A consistent finite difference local inertial model for shallow water simulation

Hydrological-hydraulic modeling is a core technique in assessing surface water dynamics of rivers, lakes, and floodplains. The local inertial model (LIM) as a physically simplified model of the shallow water equations is essential for efficient numerical simulator of surface water dynamics. In this paper, we point out that the conventional semi-implicit finite difference scheme for the friction slope terms, despite being convenient, is not consistent in the sense that it may lead to incorrect numerical solutions if the temporal resolution is not high. We propose an alternative discretization to resolve this issue, which is more accurate and stable, and has comparable computational efficiency. The new numerical scheme is implemented into a modern hydrological-hydraulic model, demonstrating reasonable accuracy. The new scheme is also compared with a recently-proposed implicit scheme, demonstrating comparable theoretical and computational performances. The results indicate that the proposed scheme potentially serves as a new central core for numerical simulation with the LIM.