求解带源项的浅水波方程的高分辨率熵相容格式

High Resolution Entropy Consistent Scheme for Solving Shallow Water Wave Equations with Source Terms

摘要: 浅水波方程对湖泊、河流等波动问题的研究具有重要意义。源项是对底部地势的描述。带源项的浅水波方程可以归结为非线性的双曲守恒律问题。本文采用结构网格，构造了一种熵相容格式求解带源项的浅水波方程，并对熵守恒变量使用基于MUSCL格式的斜率限制器重构，构造具有2阶精度的熵相容格式。在数值实验中证明了该格式有效地避免了非物理现象的产生，并且可以准确地捕捉激波，具有良好的稳健性。

Abstract: Shallow water wave equation is of great significance to the study of wave problems in lakes and riv-ers. The source term is a description of the topography at the bottom. The shallow water wave equation with source term can be reduced to a nonlinear hyperbolic conservation law problem. In this paper, an entropy consistent scheme is constructed to solve the shallow water wave equation with the source term by using the structural grid. The entropy conservation variables are recon-structed by using a slope limiter which is based on the MUSCL scheme to construct an entropy con-sistent scheme with second-order accuracy. Numerical experiments show that the scheme can ef-fectively avoid the occurrence of non-physical phenomena, and can accurately capture shock waves, which has good robustness.