The shallow flow equations solved on adaptive quadtree grids

This paper describes an adaptive quadtree grid-based solver of the depth-av eraged shallow water equations. The model is designed to approximate flows in complicated large-scale shallow domains while focusing on important smal ler-scale localized flow features. Quadtree grids are created automatically by recursive subdivision of a rectangle about discretized boundary, bathym etric or flow-related seeding points, It can be fitted in a fractal-like se nse by local grid refinement to any boundary, however distorted, provided a bsolute convergence to the boundary is not required and a low level of step ped boundary can be tolerated. Grid information is stored as a tree data st ructure, with a novel indexing system used to link information on the quadt ree to a finite volume discretization of the governing equations. As the fl ow field develops, the grids may be adapted using a parameter based on vort icity and grid cell size. The numerical model is validated using standard b enchmark 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) 20 01 John Wiley & Sons, Ltd.