An Implicit 2-D Shallow Water Flow Model on Unstructured Quadtree Rectangular Mesh

An implicit finite volume scheme is developed to solve the depth-averaged 2-D shallow water flow equations. The computational mesh consists of rectangular cells, with quadtree technology incorporated to locally refine the mesh around structures of interest or where the topography and/or flow properties change sharply. The grid nodes are numbered by means of an unstructured index system for more flexibility. The governing equations are solved using the SIMPLEC algorithm on non-staggered grid to handle the coupling of water level and velocity. In this non-staggered system, primary variables u-, v-velocity, and water level are stored on the same set of grid points, and fluxes at cell faces are determined using the Rhie and Chow's momentum interpolation method to avoid spurious checkerboard oscillations. The discretized algebraic equations are solved iteratively using the GMRES method. The model has been tested against measurement data for steady flow around a spur-dyke in a laboratory flume and tidal flows in Gironde Estuary, France and Grays Harbor, USA. The model reasonably well reproduces the temporal and spatial variations of water level and current speed observed in the measurements. The laboratory test has demonstrated that the quadtree mesh is cost-effective, while the two field cases have shown that the model is very stable and handles wetting and drying efficiently.