Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation
A two-dimensional stochastic solver for the incompressible Navier-Stokes equations is developed. The vorticity-stream function formulation is considered. The polynomial chaos expansion was integrated with an unstructured node-centered finite-volume solver. A second-order upwind scheme is used in the...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/903618 |
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| author | Mohamed A. El-Beltagy Mohamed I. Wafa |
| author_facet | Mohamed A. El-Beltagy Mohamed I. Wafa |
| author_sort | Mohamed A. El-Beltagy |
| collection | DOAJ |
| description | A two-dimensional stochastic solver for the incompressible Navier-Stokes equations is developed. The vorticity-stream function formulation is considered. The polynomial chaos expansion was integrated with an unstructured node-centered finite-volume solver. A second-order upwind scheme is used in the convection term for numerical stability and higher-order discretization. The resulting sparse linear system is solved efficiently by a direct parallel solver. The mean and variance simulations of the cavity flow are done for random variation of the viscosity and the lid velocity. The solver was tested and compared with the Monte-Carlo simulations and with previous research works. The developed solver is proved to be efficient in simulating the stochastic two-dimensional incompressible flows. |
| format | Article |
| id | doaj-art-841814d9e73b449dbeeb02bef3165692 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-841814d9e73b449dbeeb02bef31656922025-02-03T05:53:31ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/903618903618Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function FormulationMohamed A. El-Beltagy0Mohamed I. Wafa1Department of Engineering Mathematics and Physics, Engineering Faculty, Cairo University, Orman, Giza 12221, EgyptDepartment of Engineering Mathematics and Physics, Engineering Faculty, Cairo University, Orman, Giza 12221, EgyptA two-dimensional stochastic solver for the incompressible Navier-Stokes equations is developed. The vorticity-stream function formulation is considered. The polynomial chaos expansion was integrated with an unstructured node-centered finite-volume solver. A second-order upwind scheme is used in the convection term for numerical stability and higher-order discretization. The resulting sparse linear system is solved efficiently by a direct parallel solver. The mean and variance simulations of the cavity flow are done for random variation of the viscosity and the lid velocity. The solver was tested and compared with the Monte-Carlo simulations and with previous research works. The developed solver is proved to be efficient in simulating the stochastic two-dimensional incompressible flows.http://dx.doi.org/10.1155/2013/903618 |
| spellingShingle | Mohamed A. El-Beltagy Mohamed I. Wafa Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation Journal of Applied Mathematics |
| title | Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation |
| title_full | Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation |
| title_fullStr | Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation |
| title_full_unstemmed | Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation |
| title_short | Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation |
| title_sort | stochastic 2d incompressible navier stokes solver using the vorticity stream function formulation |
| url | http://dx.doi.org/10.1155/2013/903618 |
| work_keys_str_mv | AT mohamedaelbeltagy stochastic2dincompressiblenavierstokessolverusingthevorticitystreamfunctionformulation AT mohamediwafa stochastic2dincompressiblenavierstokessolverusingthevorticitystreamfunctionformulation |