Advancing Finite Difference Solutions for Two-Dimensional Incompressible Navier–Stokes Equations Using Artificial Compressibility Method and Sparse Matrix Computation
In this article, a numerical scheme for solving two-dimensional (2D) time-dependent incompressible Navier–Stokes equations is presented. The artificial compressibility technique is used to incorporate a time derivative of pressure term to the continuity equation. It is employed for pressure–velocity...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/5506715 |
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| author | Endalew Getnet Tsega |
| author_facet | Endalew Getnet Tsega |
| author_sort | Endalew Getnet Tsega |
| collection | DOAJ |
| description | In this article, a numerical scheme for solving two-dimensional (2D) time-dependent incompressible Navier–Stokes equations is presented. The artificial compressibility technique is used to incorporate a time derivative of pressure term to the continuity equation. It is employed for pressure–velocity coupling. The scheme consists of backward difference approximation for time derivatives and central difference approximation for spatial derivatives, implemented on a collocated grid. The discretization of the differential equations yields a system of algebraic equations with a block coefficient matrix. To solve this system efficiently, matrix inversion with sparse matrix computation is employed. The proposed numerical scheme is applied to solve three flow problems (lid-driven cavity flow, rectangular channel flow, and Taylor–Green vortex problem) to validate the accuracy and applicability of the scheme. The results affirm the scheme’s capability to provide precise approximations for solutions to the Navier–Stokes equations. With slight modifications, the scheme can be applied to solve various flow problems with high accuracy, less memory usage, and reduced computational time. |
| format | Article |
| id | doaj-art-07c284678d5b4b4d85505977bca84eb0 |
| institution | OA Journals |
| issn | 1687-0042 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-07c284678d5b4b4d85505977bca84eb02025-08-20T02:01:35ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/5506715Advancing Finite Difference Solutions for Two-Dimensional Incompressible Navier–Stokes Equations Using Artificial Compressibility Method and Sparse Matrix ComputationEndalew Getnet Tsega0Department of MathematicsIn this article, a numerical scheme for solving two-dimensional (2D) time-dependent incompressible Navier–Stokes equations is presented. The artificial compressibility technique is used to incorporate a time derivative of pressure term to the continuity equation. It is employed for pressure–velocity coupling. The scheme consists of backward difference approximation for time derivatives and central difference approximation for spatial derivatives, implemented on a collocated grid. The discretization of the differential equations yields a system of algebraic equations with a block coefficient matrix. To solve this system efficiently, matrix inversion with sparse matrix computation is employed. The proposed numerical scheme is applied to solve three flow problems (lid-driven cavity flow, rectangular channel flow, and Taylor–Green vortex problem) to validate the accuracy and applicability of the scheme. The results affirm the scheme’s capability to provide precise approximations for solutions to the Navier–Stokes equations. With slight modifications, the scheme can be applied to solve various flow problems with high accuracy, less memory usage, and reduced computational time.http://dx.doi.org/10.1155/2024/5506715 |
| spellingShingle | Endalew Getnet Tsega Advancing Finite Difference Solutions for Two-Dimensional Incompressible Navier–Stokes Equations Using Artificial Compressibility Method and Sparse Matrix Computation Journal of Applied Mathematics |
| title | Advancing Finite Difference Solutions for Two-Dimensional Incompressible Navier–Stokes Equations Using Artificial Compressibility Method and Sparse Matrix Computation |
| title_full | Advancing Finite Difference Solutions for Two-Dimensional Incompressible Navier–Stokes Equations Using Artificial Compressibility Method and Sparse Matrix Computation |
| title_fullStr | Advancing Finite Difference Solutions for Two-Dimensional Incompressible Navier–Stokes Equations Using Artificial Compressibility Method and Sparse Matrix Computation |
| title_full_unstemmed | Advancing Finite Difference Solutions for Two-Dimensional Incompressible Navier–Stokes Equations Using Artificial Compressibility Method and Sparse Matrix Computation |
| title_short | Advancing Finite Difference Solutions for Two-Dimensional Incompressible Navier–Stokes Equations Using Artificial Compressibility Method and Sparse Matrix Computation |
| title_sort | advancing finite difference solutions for two dimensional incompressible navier stokes equations using artificial compressibility method and sparse matrix computation |
| url | http://dx.doi.org/10.1155/2024/5506715 |
| work_keys_str_mv | AT endalewgetnettsega advancingfinitedifferencesolutionsfortwodimensionalincompressiblenavierstokesequationsusingartificialcompressibilitymethodandsparsematrixcomputation |