A meshless artificial viscosity method for wet-dry moving interfaces problems of shallow water flow. (15th September 2021) - Zhang, Ting; Zhan, Chang-Xun; Wang, Hai-Wei; Lin, Chuan; Guo, Xiao-Mei
Abstract: In this paper, an improved meshless artificial viscosity (AV) method is proposed and combined with the local radial point interpolation method (LRPIM) and the MacCormack method to establish a newly-developed meshless numerical model, which can efficiently and accurately solve wet-dry moving interfaces problems of shallow water flow. As an important model describing shallow water flow, the two-dimensional (2D) shallow water equations (SWEs) are a hyperbolic system of 1st-order nonlinear partial differential equations which have a characteristic of strong gradient. The LRPIM and MacCormack method are adopted to discretize the 2D SWEs spatially and temporally, respectively. Meanwhile, the method of selecting the different shape of support domain in the LRPIM is employed for properly cooperating with the MacCormack method to accurately capture the direction of wave propagation. For eliminating the non-physical oscillation at the discontinuity of shallow water flow, the improved meshless AV form is first presented. Four challenging numerical examples were selected to verify the proposed model by comparing with the other solutions and experimental observations. The results indicate that the proposed method with improved meshless AV can accurately capture the shock waves and efficiently simulate the wet-dry front changes. Highlights: A new form of artificial viscosity (AV) developed based on the meshless method is proposed to minimize the non-physical oscillation at the shock wave. Introduce the AV to improve the numerical algorithm that can easily and efficiently solve the wet-dry moving interfaces problems on complex terrain. In order to accurately capture the wave propagation direction, the selection method of the support region in the local radial point interpolation method (LRPIM) is improved to cooperate with the MacCormack method. Combining the meshless AV method, the LRPIM and the MacCormack method can accurately and stably simulate shallow water flow with wet-dry moving interfaces and complex bottom slope.