A High-Order Symmetric Interior Penalty Discontinuous Galerkin Scheme to Simulate Vortex Dominated Incompressible Fluid Flow
A high-order Symmetric Interior Penalty discontinuous Galerkin (SIPG) method has been used for solving the incompressible Navier-Stokes equation. We apply the temporal splitting scheme in time and the SIPG discretization in space with the local Lax-Friedrichs flux for the discretization of nonlinear...
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| Format: | Article |
| Language: | English |
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AIMS Press
2016-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/10.3934/Math.2016.1.43/fulltext.html |
| _version_ | 1811271897724223488 |
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| author | Lunji Song Charles O’Neill |
| author_facet | Lunji Song Charles O’Neill |
| author_sort | Lunji Song |
| collection | DOAJ |
| description | A high-order Symmetric Interior Penalty discontinuous Galerkin (SIPG) method has been used for solving the incompressible Navier-Stokes equation. We apply the temporal splitting scheme in time and the SIPG discretization in space with the local Lax-Friedrichs flux for the discretization of nonlinear terms. A fully discrete semi-implicit splitting scheme has been presented and high-order discontinuous Galerkin (DG) finite elements are available. Under a constraint of the CFL condition, two benchmark problems in 2D are investigated: one is a lid-driven cavity flow to verify the high-order discontinuous Galerkin method is accurate and robust; the other is a flow past a circular cylinder, for which we mainly check the Strouhal numbers with the von K´arm´an vortex street, and also simulate the boundary layers with walls and corresponding dynamical behavior with Neumann conditions on the top and bottom boundaries, respectively. We predict the Strouhal number for the range of Reynolds number 50 ≤ Re ≤ 400, making a comparison between the predicted values by our numerical method and the referenced values from physical experiments. |
| first_indexed | 2024-04-12T22:30:27Z |
| format | Article |
| id | doaj.art-49f96a07cde2443e8216e3904b09b2bb |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-12T22:30:27Z |
| publishDate | 2016-04-01 |
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| spelling | doaj.art-49f96a07cde2443e8216e3904b09b2bb2022-12-22T03:13:59ZengAIMS PressAIMS Mathematics2473-69882016-04-0111436310.3934/Math.2016.1.43A High-Order Symmetric Interior Penalty Discontinuous Galerkin Scheme to Simulate Vortex Dominated Incompressible Fluid FlowLunji SongCharles O’NeillA high-order Symmetric Interior Penalty discontinuous Galerkin (SIPG) method has been used for solving the incompressible Navier-Stokes equation. We apply the temporal splitting scheme in time and the SIPG discretization in space with the local Lax-Friedrichs flux for the discretization of nonlinear terms. A fully discrete semi-implicit splitting scheme has been presented and high-order discontinuous Galerkin (DG) finite elements are available. Under a constraint of the CFL condition, two benchmark problems in 2D are investigated: one is a lid-driven cavity flow to verify the high-order discontinuous Galerkin method is accurate and robust; the other is a flow past a circular cylinder, for which we mainly check the Strouhal numbers with the von K´arm´an vortex street, and also simulate the boundary layers with walls and corresponding dynamical behavior with Neumann conditions on the top and bottom boundaries, respectively. We predict the Strouhal number for the range of Reynolds number 50 ≤ Re ≤ 400, making a comparison between the predicted values by our numerical method and the referenced values from physical experiments.http://www.aimspress.com/article/10.3934/Math.2016.1.43/fulltext.htmlNavier-Stokes equations| von K´arm´an vortex street| discontinuous Galerkin method| interior penalty |
| spellingShingle | Lunji Song Charles O’Neill A High-Order Symmetric Interior Penalty Discontinuous Galerkin Scheme to Simulate Vortex Dominated Incompressible Fluid Flow AIMS Mathematics Navier-Stokes equations| von K´arm´an vortex street| discontinuous Galerkin method| interior penalty |
| title | A High-Order Symmetric Interior Penalty Discontinuous Galerkin Scheme to Simulate Vortex Dominated Incompressible Fluid Flow |
| title_full | A High-Order Symmetric Interior Penalty Discontinuous Galerkin Scheme to Simulate Vortex Dominated Incompressible Fluid Flow |
| title_fullStr | A High-Order Symmetric Interior Penalty Discontinuous Galerkin Scheme to Simulate Vortex Dominated Incompressible Fluid Flow |
| title_full_unstemmed | A High-Order Symmetric Interior Penalty Discontinuous Galerkin Scheme to Simulate Vortex Dominated Incompressible Fluid Flow |
| title_short | A High-Order Symmetric Interior Penalty Discontinuous Galerkin Scheme to Simulate Vortex Dominated Incompressible Fluid Flow |
| title_sort | high order symmetric interior penalty discontinuous galerkin scheme to simulate vortex dominated incompressible fluid flow |
| topic | Navier-Stokes equations| von K´arm´an vortex street| discontinuous Galerkin method| interior penalty |
| url | http://www.aimspress.com/article/10.3934/Math.2016.1.43/fulltext.html |
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