Implementation of a Discontinuous Galerkin Discretization of the Conversation of Mass Equation in QUODDY
Formal rept. 29-31 Oct 2002
NAVAL RESEARCH LAB STENNIS SPACE CENTER MS OCEANOGRAPHY DIV
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Two variations of a discontinuous Galerkin method are investigated for the primitive form of the time-dependent, 2-D, depth-averaged conservation of mass equation for shallow water. Linear approximating functions are employed, which are defined locally on each element, providing three degrees of freedom per element. In the first method, the degrees of freedom are the nodal values for each element. Analytical integration rules are developed to evaluate the volume integrals, and Gaussian quadrature is to evaluate the element edge integrals produced by the finite element approximation. Time integration is achieved using a second-order Runge-Kutta method. The method is implemented into the computer code QUODDY, replacing the generalized wave continuity equation GWCE formulation into the code. The implementation is validated on a test case involving tidal boundary conditions in the Gulf of Maine.
- Hydrology, Limnology and Potamology
- Numerical Mathematics
- Computer Programming and Software