High-order well-balanced central WENO scheme for pre-balanced shallow water equations

•A well-balanced central WENO scheme is designed for prebalanced shallow water equations.•The scheme can preserve the exact conservation property.•The scheme achieves high-order accuracy.•The scheme maintains essentially non-oscillatory property near discontinuities and keeps sharp shock transition.

In this paper, we are concerned with numerically solving shallow water equations with a source term. The equations admit steady state solutions in which the non-zero flux gradient is exactly balanced by the source term. It is difficult for numerical schemes to preserve the delicate balance between the flux gradient and the source term.By virtue of a modified governing equations as well as an original reconstruction procedure for the Runge–Kutta flux, we present a central weighted essentially non-oscillatory scheme. Extensive test cases are carried out to demonstrate the performance of the resulting scheme: exact conservation property, high-order accuracy and good resolution near discontinuities.