Graduate School in Nonlinear Science

Sponsored by The Danish Research Agency

MIDIT                              OFD                          CATS
Modelling, Nonlinear Dynamics      Optics and Fluid Dynamics    Chaos and Turbulence Studies
and Irreversible Thermodynamics    Risø National Laboratory     Niels Bohr Institute and 
Technical University of Denmark    Building 128                 Department of Chemistry
Building 321                       P.O. Box 49                  University of Copenhagen 
DK-2800 Lyngby                     DK-4000 Roskilde             DK-2100 Copenhagen Ø
Denmark                            Denmark                      Denmark


by E.A. Coutsias
Dept. Mathematics and Statistics
University of New Mexico,
Albuquerque, NM 87131, USA

Tuesday, May 15, 2001, 14.00 h
at OFD Meeting Room, Building 130, Risø National Laboratory

Abstract: A Fourier-Chebyshev pseudospectral algorithm for the accurate numerical solution of the 2-dimensional Navier-Stokes (NS) and related equations in a circular basin will be discussed. The presence of no-slip walls provides a nonlinear self-excitation mechanism for injecting enstrophy into the flow. This injection occurs in the form of coherent dipolar structures arising from the rollup of strong boundary layers. This phenomenon puts a strain on most numerical techniques. Our spectral algorithm takes advantage of the azimuthal periodicity, to separate variables and employ Chebyshev expansions, which are capable of optimal resolution at the boundaries, while they can be computed by Fast Fourier Transforms. This separation incurs the price of a coordinate system singularity at the center, whose treatment requires additional care. Our method for solving the Poisson and Helmholtz equations resulting from the time discretization of the NS-equations will be presented. We will discuss computations of decay from random initial conditions with and without random forcing, as well as in the presence of circular shear Ekman forcing.