Numerical simulation of flood due to dam-break flow using an implicit method

In this paper, the depth-averaged 2D shallow water equations in the non-conservative form are solved based on the 'Beam and Warming' implicit method by means of the finite difference method (FDM) having a second-order accurate on time and first-order accurate on space. Variations in each time step are calculated considering equations in both x and y directions. Due to solving an equation system in any row, a special algorithm, so-called block-tridiagonal system of equations algorithm, is utilised. To solve the aforementioned dam break equations, a computer programme based on the numerical equations has been developed. Finally, this programme has been validated against the analytical and numerical solutions of some problems obtained from the literature and comparison between this method and other solutions shows a good agreement.