EFFICIENT AND FAST FINITE ELEMENT VISCOELASTIC FLUID FLOW SIMULATION EFFORTS

Yıl 2008, Sayı: 017, 91 - 104, 15.12.2008

Bayram Alakuş

Öz

In this research, we provide finite element computational developments to predict the flow behavior of a

viscoelastic fluid flow. The developments predict the velocity, pressure, and polymeric stress by modeling the

conservation laws (e.g. mass and momentum) of the flow field coupled with constitutive equations for polymeric

stress field. The simulations target a variety of viscoelastic models (e.g. Upper-Convected-Maxwell Model,

Oldroyd-B model and Giesekus model) to provide a fundamental understanding of the elastic effects on the flow

field. To solve the complex coupled nonlinear equations of the mathematical model described above, a

combination of Newton linearization and the Galerkin and Streamline-Upwinding-Petrov-Galerkin (SUPG) finite

element procedures are employed to accurately capture the representative physics.

Anahtar Kelimeler

EVSS-1 ve EVSS-2 Finite element method, viscoelastic flows, GMRES solver

VİSKOELASTİK AKIŞKAN AKIŞININ SONLU ELEMANLAR METODU İLE HIZLI VE ETKİLİ SİMULASYONU

Öz

Bu çalışmada, sonlu elemanlar metodunu kullanarak viskoelastik akışkanların etkili ve hızlı olarak sayısal

çözümü için gerekli algoritma verildi. Akış alanına ait hız, basınç, Newtonian ve polimerik gerilmeler çözüm

olarak sunuldu. Temel korunum yasaları çeşitli viskoelastik modeller (e.g. Upper-Convected-Maxwell Model,

Oldroyd-B model and Giesekus model) kullanılarak matematiksel model elde edildi. Bu model, Newton

lineerleştirme metodu, SUPG sonlu elemanlar metodu ve GMRES iterative çözüm tekniği kullanılarak çözümler

elde edildi.

Anahtar Kelimeler

EVSS-1 ve EVSS-2Sonlu elemanlar methodu, viskoelastik akışkanla, GMRES solver

Kaynakça

• [1] R. B. Bird, R. C. Armstrong, O. Hassager. “Dynamics of Polymeric Liquids, Vol. 1, Fluid Mechanics “,2nd ed., Wiley Interscience, 1987.
• [2] A.N. Brooks and T.J.R. Hughes. “Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations”, Comput. Methods Appl. Mech. Eng., 32:199, 1982
• [3] F. Shakib. “Finite element analysis of the compressible Eular and Navier-Stokes equations”, Ph.D. Dissertation, Stanford University, 1989.
• [4] R.C. King, M.R. Apelian, R.C. Armstrong and R.A. Brown. “Numerically stable finite element techniques for viscoelastic calculations in smooth and singular geometries”, J. Non-Newtonian Fluid Mech., 29:147- 216, 1988
• [5] Y. Saad and M.H. Schulz. “GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear system”, SIAM, J. Sci. Statist. Comput., 7:856-869, 1986
• [6] B. Alakus. “Finite element computations of viscoelastic fluid flows employing quasi-linear and nonlinear models”, Ph.D. Dissertation, The University of Minnesota, 2001.
• [7] M.R. Apelian, R.C. Armstrong and R.A. Brown. “Impact of the constitutive equation and singularity on the calculation of Stick-Slip flow: The modified upper-convected Maxwell model (MUCM)”, Journal of Non- Newtonian Fluid Mechanics, 27:299-321, 1988
• [8] J.M. Marchal and M.J. Crochet. “A new mixed finite element for calculating viscoelastic flow” Journal of Non-Newtonian Fluid Mechanics, 26:77-114, 1987