Branch Mathematics and Statistics Faculty and Staff Publications

Document Type

Article

Publication Date

1999

Abstract

An efficient and accurate algorithm for solving the two-dimensional (2D) incompressible Navier-Stokes equations on a disk with no-slip boundary conditions is described. The vorticity stream function formulation of these equations is used, and spatially the vorticity and stream functions are expressed as Fourier-Chebyshev expansions. The Poisson and Helmholtz equations which arise from the implicit-explicit time marching scheme are solved as banded systems using a postconditioned spectral tau-method. The polar coordinate singularity is handled by expanding fields radially over the entire diameter using a parity modified Chebyshev series and building partial regularity into the vorticity. The no-slip boundary condition is enforced by transferring one of the two boundary conditions imposed on the stream function onto the vorticity via a solvability constraint. Significant gains in run times were realized by parallelizing the code in message passage interface (MPI).

Publisher

Society for Industrial and Applied Mathematics

Publication Title

SIAM Journal on Scientific Computing

ISSN

1064-8275

Volume

21

Issue

1

First Page

378

Last Page

403

Language (ISO)

English

Keywords

spectral methods, coordinate singularity, parallel

Comments

AMS subject classifcations. 76D05, 35Q30, 65M70, 65N35 PII. S1064827597330157

Article author is part of the Main Campus Math Department.

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