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A DECOUPLED FINITE ELEMENT METHOD TO COMPUTE STATIONARY UPPERCONVECTED MAXWELL FLUID FLOW IN 2D CONVERGENT GEOMETRY

A DECOUPLED FINITE ELEMENT METHOD TO COMPUTE STATIONARY UPPERCONVECTED MAXWELL FLUID FLOW IN 2D... In this study, the stationary flow of a polymeric fluid governed by the upper convected Maxwell law is computed in a 2D convergent geometry. A finite element method is used to obtain nonlinear discretized equations, solved by an iterative Picard fixed point algorithm. At each step, two subsystems are successively solved. The first one represents a Newtonian fluid flow Stokes equations perturbed by known pseudobody forces expressing fluid elasticity. It is solved by minimization of a functional of the velocity field, while the pressure is eliminated by penalization. The second subsystem reduces to the tensorial differential evolution equation of the extrastress tensor for a given velocity field. It is solved by the socalled nonconsistent PetrovGalerkin streamline upwind method. As with other decoupled techniques applied to this problem, our simulation fails for relatively low values of the Weissenberg viscoelastic number. The value of the numerical limit point depends on the mesh refinement. When convergence is reached, the numerical solutions for velocity, pressure and stress fields are similar to those obtained by other authors with very costly mixed methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations: International Journal for Computer-Aided Engineering and Software Emerald Publishing

A DECOUPLED FINITE ELEMENT METHOD TO COMPUTE STATIONARY UPPERCONVECTED MAXWELL FLUID FLOW IN 2D CONVERGENT GEOMETRY

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References (13)

Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0264-4401
DOI
10.1108/eb023873
Publisher site
See Article on Publisher Site

Abstract

In this study, the stationary flow of a polymeric fluid governed by the upper convected Maxwell law is computed in a 2D convergent geometry. A finite element method is used to obtain nonlinear discretized equations, solved by an iterative Picard fixed point algorithm. At each step, two subsystems are successively solved. The first one represents a Newtonian fluid flow Stokes equations perturbed by known pseudobody forces expressing fluid elasticity. It is solved by minimization of a functional of the velocity field, while the pressure is eliminated by penalization. The second subsystem reduces to the tensorial differential evolution equation of the extrastress tensor for a given velocity field. It is solved by the socalled nonconsistent PetrovGalerkin streamline upwind method. As with other decoupled techniques applied to this problem, our simulation fails for relatively low values of the Weissenberg viscoelastic number. The value of the numerical limit point depends on the mesh refinement. When convergence is reached, the numerical solutions for velocity, pressure and stress fields are similar to those obtained by other authors with very costly mixed methods.

Journal

Engineering Computations: International Journal for Computer-Aided Engineering and SoftwareEmerald Publishing

Published: Mar 1, 1992

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