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

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. This work was partially funded by the "Programa de Apoyo a la Investigacion y Desarrollo" (PAID-06-10) and (PAID-05-12) of the Universidad Politecnica de Valencia. Angel Balaguer-Beser thanks the support of the Spanish Ministry of Education and Science in the framework of the Projects CGL2009-14220-C02-01 and CGL2010-19591. The authors express their gratitude to the anonymous reviewers for their helpful comments. Capilla Romá, MT.; Balaguer Beser, ÁA. (2013). A new well-balanced non-oscillatory central scheme for the shallow water equations on rectangular meshes. Journal of Computational and Applied Mathematics. 252:62-74. https://doi.org/10.1016/j.cam.2013.01.014