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THREE-DIMENSIONAL VISCOUS FLOW THROUGH A ROTATING CHANNEL: A PSEUDOSPECTRAL MATRIX METHOD APPROACH
Ist Teil von
International journal for numerical methods in fluids, 1996-08, Vol.23 (4), p.379-396
Ort / Verlag
Sussex: John Wiley & Sons, Ltd
Erscheinungsjahr
1996
Link zum Volltext
Quelle
Wiley Online Library Journals Frontfile Complete
Beschreibungen/Notizen
A Fourier–Chebyshev pseudospectral method is used for the numerical simulation of incompressible flows in a three‐dimensio nal channel of square cross‐section with rotation. Realistic, non‐periodic boundary conditions that impose no‐slip conditions in two directions (spanwis e and vertical directions) are used. The Navier–Stokes equations are integrated in time using a fractional step method. The Poisson equations for pressure and the Helmholtz equation for velocity are solved using a matrix diagonalization (eigenfunction decomposition) method, through which we are able to reduce a three‐dimensional matrix problem to a simple algebraic vector equation. This results in signficant savings in computer storage requirement, particularly for large‐scale computations. Verification of the numerical algorithm and code is carried out by comparing with a limiting case of an exact steady state solution for a one‐dimensional channel flow and also with a two‐dimensional rotating channel case. Two‐cell and four‐cell two‐dimensional flow patterns are observed in the numerical experiment. It is found that the four‐cell flow pattern is stable to symmetri cal disturbances but unstable to asymmetrical disturbances.