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Numerical Solution of the Dam-Break Problem with a Discontinuous Galerkin Method |
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| Authors: | Sergio Fagherazzi Patrick Rasetarinera M Youssuff Hussaini David J Furbish |
| Affiliation: | 1Assistant Professor, Dept. of Geological Sciences and School of Computational Science and Information Technology, Florida State Univ., Tallahassee, FL 32306-4120. 2Research Assistant, School of Computational Science and Information Technology, Florida State Univ., Tallahassee, FL 32306-4120. 3Professor, School of Computational Science and Information Technology, Florida State Univ., Tallahassee, FL 32306-4120. 4Professor, Dept. of Geological Sciences, Tallahassee, FL 32306. |
| Abstract: | A discontinuous Galerkin method for the solution of the dam-break problem is presented. The scheme solves the shallow water equations with spectral elements, utilizing an efficient Roe approximate Riemann solver in order to capture bore waves. The solution is enhanced by a projection limiter that eliminates spurious oscillations near discontinuities. The main advantage of the model is the flexibility in approximating smooth solutions with high-order polynomials and resolving at the same time discontinuous shock waves. Furthermore, the finite element discretization is capable of handling complex geometries and producing correct results near the boundaries. Both the h- and p-type extensions are investigated for the one-dimensional dam break, and the results are verified by comparison with analytical solutions. The application to a two-dimensional dam-break problem shows the efficiency and stability of the method. |
| Keywords: | Shallow water Floods Dams Numerical models Shock waves Finite element method |