A well-balanced element-free Galerkin method for the nonlinear shallow water equations

作者：Yuan, Xu-hua^*

来源：Applied Mathematics and Computation, 2018, 331: 46-53.

DOI：10.1016/j.amc.2018.01.061

• Element-free Galerkin method
• Moving least square approximation
• Nonlinear shallow water equations
• High-order accuracy
• Well-balanced scheme

In this paper, we consider the nonlinear shallow water equations over variable bottom topography in one dimension and propose a well-balanced element-free Galerkin method for solving this system. The proposed scheme has the features of being high-order accurate for general solutions and exactly preserving the still-water stationary solution. The main ingredient to achieve the well-balanced property is to use a special decomposition to the source term and discretize the source term as the flux term. Numerical tests are presented to illustrate the accuracy and validity of the proposed scheme.

• 出版日期2018-8-15
• 单位延安大学