Finite element solutions of nonsteady incompressible viscous flow between two rotating concentric spheres

Article

Mossad, Raos Riad. 1993. "Finite element solutions of nonsteady incompressible viscous flow between two rotating concentric spheres." Computers and Fluids. 22 (6), pp. 697-711. https://doi.org/10.1016/0045-7930(93)90034-7
Article Title

Finite element solutions of nonsteady incompressible viscous flow between two rotating concentric spheres

ERA Journal ID5111
Article CategoryArticle
AuthorsMossad, Raos Riad
Journal TitleComputers and Fluids
Journal Citation22 (6), pp. 697-711
Number of Pages15
Year1993
Place of PublicationUnited Kingdom
ISSN0045-7930
1879-0747
Digital Object Identifier (DOI)https://doi.org/10.1016/0045-7930(93)90034-7
Web Address (URL)https://www.sciencedirect.com/science/article/abs/pii/0045793093900347
Abstract

The problem of unsteady, incompressible viscous flow between two rotating concentric spheres has been investigated here. The full Navier-Stokes equations in terms of the velocity components u, v w and the pressure p, using spherical coordinates for axially symmetric flow, were solved by means of the finite element method in the spatial dimension and the alternating-direction method in the time dimension using Glowinski's algorithm. The element used is an annular-sector-type element with a bilinear approximation for the velocity components and with constant pressure within the element. Reynolds numbers in the range from 1 to 1000, gap size 0.5 and different combinations of the angular velocity of the inner and outer spheres were studied. In some of these cases a steady-state solution was possible, while in others only a transient solution was possible. This method proved to be successful and powerful in predicting the behavior of the flow for these nonlinear-type problems. © 1993.

KeywordsAlgorithms; Approximation theory; Computer software; Differential equations; Finite element method; Mathematical models; Pressure; Spheres; Unsteady flow; Velocity
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Byline AffiliationsUniversity College of Southern Queensland
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