A Well-Balanced Weighted Compact Nonlinear Scheme for Pre-Balanced Shallow Water Equations

Abstract

It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors. In this paper, a well-balanced weighted compact nonlinear scheme (WCNS) is proposed for shallow water equations in pre-balanced forms. The scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection term. Some numerical examples in one- and two-dimensions are also presented to demonstrate the well-balanced property, high order accuracy and good shock capturing capability of the proposed scheme.