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Title: Pseudospectral solution of the two-dimensional Navier-Stokes equations in a disk

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 radically 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 grains in run times were realized by parallelizing the code in message passage interface (MPI).

Authors:
;
Publication Date:
Research Org.:
Los Alamos National Lab., NM (US)
OSTI Identifier:
20015657
Resource Type:
Journal Article
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 21; Journal Issue: 1; Other Information: PBD: Sep 1999; Journal ID: ISSN 1064-8275
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; NAVIER-STOKES EQUATIONS; ALGORITHMS; TWO-DIMENSIONAL CALCULATIONS; BOUNDARY CONDITIONS; SINGULARITY; CALCULATION METHODS

Citation Formats

Torres, D.J., and Coutsias, E.A. Pseudospectral solution of the two-dimensional Navier-Stokes equations in a disk. United States: N. p., 1999. Web. doi:10.1137/S1064827597330157.
Torres, D.J., & Coutsias, E.A. Pseudospectral solution of the two-dimensional Navier-Stokes equations in a disk. United States. doi:10.1137/S1064827597330157.
Torres, D.J., and Coutsias, E.A. Wed . "Pseudospectral solution of the two-dimensional Navier-Stokes equations in a disk". United States. doi:10.1137/S1064827597330157.
@article{osti_20015657,
title = {Pseudospectral solution of the two-dimensional Navier-Stokes equations in a disk},
author = {Torres, D.J. and Coutsias, E.A.},
abstractNote = {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 radically 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 grains in run times were realized by parallelizing the code in message passage interface (MPI).},
doi = {10.1137/S1064827597330157},
journal = {SIAM Journal on Scientific Computing},
issn = {1064-8275},
number = 1,
volume = 21,
place = {United States},
year = {1999},
month = {9}
}