A positivity-preserving zero-inertia model for flood simulation

Zero-Inertia Models (ZIMs), or Diffusion-Wave Models (DWMs), have been widely used in flood modelling in the last decade. In this work, an alternative formulation is proposed based on a new depth-positivity-preserving condition to solve the zero-inertia governing equation. The new condition does not use a flux limiter and is practical for flood simulations with wetting and drying over complex domain topographies. Two time stepping methods are considered and studied along with the proposed numerical model. The first one is based on the Courant-Friedrichs-Lewy (CFL) condition, which is widely used to control the time step for the explicit shallow water equation solvers; the second one is the adaptive time stepping (ATS) reported by Hunter et al. [1], which was specifically designed for a DWM. Numerical results and root-mean-square-error (RMSE) analysis show that the new model is able to provide stable and accurate solutions without the necessity for a flux limiter. Computational efficiency is significantly improved under the CFL constraint.