Well‐balanced nonstaggered central schemes based on hydrostatic reconstruction for the shallow water equations with Coriolis forces and topography

Abstract

The objective of this paper is to present a nonstaggered central scheme based on hydrostatic reconstruction (HR) for the shallow water equations with Coriolis forces and nonflat bottom topography. The discretization of the bed slope source term is based on the HR method to ensure the well‐balanced property for the stationary solution. We use the cell average of the discharge on the staggered cell to discretize the source term due to the effect of Coriolis forces. The positivity‐preserving property of the water depth is obtained by providing an appropriate CFL condition with the help of a “draining” time‐step technique. Finally, several two‐dimensional numerical results of classical problems of the system are presented to test these properties of the current scheme.