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Multivariant finite elements for three‐dimensional simulation of viscous incompressible flows
Author(s) -
Gupta Mahesh,
Kwon Tai H.,
Jaluria Yogesh
Publication year - 1992
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.1650140505
Subject(s) - classification of discontinuities , mathematics , compressibility , geometry , finite element method , mathematical analysis , boundary value problem , slip (aerodynamics) , flow (mathematics) , mechanics , physics , thermodynamics
Within multivariant elements, which have restricted degrees of freedom at some nodes, different velocity components have different variations. Shape functions for the multivariant elements Q 1 +P o and R 2 +P o are developed. With such shape functions the value of a velocity component within a multivariant element is shown to depend upon all the independent components of velocity at the nodes of the element. The use of the Q 1 P 0 element to simulate flows with discontinuous boundary conditions generated disturbance throughout the flow domain, giving erroneous pressure and velocity distributions. The Q 1 +P o element restricted the disturbance due to such discontinuities to a small region near the singular points, whereas the P 2 +P o element completely eliminated the fluctuations. Flows with discontinuous boundary conditions were simulated with reasonable accuracy by partially relaxing the no‐slip condition on the Q 1 P o elements near the singular points.