Modelling of shallow water equations by

This paper investigates dam-break flow problem with the aim to capture fluid flow in transition to solve two-dimensional shallow-water equations (SWE). Applying compact MacCormack type schemes with high accuracy approach, governing equations are solved using one-sided implicit stencil with five-point explicit boundary stencil. Spatial derivatives are obtained numerically by solving a bi-diagonal matrix along the grid line instead of three-diagonal matrix inversion. The model results are validated for dam-break flow problem and compared with the Stoker solution for one-dimensional case and experimental results of two-dimensional case. Considering various parameters for one-dimensional flow problem with respect to water depth and velocity, L1 errors are computed for wet bed case using second order and fourth order MacCormack schemes. The comparison of L1 errors with respect to the grid size and dissipative effect also analyzed for both the schemes. The model results are found to be in good agreement with the analytical solution and experimental results for dry and wet bed conditions. The present model proved to be more versatile even for the coarser grids and can provide a useful framework for spatial discretization.