Sergio Cruz Leon

Doctor of Philosophy, University of Oxford, Trinity Term 1997

Numerical Solution of the Shallow Water Equations


This thesis describes a numerical model of the 2-D shallow water equations which are solved on adaptive hierarchical quadtree grids. The main aim of the model is its application to shallow flow geometries with highly irregular boundaries. A Cartesian quadtree mesh is straightforward to generate by recursive domain decomposition. It can easily be fitted in a fractal 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. The grid information is stored as a tree data structure, wit the labelling system designed to account for the finite volume or finite difference methods to be utilised on the grid. The shallow water equations are discretized using finite volumes with the depth-averaged velocity variables staggered spatially with respect to all other variables. A time-stepping explicit scheme is used to solve the discretized equations. As the flow field develops, the grids may be adapted using a parameter based on the vorticity and local mesh cell dimension.

The numerical model has been carefully validated against results from a comprehensive series of validation tests. These tests have been chosen because they are well documented flows with regard to experimental measurements and alternative theoretical simulations, and they highlight the effects of certain terms in the governing equations. The numerical model has also been used to estimate wind induced circulation in Lake Balaton, Hungary and the Nichupte Lagoon in Mexico.

(no thesis available)