In this paper, a meshfree numerical scheme, which is based on the reproducing kernel particle method (RKPM), is proposed to solve the shallow water equations (SWEs). By applying the split coefficient matrix method on SWEs, RK approximation with upstream scheme can be employed for spatial discretization. Temporal discretization of SWEs is handled by the secondorder total-variation diminishing Runge-Kutta method. The merits of the present method are verified by performing three numerical experiments, which are problems related to open channel flow, oblique hydraulic jump and two-dimensional dam break. It is found that the proposed meshfree numerical scheme is able to efficiently model the shallow water problems with high convergence rate and accuracy. When non-uniform discretization is used in conjunction with the proposed method, the order of approximation and accuracy can still be maintained.
Sun, Chien-Ting; Kwok, On-Lei Annie; Guan, Pai-Chen; and Shih, Wen-Kai
"USING REPRODUCING KERNEL PARTICLE METHOD FOR SHALLOW WATER PROBLEMS,"
Journal of Marine Science and Technology: Vol. 26:
3, Article 14.
DOI: DOI: 10.6119/JMST.201806_26(3).0014
Available at: https://jmstt.ntou.edu.tw/journal/vol26/iss3/14