Mathematical approach for shock wave problem: a case study of hydrodynamic flow for two-dimensional dam-break problems

Abstract

A numerical scheme of the two-dimensional shallow water equations for the dam break problem is presented. The methods are based on Godunov associated finite volume Roe’s Riemann solver. Numerical results are presented for one- and two-dimensional dam break problems without source term present. For analytical test problem in one-dimensional has been derived by stoker (1957). Thus, for two-dimensional test problem we tested the same case from stoker, but we just expand the test cases on the y-direction.