非线性浅水波方程的保持平衡的中心间断伽辽金法
Well-Balanced Central Discontinuous Galerkin Methods for the Nonlinear Shallow Water Equations
DOI: 10.12677/AAM.2017.64071, PDF,    科研立项经费支持
作者: 陈爱敏：重庆大学城市科技学院，重庆；李茂军：重庆大学数学与统计学院，重庆
关键词: 中心间断伽辽金法；非线性浅水波方程；保持平衡性；Central Discontinuous Galerkin Method； Nonlinear Shallow Water Equations； Well-Balanced Property
摘要: 提出了一个求解非线性浅水波方程的高阶的保持平衡的中心间断伽辽金法，并证明了该方法的保持平衡性。与传统的中心间断伽辽金法相比，该方法能够精确地保持非线性浅水波方程的静水稳定解，因而消除了数值震荡。数值算例验证了方法的精度和可靠性。
Abstract: A high order well-balanced central discontinuous Galerkin method is developed for solving the nonlinear shallow water equations and the well-balanced property is proved. Compared to the standard central discontinuous Galerkin method, the present method can maintain the still water stationary solutions of the nonlinear shallow water equations, and thus remove the numerical os-cillations. Numerical examples are presented to show the accuracy and reliability of the proposed method.
文章引用：陈爱敏, 李茂军. 非线性浅水波方程的保持平衡的中心间断伽辽金法[J]. 应用数学进展, 2017, 6(4): 611-618. https://doi.org/10.12677/AAM.2017.64071

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