Numerical hydrodynamic modeling of free surface flow by solving shallow water equations

Abstract

A numerical model for solving the conservative form of the two-dimensional shallow water equations (SWEs) has been developed to simulate the hydrodynamics of surface water bodies and the flooding of adjacent land during extreme hydrological events. The solution is obtained using an Arakawa C-grid structure and an explicit finite difference technique with up-winding for advective terms. The model is verified by comparing its results with reported analytical and numerical solutions for standard one-dimensional and two-dimensional flow problems. It is demonstrated that the developed model accurately simulates surface water hydrodynamics for various scenarios involving hydrodynamic changes with varying shock strengths. The developed algorithm is shown to be superior to the Lax-Friedrichs and Lax-Wendroff schemes in terms of accuracy and stability. Moreover, the conservative form of the SWE is found to be better than the non-conservative form in handling discontinuities and sudden hydrodynamic changes.