TY - JOUR
T1 - Three-dimensional viscous flow through a rotating channel
T2 - A pseudospectral matrix method approach
AU - Chen, H. B.
AU - Nandakumar, K.
AU - Finlay, W. H.
AU - Ku, H. C.
PY - 1996/8/30
Y1 - 1996/8/30
N2 - A Fourier-Chebyshev pseudospectral method is used for the numerical simulation of incompressible flows in a three-dimensional channel of square cross-section with rotation. Realistic, non-periodic boundary conditions that impose no-slip conditions in two directions (spanwise 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 symmetrical disturbances but unstable to asymmetrical disturbances.
AB - A Fourier-Chebyshev pseudospectral method is used for the numerical simulation of incompressible flows in a three-dimensional channel of square cross-section with rotation. Realistic, non-periodic boundary conditions that impose no-slip conditions in two directions (spanwise 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 symmetrical disturbances but unstable to asymmetrical disturbances.
KW - Eigenvalue decomposition
KW - Pseudospectral matrix method
KW - Rotating flow
KW - Three-dimensional rectangular channel
KW - Two- and four-cell flow pattern
UR - http://www.scopus.com/inward/record.url?scp=0030221494&partnerID=8YFLogxK
U2 - 10.1002/(sici)1097-0363(19960830)23:4<379::aid-fld427>3.0.co;2-6
DO - 10.1002/(sici)1097-0363(19960830)23:4<379::aid-fld427>3.0.co;2-6
M3 - 文章
AN - SCOPUS:0030221494
SN - 0271-2091
VL - 23
SP - 379
EP - 396
JO - International Journal for Numerical Methods in Fluids
JF - International Journal for Numerical Methods in Fluids
IS - 4
ER -