Flux closures and source term models for shallow water models with depth-dependent integral porosity

Abstract

Abstract A two-dimensional shallow water model with depth-dependent porosity is presented. The purpose is the coarse grid simulation of shallow flows over complex topographies and geometries. Two flux closures are examined: the Integral Porosity (IP) and Dual Integral Porosity (DIP) closures. Energy losses are described using a subgrid scale model that accounts for bottom and wall friction, transient momentum dissipation and energy losses induced by obstacle submersion. A complete wave propagation property analysis is provided for the IP and DIP closures, yielding more accurate numerical stability constraints than published previously. Five computational examples are presented, including transients in compound and meandering channels, urban dambreak problems with building submersion and runoff over variable microtopography. The ability of the model to deal with subgrid-scale features is confirmed. The DIP flux is shown to be superior to the IP closure. The transient dissipation term is essential in reproducing the effect of obstacles and microtopography. Distinguishing between the building wall- and building roof-induced friction is seen to be essential. The model is validated successfully against a scale model experimental dataset for the submersion of a coastal urban area by a tsunami wave.