Application of an unstructured finite volume method to the shallow water equations with porosity for urban flood modelling

Abstract

We present a finite volume model for the simulation of floods in urban areas. The model consists of the two-dimensional shallow water equations with variable horizontal porosity which is introduced in order to reflect the effects of obstructions. An extra porosity source term appears in the momentum equations. The main advantage of this model is the significant reduction of the computational cost while preserving an acceptable level of accuracy. The finite volume method uses a modified Roe’s scheme involving the sign of the Jacobian matrix in the system for the discretization of gradient fluxes. The performance of the numerical model is demonstrated by comparing the results obtained using the proposed method to laboratory experiments for a flow problem over an array of obstacles.