LetterA second-order accurate fluid-in-cell (FLIC) method for the 2D shallow water equations with topography

•The fluid-in-cell (FLIC) method is applied for the numerical solution of the non-linear shallow water (NLSW) equations with non-trivial topography.•The resulting scheme is shock capturing and well-balanced for flows over complex bathymetry.•A straightforward extension of the FLIC method to second-order accuracy in space is proposed.•The resulting scheme is relatively simple, robust, stable, and efficient.

The fluid-in-cell (FLIC) approach of Gentry et al. (1966) is extended to second-order accuracy in space and applied to solve the 2D shallow water equations with topography. The FLIC method can be interpreted in a finite volume sense, it therefore conserves both water mass and momentum. Like the original FLIC method the second-order FLIC method presented here is able to handle wetting-drying fronts without any special treatment. Moreover, the resulting method is shock capturing and well-balanced, satisfying both the C- and extended C-properties exactly.