The shallow flow equations solved on adaptive quadtree grids

This paper describes an adaptive quadtree grid-based solver of the depth-averaged shallow water equations. The model is designed to approximate flows in complicated large-scale shallow domains while focusing on important smaller-scale localized flow features. Quadtree grids are created automatically by recursive subdivision of a rectangle about discretized boundary, bathymetric or flow-related seeding points, It can be fitted in a fractal-like sense by local grid refinement to any boundary, however distorted, provided absolute convergence to the boundary is not required and a low level of stepped boundary can be tolerated. Grid information is stored as a tree data structure, with a novel indexing system used to link information on the quadtree to a finite volume discretization of the governing equations. As the flow field develops, the grids may be adapted using a parameter based on vorticity and grid cell size. The numerical model is validated using standard benchmark tests, including seiches, Coriolis-induced set-up, jet-forced flow in a circular reservoir, and wetting and drying. Wind-induced flow in the Nichupte Lagoon. Mexico, provides an illustrative example of an application to flow in extremely complicated multi-connected regions. Copyright (C) 2001 John Wiley & Sons, Ltd.