Author(s): D. Satyaprasad; S. Sundar; Somendra Nath Kuiry

Linked Author(s):

Keywords: Shallow water equation; Weighted least square; Cloud of points; HLL Riemann solver

Abstract: The numerical methods are used to solve the non-linear one-dimensional (1D) shallow water equations for simulating flows in open channels. The shock-capturing HLL approximate Riemann solver is popular for computing the convective fluxes through the interfaces of a computational cell. In this study, a meshless numerical method on irregularly distributed points over the physical domain is proposed to solve the 1D shallow water equations. A weighted least square form of the HLL Riemann solver is formulated for computing the convective flux. The conservative variables are also reconstructed using the weighted least square approximation. The performance of this new method is evaluated by simulating a variety of analytical test cases on the dam-break flow over a rectangular channel and transcritical flow over a bump. Comparisons of the computed results with the analytic solutions show that the proposed method is accurate and robust. The proposed meshless method can be extended to two-dimensional domain for simulating realistic open channel flows without investing much time on grid generation.

DOI: https://doi.org/10.3850/IAHR-39WC252171192022812

Year: 2022