On three classes of mesh for the solution of a singularly perturbed two-point boundary value problem
There are several mesh types on which the solutions of discretized governing equations are obtained in computational fluid dynamics. Main classes include uniform, piecewise-uniform, exponential expanding, and hybrid meshes. Despite of their successful stories, their unwitting applications often resu...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Book Section |
| Language: | English |
| Published: |
Penerbit UTHM
2020
|
| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/3096/ http://eprints.uthm.edu.my/3096/1/Ch08.pdf |
| _version_ | 1848887927443030016 |
|---|---|
| author | Abdullah, Aslam |
| author2 | Ismail, Al Emran |
| author_facet | Ismail, Al Emran Abdullah, Aslam |
| author_sort | Abdullah, Aslam |
| building | UTHM Institutional Repository |
| collection | Online Access |
| description | There are several mesh types on which the solutions of discretized governing equations are obtained in computational fluid dynamics. Main classes include uniform, piecewise-uniform, exponential expanding, and hybrid meshes. Despite of their successful stories, their unwitting applications often result in bad solutions which involve, for instance, spurious oscillations, over- or under-estimations, and excessive computation time. This paper pays attention on three mesh classes, namely the uniform mesh, the piecewise-uniform mesh as represented by Shishkin mesh, and Shishkin-exponential expanding mesh which signifies the hybrid mesh. In particular, we examine the comparative effectiveness of the meshes for the solution of a singularly perturbed two-point boundary value problem. This is done by employing an error model based on the singular perturbation parameter and mesh number, with the assumption that the spatial error grows with respect to space. It is found that the number of mesh is reduced by at least half if the Shishkin mesh is replaced by the uniform and the Shishkin-exponential expanding meshes, in order to prevent spurious oscillations. The finding serves as a guideline for the researchers and engineers in selecting appropriate meshes on which flow problems are numerically solved. |
| first_indexed | 2025-11-15T20:02:10Z |
| format | Book Section |
| id | uthm-3096 |
| institution | Universiti Tun Hussein Onn Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T20:02:10Z |
| publishDate | 2020 |
| publisher | Penerbit UTHM |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | uthm-30962022-01-03T07:50:19Z http://eprints.uthm.edu.my/3096/ On three classes of mesh for the solution of a singularly perturbed two-point boundary value problem Abdullah, Aslam TJ Mechanical engineering and machinery TL500-777 Aeronautics. Aeronautical engineering There are several mesh types on which the solutions of discretized governing equations are obtained in computational fluid dynamics. Main classes include uniform, piecewise-uniform, exponential expanding, and hybrid meshes. Despite of their successful stories, their unwitting applications often result in bad solutions which involve, for instance, spurious oscillations, over- or under-estimations, and excessive computation time. This paper pays attention on three mesh classes, namely the uniform mesh, the piecewise-uniform mesh as represented by Shishkin mesh, and Shishkin-exponential expanding mesh which signifies the hybrid mesh. In particular, we examine the comparative effectiveness of the meshes for the solution of a singularly perturbed two-point boundary value problem. This is done by employing an error model based on the singular perturbation parameter and mesh number, with the assumption that the spatial error grows with respect to space. It is found that the number of mesh is reduced by at least half if the Shishkin mesh is replaced by the uniform and the Shishkin-exponential expanding meshes, in order to prevent spurious oscillations. The finding serves as a guideline for the researchers and engineers in selecting appropriate meshes on which flow problems are numerically solved. Penerbit UTHM Ismail, Al Emran 2020 Book Section PeerReviewed text en http://eprints.uthm.edu.my/3096/1/Ch08.pdf Abdullah, Aslam (2020) On three classes of mesh for the solution of a singularly perturbed two-point boundary value problem. In: Advances in Mechanical, Manufacturing and Aerospace Engineering. Penerbit UTHM, pp. 115-132. ISBN 978-967-2916-56-7 |
| spellingShingle | TJ Mechanical engineering and machinery TL500-777 Aeronautics. Aeronautical engineering Abdullah, Aslam On three classes of mesh for the solution of a singularly perturbed two-point boundary value problem |
| title | On three classes of mesh for the solution of a singularly perturbed two-point boundary value problem |
| title_full | On three classes of mesh for the solution of a singularly perturbed two-point boundary value problem |
| title_fullStr | On three classes of mesh for the solution of a singularly perturbed two-point boundary value problem |
| title_full_unstemmed | On three classes of mesh for the solution of a singularly perturbed two-point boundary value problem |
| title_short | On three classes of mesh for the solution of a singularly perturbed two-point boundary value problem |
| title_sort | on three classes of mesh for the solution of a singularly perturbed two-point boundary value problem |
| topic | TJ Mechanical engineering and machinery TL500-777 Aeronautics. Aeronautical engineering |
| url | http://eprints.uthm.edu.my/3096/ http://eprints.uthm.edu.my/3096/1/Ch08.pdf |