A Well-balanced Finite Volume Scheme for Shallow Water Equations with Porosity: Application to Modelling Flow through Rigid Vegetation

Abstract

Strong interactions exist between flow dynamics and vegetation in open-channel. Depth-averaged shallow water equations can be used for such a study. However, explicit representation of vegetation can lead to very high resolution of the mesh since the vegetation is often modelled as vertical cylinders. Our work aims to study the ability of a single porosity-based shallow water model for these applications. More attention on flux and source terms discretizations are required in order to archive the well-balancing and shock capturing properties. We present a new Godunov-type finite volume scheme based on a simple-wave approximation and compare it with some other methods in the literature. A first application with experimental data was performed.

A Shallow Water Model for Water Flow on Vegetated Hillslope

“…In this paper, we introduce a model that extends the shallow water equations and takes into account the presence of vegetation on the soil surface. Such kind of extension is not new; we remind here some applications that use similar models: flow through rigid vegetation [32], flash food propagation in the urban area [18,19] and tsunami advance in the coastal region [48]. Our model results as an asymptotic limit of a space averaged version of the mass conservation equation and linear momentum balance equations [27,28].…”