A computational study of some numerical schemes for a test case with steep boundary layers

A. R. Appadu, J. K. Djoko, H. H. Gidey

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, three numerical methods have been used to solve a 1-D Convection-Diffusion equation with specified initial and boundary conditions. The methods used are the third order upwind scheme [1], fourth order upwind scheme [1] and a Non-Standard Finite Difference (NSFD) scheme [4]. The problem we considered has steep boundary layers near x=1 [3] and this is a challenging test case as many schemes are plagued by nonphysical oscillation near steep boundaries. We compute the L2 and L errors, dissipation and dispersion errors when the three numerical schemes are used and observe that the NSFD is much better than the other two schemes for both coarse and fine grids and also at low and high Reynolds numbers.

Original languageEnglish
Title of host publicationProceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
EditorsTheodore E. Simos, Theodore E. Simos, Theodore E. Simos, Charalambos Tsitouras
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735412873
DOIs
Publication statusPublished - Mar 10 2015
EventInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece
Duration: Sep 22 2014Sep 28 2014

Publication series

NameAIP Conference Proceedings
Volume1648
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
Country/TerritoryGreece
CityRhodes
Period9/22/149/28/14

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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