Adaptive quadtree model of shallow-flow hydrodynamics

Natural shallow-flow domains have irregular boundaries which can strongly influence the interior flow field. Here, the nonlinear shallow water equations are solved on adaptive quadtree grids that can approximate any two-dimensional boundary topology and are easy to enrich or coarsen. A special indexing system matches the quadtree structure to conventional finite volume notation. Grid adaptation is controlled by a cell circulation parameter. Simulations of standard test flows are in close agreement with analytical and other numerical data. The sample application of wind-induced circulation in Lake Balaton, Hungary, demonstrates the ability of the model to deal with a complicated shallow-flow geometry.