Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method
This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived. In addition, the consistency and stability of t...
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University of Baghdad, College of Science for Women
2022-04-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5807 |
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| author | Maan A. Rasheed Suad Naji Kadhim |
| author_facet | Maan A. Rasheed Suad Naji Kadhim |
| author_sort | Maan A. Rasheed |
| collection | DOAJ |
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This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived. In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.
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| format | Article |
| id | doaj-art-27d887b3af944b30b6d60dc15ef45cc7 |
| institution | DOAJ |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2022-04-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-27d887b3af944b30b6d60dc15ef45cc72025-08-20T03:14:36ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862022-04-0119210.21123/bsj.2022.19.2.0321Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson MethodMaan A. Rasheed0Suad Naji Kadhim1Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, IraqDepartment of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived. In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5807Finite difference, Reynolds number, Stream function, Truncation error, Vorticity function. |
| spellingShingle | Maan A. Rasheed Suad Naji Kadhim Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method مجلة بغداد للعلوم Finite difference, Reynolds number, Stream function, Truncation error, Vorticity function. |
| title | Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method |
| title_full | Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method |
| title_fullStr | Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method |
| title_full_unstemmed | Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method |
| title_short | Numerical Solutions of Two-Dimensional Vorticity Transport Equation Using Crank-Nicolson Method |
| title_sort | numerical solutions of two dimensional vorticity transport equation using crank nicolson method |
| topic | Finite difference, Reynolds number, Stream function, Truncation error, Vorticity function. |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/5807 |
| work_keys_str_mv | AT maanarasheed numericalsolutionsoftwodimensionalvorticitytransportequationusingcranknicolsonmethod AT suadnajikadhim numericalsolutionsoftwodimensionalvorticitytransportequationusingcranknicolsonmethod |