A new well-balanced non-oscillatory central scheme for the shallow water equations on rectangular meshes

Autores UPV
Año
Revista JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

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 Runge¿Kutta 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.