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

Xu-hua Yuan

Applied Mathematics and Computation, 2018, vol. 331, issue C, 46-53

Abstract: 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.

Keywords: Element-free Galerkin method; Moving least square approximation; Nonlinear shallow water equations; High-order accuracy; Well-balanced scheme (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:331:y:2018:i:c:p:46-53

DOI: 10.1016/j.amc.2018.01.061

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