基于移动网格的HLL格式求解浅水波方程
Solving Shallow Water Wave Equation with HLL Scheme Based on Moving Grid
摘要: 本文提出了一种基于移动网格的HLL格式来求解浅水波方程。移动网格法基于迭代过程，在每次迭代中利用等分布原理对网格进行重新分布，然后利用保守插值公式对其数值解进行更新，该方法的主要思想是保持每个重新分布步骤下的数值解的质量守恒。HLL格式是具有良好鲁棒性的数值通量，可消除红斑现象。时间方向采用三阶强稳定龙格–库塔方法进行推进，通过数值结果的对比发现基于移动网格的HLL格式具有分辨率高的良好特性。
Abstract: In this paper, an HLL scheme based on moving grid is proposed to solve shallow water wave equations. Based on the iterative process, the moving mesh method redistributes the mesh in each iteration by using the equal distribution principle, and then updates its numerical solution by using the conservative interpolation formula, the main idea of this method is to preserve the mass conservation of the numerical solution under each redistribution step. HLL scheme is a numerical flux with good robustness and can eliminate the carbuncle. The time direction is advanced by the third- order strongly stable Runge-Kutta method, and the comparison of numerical results shows that the HLL scheme based on the moving grid has good resolution.
文章引用：李霄. 基于移动网格的HLL格式求解浅水波方程[J]. 应用数学进展, 2021, 10(10): 3317-3324. https://doi.org/10.12677/AAM.2021.1010348

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