CWENO-type central-upwind schemes for multidimensional Saint-Venant system of shallow water equations

Simple central-upwind schemes based on central weighted essentially non-oscillatory reconstructions are proposed in this paper for computing the approximate solutions of one- and two-dimensional Saint-Venant system of shallow water equations with high-resolution. Since the nonuniform width of the different local Riemann fans is calculated more accurately, the central-upwind schemes enjoy a much smaller numerical viscosity and the staggering between two neighboring sets of grids is avoided. Since the central-upwind schemes are combined with fourth-order central weighted essentially non-oscillatory reconstructions, the hereafter called CWENO-type central-upwind schemes have non-oscillatory behavior. The numerical results show the desired accuracy and high-resolution of our methods.