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A poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows
Author(s) -
Sohn J. L.,
Heinrich J. C.
Publication year - 1990
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620300209
Subject(s) - poisson's equation , penalty method , finite element method , compressibility , mathematics , spurious relationship , laminar flow , pressure correction method , poisson distribution , discrete poisson equation , mathematical analysis , uniqueness theorem for poisson's equation , physics , mathematical optimization , mechanics , boundary value problem , statistics , thermodynamics
The calculation of pressures when the penalty function approximation is used in finite element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C 0 velocity approximation using a least squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.