Object-oriented Modelling of an Adaptive, Quadtree-based, Finite Volume Method for the Shallow Water Equations

The results of an investigation in developing a generalized toolkit for Quadtree based Finite Volume models, exemplarily applied on the Shallow Water Equations, are given in this report. The developed application model: (i) discretizes a given topography using a quadtreebased grid system and (ii) solves the Shallow Water Equations by a numerical method based on the Finite Volume Method on the adaptive quadtree grid system. The above tasks are accomplished through the use of specialized descriptors and adaptors, developed during the study. The developed components with their descriptors and adaptors augment the existing generalized quadtree components in the JAVA Bauinformatik packages, and form an integral part of the toolkit. The descriptors store the cell variables, necessary for the calculations, and also give directives to expand and collapse a cell. The grid is adapted by specialized adaptation criteria, based on vorticity, elevation slope etc., defined within the adapters.