A well-balanced and positivity-preserving numerical model for overland flow under vegetation effects

Abstract

In this study, we used the depth-averaged shallow water equations for modeling flows through vegetation field. The vegetation effects on flow are modeled using Morison’s equation taking into account drag and inertia forces which depend on both vegetation and flow properties. We compute and compare different formulations for the stem drag coefficient based on the Froude number or the vegetation volume fraction. Vegetation-induced turbulence is taken into account by adding diffusion terms in the momentum equations. The resulting system of equations is solved using a well-balanced and positivity preserving finite volume method to guarantee the balance between the flux and bed topography source terms, and the positivity of the computed water depth. In our approach, the drag force and bed friction source terms are combined into a unified form. We propose to discretize the obtained term using an implicit temporal method where an analytical technique is used. Special discretization techniques are used for the inertia force and turbulent diffusion terms. Numerical simulations are performed to validate the accuracy of the proposed numerical model. We investigate and compare different formulations for the stem drag coefficient in the vegetation model. Our results confirm the capability of the proposed numerical model for simulating overland flows under vegetation effects.