An improved meshless artificial viscosity technology combined with local radial point interpolation method for 2D shallow water equations. (1st December 2021)

• Record Type: Journal Article
• Authors: Zhang, Ting; Zhan, Chang-xun; Cai, Bin; Lin, Chuan; Guo, Xiao-Mei
• Is Part Of: Engineering analysis with boundary elements. Volume 133(2021)
• Page Start: 303
• Page End: 318
• Publication Date: 2021-12-01
• Subjects: Two-dimensional shallow water equations -- Local radial point interpolation method -- Artificial viscosity -- Shock wave -- Numerical simulation; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.09.002
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: The two-dimensional shallow water equations (SWEs) are a hyperbolic system of first-order nonlinear partial differential equations which have a characteristic of strong gradient. In this study, a newly-developed numerical model, based on local radial point interpolation method (LRPIM), is adopted to simulate discontinuity in shallow water flows. In order to accurately capture the information of wave propagation, the LRPIM is combined with the split-coefficient matrix (SCM) method to transform the SWEs into a characteristic form and the selection of the direction of local support domain is introduced into the LRPIM. An improved meshless artificial viscosity (MAV) technique is developed to minimize the non-physical oscillations near the discontinuities. Then, the LRPIM and the second-order Runge–Kutta method are adopted for spatial and temporal discretization of the SWEs, respectively. The feasibility and validity of the proposed numerical model are verified by the classical dam-break problem and the mixed flow pattern problem. The comparison of the obtained results with the analytical solution and other numerical results showed that the MAV method combined with LRPIM can accurately capture the shocks and has high accuracy in dealing with discontinuous flow by adding appropriate viscosity to the equations in the discontinuous region.