A Discontinuous Galerkin Method for Two-Dimensional Shock Wave Modeling
A numerical scheme based on discontinuous Galerkin method is proposed for the two-dimensional shallow water flows. The scheme is applied to model flows with shock waves. The form of shallow water equations that can eliminate numerical imbalance between flux term and source term and simplify comput...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Modelling and Simulation in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2011/782832 |
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| author | W. Lai A. A. Khan |
| author_facet | W. Lai A. A. Khan |
| author_sort | W. Lai |
| collection | DOAJ |
| description | A numerical scheme based on discontinuous Galerkin method is proposed for the two-dimensional shallow water flows. The scheme is applied to model flows with shock waves. The form of shallow water equations that can eliminate numerical imbalance between flux term and source term and simplify computation is adopted here. The HLL approximate Riemann solver is employed to calculate the mass and momentum flux. A slope limiting procedure that is suitable for incompressible two-dimensional flows is presented. A simple method is adapted for flow over initially dry bed. A new formulation is introduced for modeling the net pressure force and gravity terms in discontinuous Galerkin method. To validate the scheme, numerical tests are performed to model steady and unsteady shock waves. Applications include circular dam break with shock, shock waves in channel contraction, and dam break in channel with 45∘ bend. Numerical results show that the scheme is accurate and efficient to model two-dimensional shallow water flows with shock waves. |
| format | Article |
| id | doaj-art-81f2725ce09f410783448fb2fecc0bd2 |
| institution | Kabale University |
| issn | 1687-5591 1687-5605 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Modelling and Simulation in Engineering |
| spelling | doaj-art-81f2725ce09f410783448fb2fecc0bd22025-02-03T06:13:59ZengWileyModelling and Simulation in Engineering1687-55911687-56052011-01-01201110.1155/2011/782832782832A Discontinuous Galerkin Method for Two-Dimensional Shock Wave ModelingW. Lai0A. A. Khan1Department of Civil Engineering, Clemson University, 218 Lowry Hall, Clemson, SC 29634-0911, USADepartment of Civil Engineering, Clemson University, 218 Lowry Hall, Clemson, SC 29634-0911, USAA numerical scheme based on discontinuous Galerkin method is proposed for the two-dimensional shallow water flows. The scheme is applied to model flows with shock waves. The form of shallow water equations that can eliminate numerical imbalance between flux term and source term and simplify computation is adopted here. The HLL approximate Riemann solver is employed to calculate the mass and momentum flux. A slope limiting procedure that is suitable for incompressible two-dimensional flows is presented. A simple method is adapted for flow over initially dry bed. A new formulation is introduced for modeling the net pressure force and gravity terms in discontinuous Galerkin method. To validate the scheme, numerical tests are performed to model steady and unsteady shock waves. Applications include circular dam break with shock, shock waves in channel contraction, and dam break in channel with 45∘ bend. Numerical results show that the scheme is accurate and efficient to model two-dimensional shallow water flows with shock waves.http://dx.doi.org/10.1155/2011/782832 |
| spellingShingle | W. Lai A. A. Khan A Discontinuous Galerkin Method for Two-Dimensional Shock Wave Modeling Modelling and Simulation in Engineering |
| title | A Discontinuous Galerkin Method for Two-Dimensional Shock Wave Modeling |
| title_full | A Discontinuous Galerkin Method for Two-Dimensional Shock Wave Modeling |
| title_fullStr | A Discontinuous Galerkin Method for Two-Dimensional Shock Wave Modeling |
| title_full_unstemmed | A Discontinuous Galerkin Method for Two-Dimensional Shock Wave Modeling |
| title_short | A Discontinuous Galerkin Method for Two-Dimensional Shock Wave Modeling |
| title_sort | discontinuous galerkin method for two dimensional shock wave modeling |
| url | http://dx.doi.org/10.1155/2011/782832 |
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