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On the performance of quadrilateral finite elements in the solution to the Stokes equations in periodic structures
Author(s) -
Sáez A. E.,
Carbonell R. G.
Publication year - 1985
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.1650050702
Subject(s) - quadrilateral , mathematics , finite element method , convergence (economics) , stokes flow , newtonian fluid , flow (mathematics) , node (physics) , mathematical analysis , rate of convergence , lagrangian , boundary value problem , mechanics , geometry , physics , computer science , computer network , channel (broadcasting) , quantum mechanics , economics , thermodynamics , economic growth
The use of the finite element method in solving the problem of flow of a Newtonian fluid in periodically constricted tubes is explored. The performance of eight node serendipity and nine node Lagrangian elements is compared. It was found that the Lagrangian element results in unstable velocity fields when stagnant or recirculation regions are present. This is characteristic of tubes with large expansion zones. The eight node element does not exhibit instabilities. Both elements give accurate pressure fields. This behaviour is contrary to traditional results obtained for flow problems with similar geometrical characteristics. This suggests that the periodicity of the boundary conditions might be the cause of the instabilities in the numerical solution. The use of the continuity equation to simplify the viscous terms in the Stokes equations resulted, in this particular case, in a deterioration of the rate of convergence of the algorithm.