On a necessary requirement for re-uniform numerical methods to solve boundary layer equations for flow along a flat plate

Grigorii I. Shishkin, Paul A. Farrell, Alan F. Hegarty, John J.H. Miller, Eugene O’Riordan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider grid approximations of a boundary value problem for the boundary layer equations modeling flow along a flat plate in a region excluding a neighbourhood of the leading edge. The problem is singularly perturbed with the perturbation parameter ε = 1/Re multiplying the highest derivative. Here the parameter ε takes any values from the half-interval (0,1], and Re is the Reynolds number. It would be of interest to construct an Re-uniform numerical method using the simplest grids, i.e., uniform rectangular grids, that could provide effective computational methods. To this end, we are free to use any technique even up to fitted operator methods, however, with fitting factors independent of the problem solution. We show that for the Prandtl problem, even in the case when its solution is self-similar, there does not exist a fitted operator method that converges Re-uniformly. Thus, combining a fitted operator and uniform meshes, we do not succeed in achieving Re-uniform convergence. Therefore, the use of the fitted mesh technique, based on meshes condensing in a parabolic boundary layer, is a necessity in constructing Re-uniform numerical methods for the above class of flow problems.

Original languageEnglish
Title of host publicationNumerical Analysis and Its Applications - 2nd International Conference, NAA 2000, Revised Papers
EditorsLubin Vulkov, Plamen Yalamov, Jerzy Waniewski
PublisherSpringer Verlag
Pages723-731
Number of pages9
ISBN (Print)9783540418146
DOIs
Publication statusPublished - 2001
Event2nd International Conference on Numerical Analysis and Its Applications, NAA 2000 - Rousse, Bulgaria
Duration: 11 Jun 200015 Jun 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1988
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference2nd International Conference on Numerical Analysis and Its Applications, NAA 2000
Country/TerritoryBulgaria
CityRousse
Period11/06/0015/06/00

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