A general, non-iterative Riemann solver for Godunov's method☆
A general, non-iterative Riemann solver for Godunov's method☆
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DOI：
10.1016/0021-9991(85)90064-6
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发表时间：
1985-10
影响因子：
4.1
通讯作者：
J. Dukowicz
中科院分区：
文献类型：
--
作者：
J. Dukowicz
Godunov的方法的特点是使用黎曼问题解决方案来解决细胞之间界面的不连续。该方法的主要缺点是精确求解（非线性）黎曼问题困难且成本高，特别是对于具有复杂状态方程的材料。本文描述了一种简化的非迭代近似黎曼解算器，该解算器仅具有两个与材料有关的参数。对于给定的材料，这些参数是局部声速和在强冲击极限下与激波密度比直接相关的参数。这些参数可以方便地从各种材料的激波Hugoniot实验数据的线性拟合中得到。近似黎曼解算器保留了基本的二次非线性，使其能够处理从弱声波到强冲击的整个范围的情况。
Godunov's method is characterized by the use of a Riemann problem solution to resolve discontinuities at the interface between cells. The major drawback of this method is the difficulty and the high cost of solving the (nonlinear) Riemann problem exactly, especially for materials with complex equations of state. This paper describes a simplified and noniterative approximate Riemann solver which is characterized by only two material-dependent parameters. For a given material, these parameters are the local speed of sound and a parameter which is directly related to the shock density ratio in the limit of strong shocks. These parameters are conveniently obtained from a linear fit to the experimental data for the shock Hugoniot in various materials. The approximate Riemann solver retains the essential quadratic nonlinearity which enables it to deal with the whole range of cases from weak sound waves to strong shocks.