A Robust Three-Level Time-Split MacCormack Scheme for Solving Two-Dimensional Unsteady Convection-Diffusion Equation
A three-level time-split MacCormack method has been developed for solving the two-dimensional time-dependent convection-diffusion equation. The differential operator "splits" the two-dimensional problem into two pieces so that each subproblem is easy to solve using the original MacCormack...
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| Format: | Article |
| Language: | English |
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Shahid Chamran University of Ahvaz
2021-04-01
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| Series: | Journal of Applied and Computational Mechanics |
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| Online Access: | https://jacm.scu.ac.ir/article_16029_31a3616ec29481ac8eedeb6bf34fbc27.pdf |
| _version_ | 1818444844237848576 |
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| author | Eric Ngondiep |
| author_facet | Eric Ngondiep |
| author_sort | Eric Ngondiep |
| collection | DOAJ |
| description | A three-level time-split MacCormack method has been developed for solving the two-dimensional time-dependent convection-diffusion equation. The differential operator "splits" the two-dimensional problem into two pieces so that each subproblem is easy to solve using the original MacCormack procedure. The obtained scheme is temporal second-order convergent and spatial fourth-order accurate. This considerably reduces the computational cost of the algorithm. Under a suitable time-step restriction, both stability and convergence of the proposed technique are analyzed in the L∞(0, T; L2)-norm. A large set of numerical examples which provide the convergence rate of the new algorithm are presented. Overall, the considered approach is found to lie in the class of robust numerical schemes for solving general systems of partial differential equations. |
| first_indexed | 2024-12-14T19:22:23Z |
| format | Article |
| id | doaj.art-d975413cdf1f447bb262a771ea9ebbd6 |
| institution | Directory Open Access Journal |
| issn | 2383-4536 2383-4536 |
| language | English |
| last_indexed | 2024-12-14T19:22:23Z |
| publishDate | 2021-04-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| series | Journal of Applied and Computational Mechanics |
| spelling | doaj.art-d975413cdf1f447bb262a771ea9ebbd62022-12-21T22:50:18ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362383-45362021-04-017255957710.22055/jacm.2020.35224.260116029A Robust Three-Level Time-Split MacCormack Scheme for Solving Two-Dimensional Unsteady Convection-Diffusion EquationEric Ngondiep0Department of Mathematics and Statistics, College of Science, Al-Imam, Muhammad Ibn Saud, Islamic University (IMSIU), 90950 Riyadh, Saudi ArabiaA three-level time-split MacCormack method has been developed for solving the two-dimensional time-dependent convection-diffusion equation. The differential operator "splits" the two-dimensional problem into two pieces so that each subproblem is easy to solve using the original MacCormack procedure. The obtained scheme is temporal second-order convergent and spatial fourth-order accurate. This considerably reduces the computational cost of the algorithm. Under a suitable time-step restriction, both stability and convergence of the proposed technique are analyzed in the L∞(0, T; L2)-norm. A large set of numerical examples which provide the convergence rate of the new algorithm are presented. Overall, the considered approach is found to lie in the class of robust numerical schemes for solving general systems of partial differential equations.https://jacm.scu.ac.ir/article_16029_31a3616ec29481ac8eedeb6bf34fbc27.pdf2d unsteady convection-diffusion equationone-dimensional operators (splitting)explicit maccormack schemeexplicit time-split methodstability and convergence rate |
| spellingShingle | Eric Ngondiep A Robust Three-Level Time-Split MacCormack Scheme for Solving Two-Dimensional Unsteady Convection-Diffusion Equation Journal of Applied and Computational Mechanics 2d unsteady convection-diffusion equation one-dimensional operators (splitting) explicit maccormack scheme explicit time-split method stability and convergence rate |
| title | A Robust Three-Level Time-Split MacCormack Scheme for Solving Two-Dimensional Unsteady Convection-Diffusion Equation |
| title_full | A Robust Three-Level Time-Split MacCormack Scheme for Solving Two-Dimensional Unsteady Convection-Diffusion Equation |
| title_fullStr | A Robust Three-Level Time-Split MacCormack Scheme for Solving Two-Dimensional Unsteady Convection-Diffusion Equation |
| title_full_unstemmed | A Robust Three-Level Time-Split MacCormack Scheme for Solving Two-Dimensional Unsteady Convection-Diffusion Equation |
| title_short | A Robust Three-Level Time-Split MacCormack Scheme for Solving Two-Dimensional Unsteady Convection-Diffusion Equation |
| title_sort | robust three level time split maccormack scheme for solving two dimensional unsteady convection diffusion equation |
| topic | 2d unsteady convection-diffusion equation one-dimensional operators (splitting) explicit maccormack scheme explicit time-split method stability and convergence rate |
| url | https://jacm.scu.ac.ir/article_16029_31a3616ec29481ac8eedeb6bf34fbc27.pdf |
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