A simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications
نویسنده
چکیده
This paper presents the decoupled hydrological discretization (DHD) scheme for solving the shallow water equations in hydrological applications involving surface runoff in rural and urban basins. The name of the scheme is motivated by the fact that the three equations which form the two-dimensional shallow water system are discretized independently from each other and thus, the numerical scheme is decoupled in a mathematical sense. Its main advantages compared to other classic finite volume schemes for the shallow water equations are its simplicity to code and the lower computational cost per time step. The validation of the scheme is presented in five test cases involving overland flow and rainfall-runoff transformation over topographies of different complexity. The scheme is compared to the finite volume scheme of Roe (1986), to the simple inertia formulation, and to the diffusive wave model. The test cases show that the DHD scheme is able to compute subcritical and supercritical flows in rural and urban environments, and that in overland flow applications it gives similar results to the second-order scheme of Roe with a lower computational cost. The results obtained with the simple inertia and diffusive wave models are very similar to those obtained with the DHD scheme in rural basins in which the bed friction and topography dominate the flow hydrodynamics but they deteriorate in typical urban configurations in which the presence of supercritical flow conditions and small-scale patterns boost the relevance of the inertial terms in the momentum equations.
منابع مشابه
Pressure-Velocity Coupled Finite Volume Solution of Steady Incompressible Invscid Flow Using Artificial Compressibility Technique
Application of the computer simulation for solving the incompressible flow problems motivates developing efficient and accurate numerical models. The set of Inviscid Incompressible Euler equations can be applied for wide range of engineering applications. For the steady state problems, the equation of continuity can be simultaneously solved with the equations of motion in a coupled manner using...
متن کاملA Composite Finite Difference Scheme for Subsonic Transonic Flows (RESEARCH NOTE).
This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...
متن کاملEfficient scheme for the shallow water equations on unstructured grids with application to the Continental Shelf
In this paper, a shallow-water flow solver is presented, based on the finite-volume method on unstructured grids The method is suitable for flows that occur in rivers, channels, sewer systems (1D), shallow seas, rivers, overland flow (2D), and estuaries, lakes and shelf breaks (3D). We present an outline of the numerical approach and show three 2D test cases and an application of tidal propagat...
متن کاملOverland flow modelling with the Shallow Water Equation using a well balanced numerical scheme: Adding efficiency or just more complexity?
In the last decades, more or less complex physically-based hydrological models, have been developed that solve the shallow water equations or their approximations using various numerical methods. Model users may not necessarily know the different hypothesis lying behind these development and simplifications, and it might therefore be difficult to judge if a code is well adapted to their objecti...
متن کاملAn efficient unstructured MUSCL scheme for solving the 2D shallow water equations
The aim of this paper is to present a novel monotone upstream scheme for conservation law (MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to construct the required values at the midpoint of cell edges in a more straightforward and effective way compared to other conventional approaches, by making better use of the geometrical property of the triangular grids. The sch...
متن کامل