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

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Keywords: Shallow water equations; Weighted least square; HLL Riemann solver; Meshless method; Dam-break flow

Abstract: The numerical methods are used to solve the nonlinear two-dimensional (2D) shallow water equations (SWEs) for simulating flows in open channels. In this regard, approximate Riemann solvers are popular for accurately predicting flows characterized by discontinuities and shocks that are common on highly variable real topography. In this study, a meshless numerical method on irregularly distributed points over the physical domain is proposed to solve the 2D SWEs. We solve the 2D SWEs using the HLL approximate Riemann solver within the framework of the weighted least square (WLS) meshless method. For this purpose, the computational domain is delineated by randomly positioned points. For each of these points, several neighbouring points are chosen to form a cloud of points, called satellites. These points are numerical grid points which are not necessarily to be connected with each other. The WLS form of the HLL approximate Riemann solver is then formulated for computing the convective fluxes. In the WLS method, the spatial derivatives are evaluated at every point using the values at its cloud of points and a weight function, which determines the influence of cloud of points on the considered point. The primitive variables are also reconstructed using the WLS approximation. The performance of this method is validated by simulating a 2D partial dam-break flow and hydrographs at different stations are presented. It is found that the proposed meshless method is robust and capable of accurately predicting dam-break flow.

DOI: https://doi.org/10.1007/978-981-97-6009-1_39

Year: 2022