A finite volume approach for shallow water flow accounting for high‐resolution bathymetry and roughness data

Abstract

[1] This study presents a finite volume hydrodynamic model for shallow water flow that computes on a coarse grid, but accounts for high-resolution bathymetry and roughness variations on a subgrid. The detailed information can be incorporated by using the assumption of a uniform flow direction and a uniform friction slope within a part of a coarse-grid cell. It is shown in two examples that the results of coarse-grid simulations become as good as high-resolution results, but at much lower computational cost.Citation: Volp, N. D., B. C. van Prooijen, and G. S. Stelling (2013), A finite volume approach for shallow water flow accounting for high-resolution bathymetry and roughness data, Water Resour. Res., 49,[4126][4127][4128][4129][4130][4131][4132][4133][4134][4135]

A subgrid based approach for morphodynamic modelling

“…In the classic approach for morphodynamic models all variables and operators of the hydrodynamic and morphodynamic simulations are defined on a single computational grid. In contrast, the method presented here solves the hydrodynamic equations on a coarse hydrodynamic grid, while using high resolution information defined on the subgrid [10]. In addition to that, the morphodynamic computations are carried out on the bed grid.…”

“…The hydrodynamic part is modelled with a subgrid based, two dimensional, depth-averaged model [10]. This subgrid approach is relatively new and as it forms an essential part of this paper, we will discuss the key aspects of the model.…”

“…For the strictly momentum conserving formulation of the advection, subgrid effects are also taken into account. For a more thorough explanation we refer to the original manuscripts [8,10].…”

“…This method has been shown to be accurate, computationally efficient and elegantly deals with flooding and drying. This method was combined with a subgrid based approach for friction and strict momentum conservation [10]. Thanks to this approach we can now take advantage of high resolution bathymetry data in numerical simulations.…”

Upscaling the shallow water model with a novel roughness formulation

“…The main advantage of using roughness formulations instead of more sophisticated upscaling approaches for shallow water models, e.g. Guinot and Soares-Frazão (2006), Volp et al (2013), Hughes et al (2011), McMillan andBrasington (2007), Liang et al (2007), is their easy implementation into existing models without the need to modifiy the governing equations or numerical methods.…”