Author(s): Longxiang Li, Qinghe Zhang
Linked Author(s): Longxiang Li
Keywords: Shallow water equations, nodal discontinuous Galerkin method, quadrilateral elements, computational efficiency
Abstract: The discontinuous Galerkin methods are very attractive to shallow water models nowadays, as they can give more accurate results and achieve high parallel efficiency. However, recent researches reported that the discontinuous Galerkin methods on the unstructured triangle meshes suffer from being computationally expensive when compared with those traditional numerical methods. Therefore, a nodal discontinuous Galerkin model with quadrilateral meshes is proposed for shallow water equations in this study. The arbitrary quadrilateral elements along with the quadrature-free approach are introduced to improve the computational efficiency of nodal discontinuous Galerkin methods. Some numerical methods are also implemented in the model, such as the wetting and drying treatment, the maintaining of the well-balanced properties, and the positivity preserving of water depth. The developed model is verified with the oscillatory flow in the parabolic bowl problem. It is shown that the model with quadrilateral meshes is approximately 1. 21 to 1. 62 times more efficient, and the numerical error is 1. 11 to 1. 72 times smaller when comparing with the triangle meshes
Year: 2017