performed. Three traditional hydraulic problems were computed by this collection of solvers cooperated with high-order RKDG methods. A comparison of the performance of the solvers was carried out di...