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Periodic viscous flow: A bench‐mark problem
Author(s) -
Goldberg I. S.,
Carey G. F.,
McLay R.,
Phinney L.
Publication year - 1990
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650110106
Subject(s) - rotational symmetry , flow (mathematics) , mathematics , cylinder , computational fluid dynamics , mechanics , potential flow around a circular cylinder , stokes flow , series (stratigraphy) , geometry , open channel flow , physics , geology , paleontology
A double‐transform technique provides a semi‐analytic solution in the form of a series expansion for unsteady axisymmetric Stokes flow in the entrance region of a semi‐infinite rigid cylindrical tube. This in turn offers an appropriate bench‐mark problem for evaluating the quality of numerical approximations. To illustrate this, periodic axial flow in a circular cylinder is considered. Some aspects of the bench‐mark problem that are of interest include the reverse flow in the wall layers, the accuracy of the approximate method in different flow regimes and the mesh grading. This bench‐mark problem and the numerical study provide some insight into practical issues pertinent to the approximate solution of unsteady and periodic flows.