Characteristic-Based, Parallel, Numerical Solver for the Shallow Water Equations on Unstructured Grids with Wet/Dry Interfaces
A Dissertation Presented for the Doctor of Philosophy in Computational Engineering, The University of Tennessee at Chattanooga
Pradeep Sivakumar, December 2006
A method for solving the system of shallow water equations with wetting and drying is presented. A Roe type flux-difference formulation is developed using non-dimensional primitive variables. The primitive variable formulation has the advantage that the discretized equations are balanced at equilibrium and gives a way of solving wetting and drying on plane beaches. The numerical solver is validated with the analytical solution of the dam break problem and the tidal wave problem before demonstrating wetting and drying by flow simulation in the Gulf of Mexico. A scalable, efficient, and modular parallel code was developed using C++. An unstructured mesh generation method which uses a hierarchical tree structure and recursive cell division is used to obtain a high resolution grid with high local refinement to fit islands and coastlines. The proposed algorithm has the ability to predict watershed and flooding in coastal areas, estuaries, rivers and other shallow water regions.