A Proposed Implicit Friction Source Term Treatment for Simulating Overland Flow

Abstract

The fully 2D dynamic shallow water equations have been widely applied for numerical simulation of overland flow in the recent years. However, most of the existing friction term discretisation schemes do not recover the correct asymptotic flow behaviour as water depths becomes small. In this model, the shallow water equations were discretized by the framework of the Godunov-type finite volume scheme. The hydrostatic reconstruction is applied to reconstruct non-negative water depths at wet- dry interfaces. Numerical fluxes are computed with a HLLC solver. The novel aspects of the model include the slope source term treatment. Specific treatment of friction source terms has been proposed to discretize the friction terms to recover the correct asymptotic behaviour of SWEs when the water depth becomes small. The accuracy and robustness of the proposed model are verified by comparing with analytical solutions. The results demonstrate that the proposed method treating friction source term is a relatively more accurate, efficient, straightforward and universal one for evaluating overland flow problems.