Abstract
This paper is concerned with the development of high-order well-balanced central schemes to solve the shallow water equations in two spatial dimensions. A RungeKutta scheme is applied for time discretization. A Gaussian quadrature rule is used to evaluate time integrals and a three-degree polynomial which calculates point-values or flux values.
A new procedure has been defined to evaluate the flux integrals and to approach the 2D
source term integrals in order to verify the exact C-property, using the water surface elevation instead of the water depth as a variable. Numerical experiments have confirmed the high-resolution properties of our numerical scheme in 2D test problems.
