Mathematics Commons^™

Pseudospectral Solution Of The Two-Dimensional Navier{Stokes Equations In A Disk, Evangelos A. Coutsias, David J. Torres

Branch Mathematics and Statistics Faculty and Staff Publications

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 …