Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows
A well-balanced scheme with total variation diminishing Runge-Kutta discontinuous Galerkin (TVD-RK DG) method for solving shallow water equations is presented. Generally, the flux function at cell interface in the TVD-RK DG scheme is approximated by using the Harten-Lax-van Leer (HLL) method. Here,...
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| Format: | Article |
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Wiley
2015-01-01
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| Series: | Modelling and Simulation in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2015/591282 |
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| author | Thida Pongsanguansin Montri Maleewong Khamron Mekchay |
| author_facet | Thida Pongsanguansin Montri Maleewong Khamron Mekchay |
| author_sort | Thida Pongsanguansin |
| collection | DOAJ |
| description | A well-balanced scheme with total variation diminishing Runge-Kutta discontinuous Galerkin (TVD-RK DG) method for solving shallow water equations is presented. Generally, the flux function at cell interface in the TVD-RK DG scheme is approximated by using the Harten-Lax-van Leer (HLL) method. Here, we apply the weighted average flux (WAF) which is higher order approximation instead of using the HLL in the TVD-RK DG method. The consistency property is shown. The modified well-balanced technique for flux gradient and source terms under the WAF approximations is developed. The accuracy of numerical solutions is demonstrated by simulating dam-break flows with the flat bottom. The steady solutions with shock can be captured correctly without spurious oscillations near the shock front. This presents the other flux approximations in the TVD-RK DG method for shallow water simulations. |
| format | Article |
| id | doaj-art-62ff31cb68f246bb825be7e53b7e5190 |
| institution | Kabale University |
| issn | 1687-5591 1687-5605 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Modelling and Simulation in Engineering |
| spelling | doaj-art-62ff31cb68f246bb825be7e53b7e51902025-08-20T03:34:40ZengWileyModelling and Simulation in Engineering1687-55911687-56052015-01-01201510.1155/2015/591282591282Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water FlowsThida Pongsanguansin0Montri Maleewong1Khamron Mekchay2Department of Mathematics and Computer Science, Chulalongkorn University, Bangkok 10330, ThailandDepartment of Mathematics, Kasetsart University, Bangkok 10900, ThailandDepartment of Mathematics and Computer Science, Chulalongkorn University, Bangkok 10330, ThailandA well-balanced scheme with total variation diminishing Runge-Kutta discontinuous Galerkin (TVD-RK DG) method for solving shallow water equations is presented. Generally, the flux function at cell interface in the TVD-RK DG scheme is approximated by using the Harten-Lax-van Leer (HLL) method. Here, we apply the weighted average flux (WAF) which is higher order approximation instead of using the HLL in the TVD-RK DG method. The consistency property is shown. The modified well-balanced technique for flux gradient and source terms under the WAF approximations is developed. The accuracy of numerical solutions is demonstrated by simulating dam-break flows with the flat bottom. The steady solutions with shock can be captured correctly without spurious oscillations near the shock front. This presents the other flux approximations in the TVD-RK DG method for shallow water simulations.http://dx.doi.org/10.1155/2015/591282 |
| spellingShingle | Thida Pongsanguansin Montri Maleewong Khamron Mekchay Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows Modelling and Simulation in Engineering |
| title | Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows |
| title_full | Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows |
| title_fullStr | Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows |
| title_full_unstemmed | Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows |
| title_short | Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows |
| title_sort | consistent weighted average flux of well balanced tvd rk discontinuous galerkin method for shallow water flows |
| url | http://dx.doi.org/10.1155/2015/591282 |
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