A streamline element scheme for solving viscoelastic flow problems. Part I. Differential constitutive equations

1986 ◽  
Vol 21 (2) ◽  
pp. 179-199 ◽  
Author(s):  
X.-L. Luo ◽  
R.I. Tanner
Keyword(s):  
Constitutive Equations ◽  
Viscoelastic Flow ◽  
Element Scheme ◽  
Flow Problems

Viscoelastic flow analysis using the software OpenFOAM and differential constitutive equations

2010 ◽  
Vol 165 (23-24) ◽  
pp. 1625-1636 ◽  
Author(s):  
J.L. Favero ◽  
A.R. Secchi ◽  
N.S.M. Cardozo ◽  
H. Jasak
Keyword(s):  
Constitutive Equations ◽  
Flow Analysis ◽  
Viscoelastic Flow

scholarly journals A Convergent three Field Quadrilateral Finite Element Method for Simulating Viscoelastic Flow on Irregular Meshes

1992 ◽  
pp. 391-406
Author(s):  
Victoriano Ruas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fluid Flow ◽  
Stokes System ◽  
Viscoelastic Flow ◽  
Flow Problems ◽  
Extra Stress Tensor ◽  
Irregular Meshes ◽  
Quadrilateral Finite Element ◽  
Extra Stress

In a recent paper a finite elemenJ method for solving the three field Stokes system as a basis for the numerical solution of viscoelastic fluid flow problems was introduced. The method constructed upon a biquadratic velocity, a discontinuous linear pressure and a bilinear extra stress tensor interpolation in quadrilaterals, enriched with fifteen bubble tensors, has been proved to yield second order approximations of these variables, in the case of rectangular meshes. In this work equivalent results are proven to hold in the case of irregular meshes.  

scholarly journals 50 Years of the K-BKZ Constitutive Relation for Polymers

2013 ◽  
Vol 2013 ◽  
pp. 1-22 ◽  
Author(s):  
Evan Mitsoulis
Keyword(s):  
Mathematical Modeling ◽  
Constitutive Model ◽  
Particle Tracking ◽  
Constitutive Equations ◽  
Historical Perspective ◽  
Governing Equations ◽  
Dimensionless Numbers ◽  
Flow Problems ◽  
Polymer Flows ◽  
Method Of Solution

The K-BKZ constitutive model is now 50 years old. The paper reviews the connections of the model and its variants with continuum mechanics and experiment, presenting an up-to-date recap of research and major findings in the open literature. In the Introduction a historical perspective is given on developments in the last 50 years of the K-BKZ model. Then a section follows on mathematical modeling of polymer flows, including governing equations of flow, rheological constitutive equations (with emphasis on viscoelastic integral constitutive equations of the K-BKZ type), dimensionless numbers, and boundary conditions. The Method of Solution section reviews the major developments of techniques necessary for particle tracking and calculation of the integrals for the viscoelastic stresses in flow problems. Finally, selected examples are given of successful application of the K-BKZ model in polymer flows relevant to rheology.

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