Pseudospectral Solution of the Two-Dimensional Navier--Stokes Equations in a Disk

Authors:
D. J. Torres;E. A. Coutsias
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1999

Citing 0
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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).