Studying an efficient second order accurate scheme for solving two-dimensional shallow flow model

Abstract

   The aim of this paper is to present an efficient high order accuracy numerical scheme for conservation law on structure grids. The Monotone Upstream Centered Scheme for Conservation Laws (MUSCL) procedure renders the model to preserve the well-balanced property and achieve high accuracy and efficiency for solving nonlinear two dimensional shallow water equations (2D-SWE). The effectiveness and robustness of the above scheme is shown by comparison the solution obtained by aforementioned scheme with those obtained by first order one or 1D result through three tests: 2D Riemann problem; circular dam break and run-up wave over conical island. Then, it is applied to simulate dam break flow over adverse slope which has experiment data. The Nash values are approximated 90%.