On three classes of mesh for the solution of a singularly perturbed two-point boundary value problem

• Main Author: Abdullah, Aslam
• Other Authors: Ismail, Al Emran
• Format: Book Section
• Language: English
• Published: Penerbit UTHM 2020
• Subjects: TJ Mechanical engineering and machinery; TL500-777 Aeronautics. Aeronautical engineering
• Online Access: http://eprints.uthm.edu.my/3096/1/Ch08.pdf; http://eprints.uthm.edu.my/3096/

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.