A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations
A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations
复制标题
DOI：
10.1007/s10915-016-0329-z
复制
发表时间：
2017-06
影响因子：
2.5
通讯作者：
Maojun Li;P. Guyenne;Fengyan Li;Liwei Xu
中科院分区：
文献类型：
--
作者：
Maojun Li;P. Guyenne;Fengyan Li;Liwei Xu
本文讨论了中心间断Galerkin方法在求解一维和二维非线性浅水波方程中的应用。一个可靠的数值方案，这些方程应保持静水稳定的解决方案，并保持水深的非负性。我们提出了一种高阶技术，通过在基格式中加入修正项，精确地平衡了静水静止情况下的通量梯度和源项，同时通过使用特殊的底部近似和保正限制器来确保水深的非负性。数值试验验证了所提格式的准确性和有效性。
In this paper, we consider the development of central discontinuous Galerkin methods for solving the nonlinear shallow water equations over variable bottom topography in one and two dimensions. A reliable numerical scheme for these equations should preserve still-water stationary solutions and maintain the non-negativity of the water depth. We propose a high-order technique which exactly balances the flux gradients and source terms in the still-water stationary case by adding correction terms to the base scheme, meanwhile ensures the non-negativity of the water depth by using special approximations to the bottom together with a positivity-preserving limiter. Numerical tests are presented to illustrate the accuracy and validity of the proposed schemes.