A Discontinuous Galerkin Method for Three-Dimensional Shallow Water Equations
- 213 Downloads
We describe the application of a local discontinuous Galerkin method to the numerical solution of the three-dimensional shallow water equations. The shallow water equations are used to model surface water flows where the hydrostatic pressure assumption is valid. The authors recently developed a DG\linebreak method for the depth-integrated shallow water equations. The method described here is an extension of these ideas to non-depth-integrated models. The method and its implementation are discussed, followed by numerical examples on several test problems.
KeywordsShallow water equations discontinuous Galerkin method free surface
Unable to display preview. Download preview PDF.
- Aizinger, A. (2004). A Discontinuous Galerkin Method for Two- and Three-Dimensional Shallow-Water Equations, Ph.D. Dissertation, University of Texas at Austin. Google Scholar
- Cockburn, B., Shu, C.-W. 1989TVB Runge-Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: General frameworkMath. Comput.52411435Google Scholar
- Cockburn, B., Karniadakis, G., Shu , C.-W. 2000The development of discontinuous Galerkin methods.Cockburn, B.Karniadakis, G.Shu , C.-W. eds. Discontinuous Galerkin Methods Theory, Computation and Applications, Lecture Notes in Computational Science and Engineering, volume 11, Part I: OverviewSpringer-VerlagBerlin350Google Scholar
- Ippen, A. T. 1951Mechanics of supercritical flowTrans. ASCE116268295Google Scholar
- Johnson, B. H., Kim, K. W., Heath, R. E., Hsieh, B. B. and Butler, H. L. (1991). Development and verification of a three-dimensional numerical hydrodynamic, salinity and temperature model of Chesapeake Bay, Technical report HL-91-7, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.Google Scholar
- Le Veque, R. J. (1992). Numerical Methods for Conservation Laws, Basel, Birkhäuser. Google Scholar
- Luettich, R. A., Westerink, J. J., and Scheffner, N. W. (1991). ADCIRC: An Advanced Three-Dimensional Circulation Model for Shelves, Coasts and Estuaries, Report 1, U.S. Army Corps of Engineers, Washington, D.C. 20314-1000. Google Scholar
- Toro, E. F. (2001). Shock-Capturing Methods for Free-Surface Shallow Flows, Wiley, Chichester.Google Scholar
- Vreugdenhil, C. B. 1994Methods for Shallow-Water FlowKluwer Academic PublishersDordrechtGoogle Scholar
- Weiyan, T. (1992). Shallow Water Hydrodynamics, Elsevier Oceanography Series, 55, Elsevier, Amsterdam.Google Scholar