Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver
In this paper, numerical simulations are performed in a single and double lid driven square cavity to study the flow of a Bingham viscoplastic fluid. The governing equations are discretized with the help of finite element method in space and the nonconforming Stokes element Q~1/Q0 is utilized which...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/5210708 |
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| author | R. Mahmood N. Kousar M. Yaqub K. Jabeen |
| author_facet | R. Mahmood N. Kousar M. Yaqub K. Jabeen |
| author_sort | R. Mahmood |
| collection | DOAJ |
| description | In this paper, numerical simulations are performed in a single and double lid driven square cavity to study the flow of a Bingham viscoplastic fluid. The governing equations are discretized with the help of finite element method in space and the nonconforming Stokes element Q~1/Q0 is utilized which gives 2nd-order accuracy for velocity and 1st-order accuracy for pressure. The discretized systems of nonlinear equations are treated by using the Newton method and the inner linear subproablems are solved by the direct solver UMFPACK. A qualitative comparison is done with the results reported in the literature. In addition to these comparisons, some new reference data for the kinetic energy is generated. All these implementations are done in the open source software package FEATFLOW which is a general purpose finite element based solver package for solving partial differential equations. |
| format | Article |
| id | doaj-art-d7aeeb70bb4b4736a6816a1d717a50f2 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-d7aeeb70bb4b4736a6816a1d717a50f22025-02-03T01:25:43ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/52107085210708Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct SolverR. Mahmood0N. Kousar1M. Yaqub2K. Jabeen3Department of Mathematics, Air University, Islamabad, PakistanDepartment of Mathematics, Air University, Islamabad, PakistanDepartment of Mathematics, Riphah International University, Islamabad, PakistanDepartment of Mathematics, Riphah International University, Islamabad, PakistanIn this paper, numerical simulations are performed in a single and double lid driven square cavity to study the flow of a Bingham viscoplastic fluid. The governing equations are discretized with the help of finite element method in space and the nonconforming Stokes element Q~1/Q0 is utilized which gives 2nd-order accuracy for velocity and 1st-order accuracy for pressure. The discretized systems of nonlinear equations are treated by using the Newton method and the inner linear subproablems are solved by the direct solver UMFPACK. A qualitative comparison is done with the results reported in the literature. In addition to these comparisons, some new reference data for the kinetic energy is generated. All these implementations are done in the open source software package FEATFLOW which is a general purpose finite element based solver package for solving partial differential equations.http://dx.doi.org/10.1155/2017/5210708 |
| spellingShingle | R. Mahmood N. Kousar M. Yaqub K. Jabeen Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver Advances in Mathematical Physics |
| title | Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver |
| title_full | Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver |
| title_fullStr | Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver |
| title_full_unstemmed | Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver |
| title_short | Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver |
| title_sort | numerical simulations of the square lid driven cavity flow of bingham fluids using nonconforming finite elements coupled with a direct solver |
| url | http://dx.doi.org/10.1155/2017/5210708 |
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