Quadtree grids for dispersion and inverse flow models

Hierarchical quadtree grids are used in two applications to offer selective grid refinement. Problems of pollutant transport and coastal flow modelling are considered. The first application describes an adaptive hierarchical grid-based numerical scheme for predicting localised water-borne pollutant transport in two-dimensions. The prescribed initial pollutant mass is discretised into a set of masslets and the flow domain re-scaled within the unit square. The solution process uses a split operator method in which advection is modelled by discrete masslets and diffusion by finite differences. The quadtree mesh is redefined each step based on the local distribution of masslets. The second application finds a solution to the shallow water equations in a fixed quadtree mesh that is refined by the topography. The solution uses an inverse method with direct minimisation of a cost function and allows for data assimilation. When used together, the two models allow simulations to be made of effluent dispersion in coastal waters.