An efficient and accurate algorithm for solving the two-dimensional(2D) inc
ompressible Navier-Stokes equations on a disk with no-slip boundary conditi
ons is described. The vorticity-stream function formulation of these equati
ons 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 post-conditioned spectral tau-method. The polar coordinate
singularity is handled by expanding fields radially over the entire diamet
er using a parity modified Chebyshev series and building partial regularity
into the vorticity. The no-slip boundary condition is enforced by transfer
ring 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)
.