3-DIMENSIONAL VISCOUS-FLOW THROUGH A ROTATING CHANNEL - A PSEUDOSPECTRAL MATRIX-METHOD APPROACH

A Fourier-Chebyshev pseudospectral method is used for the numerical si mulation of incompressible flows in a three-dimensional channel of squ are cross-section with rotation. Realistic, non-periodic boundary cond itions that impose no-slip conditions in two directions (spanwise and vertical directions) are used. The Navier-Stokes equations are integra ted in time using a fractional step method. The Poisson equations for pressure and the Helmholtz equation for velocity are solved using a ma trix diagonalization (eigenfunction decomposition) method, through whi ch we are able to reduce a three-dimensional matrix problem to a simpl e algebraic vector equation. This results in signficant savings in com puter storage requirement, particularly for large-scale computations. Verification of the numerical algorithm and code is carried out by com paring with a limiting case of an exact steady state solution for a on e-dimensional channel flow and also with a two-dimensional rotating ch annel case, Two-cell and four-cell two-dimensional flow patterns are o bserved in the numerical experiment. It is found that the four-cell fl ow pattern is stable to symmetrical disturbances but unstable to asymm etrical disturbances.