Numerical solution of one-dimensional shallow water equations by semi-discrete central-upwind scheme

A high-resolution method for solving one-dimensional shallow water equations is presented by combing the semi-discrete central-upwind numerical flux with the third-order weighted essentially non-oscillatory(WENO) reconstruction.The discretization of bottom topography assures well-balanced approximation and the discretization of friction slop is simple and effective.The third-order strong stability preserving Runge-Kutta method is used for time discretization.Validity of several typical samples show that this method is effective and has high precision for shock waves.