一种基于熵守恒格式的浅水波方程的熵稳定格式
An Entropy Stable Scheme for Shallow Water Equations Based on Entropy Conservative Scheme
DOI: 10.12677/AAM.2022.118596, PDF,    国家自然科学基金支持
作者: 张志壮, 周翔宇, 高金梅, 李 刚*：青岛大学数学与统计学院，山东 青岛
关键词: 熵守恒；熵稳定；熵不等式；浅水波方程；Burgers方程；Entropy Conservation； Entropy Stable； Entropy Inequality； Shallow Water Equation； Burgers Equation
摘要: 在本文中，我们针对流体力学中的Burgers方程以及浅水波方程，构造了高精度熵稳定格式。我们首先以熵守恒数值通量为基础，通过添加适当的数值熵粘性的方式，构造了熵稳定数值通量，实现了熵不等式，最终建立了熵稳定数值格式。广泛的数值结果均验证了本格式保持高分辨率和无伪振荡的良好特性。我们相信该格式在流体力学领域会有着相当广泛的应用前景。
Abstract: In this article, we aim at building high-order entropy stable scheme for the Burgers equation and shallow water equation in fluid mechanics. Based on the entropy conservative numerical flux, we first construct the entropy stable numerical flux by adding appropriate numerical entropy viscosity, then achieve the entropy inequality, and achieve the entropy stable finite difference scheme even-tually. Extensive numerical results illustrate that the resulting scheme keeps high resolution and is free of spurious oscillations. We believe that this scheme will have a wide application prospect in the field of fluid mechanics.
文章引用：张志壮, 周翔宇, 高金梅, 李刚. 一种基于熵守恒格式的浅水波方程的熵稳定格式[J]. 应用数学进展, 2022, 11(8): 5648-5659. https://doi.org/10.12677/AAM.2022.118596

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