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A penalty finite element method for non‐Newtonian creeping flows
Author(s) -
Codina Ramon,
Cervera Miguel,
Oñate Eugenio
Publication year - 1993
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.1620360808
Subject(s) - finite element method , non newtonian fluid , iterated function , penalty method , iterative method , newtonian fluid , mathematics , compressibility , viscosity , work (physics) , pressure correction method , constitutive equation , mathematical optimization , incompressible flow , mathematical analysis , mechanics , physics , thermodynamics , quantum mechanics
In this paper we present an iterative penalty finite element method for viscous non‐Newtonian creeping flows. The basic idea is solving the equations for the difference between the exact solution and the solution obtained in the last iteration by the penalty method. For the case of Newtonian flows, one can show that for sufficiently small penalty parameters the iterates converge to the incompressible solution. The objective of the present work is to show that the iterative penalization can be coupled with the iterative scheme used to deal with the non‐linearity arising from the constitutive law of non‐Newtonian fluids. Some numerical experiments are conducted in order to assess the performance of the approach for fluids whose viscosity obeys the power law.