Development of a 2-D Model for Shallow Water Flow Using Godunov’s Finite Volume Method

In this effort we develop a hydrodynamic model for the 2-D shallow water equations (SWE) using a first order Godunov method. The method is formulated as a discontinuous Galerkin finite element method using constant approximating polynomials. We validate the basic implementation of the computer code using quarter annular tests where analytical solutions are available. We investigate the convergence and stability properties of the method by computing the convergence in the L² norm and verifying the stability requirement in terms of Courant number. We then apply the method to Lake Pontchartrain to provide a more realistic test of the method. We draw conclusions as to the accuracy requirements of the method and discuss extending the developed computer code to include additional physical models, as well as implementing higher degree approximating polynomials.