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.

[1]  P. Bates,et al.  A simple raster-based model for flood inundation simulation , 2000 .

[2]  P. Bates,et al.  Predicting floodplain inundation: raster‐based modelling versus the finite‐element approach , 2001 .

[3]  J. Cunge,et al.  Practical aspects of computational river hydraulics , 1980 .

[4]  Qiuhua Liang,et al.  Flood Inundation Modeling with an Adaptive Quadtree Grid Shallow Water Equation Solver , 2008 .

[5]  Qiuhua Liang,et al.  Flood Simulation Using a Well-Balanced Shallow Flow Model , 2010 .

[6]  A. Paquier,et al.  Modeling floods in a dense urban area using 2D shallow water equations , 2006 .

[7]  P. Bates,et al.  Benchmarking 2D hydraulic models for urban flooding , 2008 .

[8]  S. Lane,et al.  Urban fluvial flood modelling using a two‐dimensional diffusion‐wave treatment, part 1: mesh resolution effects , 2006 .

[9]  Paul D. Bates,et al.  An adaptive time step solution for raster-based storage cell modelling of floodplain inundation , 2005 .

[10]  P. Bates,et al.  Evaluation of 1D and 2D numerical models for predicting river flood inundation , 2002 .

[11]  P. Bates,et al.  A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling. , 2010 .

[12]  Qiuhua Liang,et al.  Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography , 2009 .

[13]  P. Bates,et al.  Two dimensional diffusion wave modelling of flood inundation using a simplified channel representation , 2004 .