Non-negative depth reconstruction for a two-dimensional partial inertial inundation model

This paper proposes a non-negative depth reconstruction method for improving the numerical performance of a partial inertial model (PIM) for applications involving steep-slope and low-friction conditions. The PIM solves the continuity equation of two-dimensional (2D) shallow water equations (SWEs) with the interface fluxes evaluated by a simplified momentum equation that partially restores the inertial terms. In applying the PIM to flood simulations, a practical challenge is to represent complex topography and to track the moving wet–dry interface without resulting in negative water depths. Another challenge is to avoid the numerical issue caused by the lack of physical diffusive terms when it is applied to low-friction cases. To cope with these difficulties, the PIM is improved by introducing a non-negative depth reconstruction method, featuring two different ways for calculating the interface fluxes. The performance of the improved PIMs is investigated through applications to several theoretical and practical benchmark test cases. The comparison of the numerical results against analytical solutions or predictions from the original PIM and a full 2D finite-volume hydrodynamic model shows that the proposed reconstruction method can avoid non-negative water depth predictions, and improve the numerical performance of the original PIM when applied to steep-slope and low-friction conditions.