A spectral method for the triangular cavity flow

TitleA spectral method for the triangular cavity flow
Publication TypeJournal Article
Year of Publication2014
AuthorsJagannathan A., Mohan R., Dhanak M.
JournalComputers & Fluids
Date Published2014/05
Type of ArticleArticle
ISBN Number0045-7930
Accession NumberWOS:000335629800003
KeywordsCoordinate mapping; driven cavity; efficient numerical techniques; equations; Influence; Lid driven cavity; matrix method; navier-stokes; Spectral collocation; steady viscous-flow

We describe the use of a spectral collocation method to compute the characteristics of incompressible, viscous flow in a lid driven right triangular cavity with wall motion away from the right angle. First, the 2-D Gauss-Lobatto grid on the square [-1,1] x [-1,1] is mapped to a triangular domain by means of a singular mapping. A singularity subtraction technique is used to account for the most singular terms of the asymptotic expansions near the top corners of the flow. The unsteady Navier-Stokes equations in the vorticity-stream function formulation are then solved in this transformed grid using an influence matrix technique. A third order Adams Bashforth/Backward differentiation method appears to provide excellent numerical stability for the scheme and also permits a larger critical time step. Detailed characteristics of the flow and comparisons with published results are presented. (C) 2014 Elsevier Ltd. All rights reserved.

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