Implementation of a Discontinuous Galerkin Discretization of the Conversation of Mass Equation in QUODDY

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Mar 19, 2003
Accession Number
ADA413152

Entities

People

  • C. A. Blain
  • C. N. Dawson
  • M. J. Guillot

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Cauchy Problem
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Engineering
  • Equations
  • Galerkin Method
  • Gaussian Quadrature
  • Mechanical Engineering
  • Military Research
  • Runge Kutta Method
  • Shallow Water
  • Stratified Fluids
  • Three Dimensional
  • Two Dimensional

Readers

  • Coastal Oceanography
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)