Alternative subcell discretisations for viscoelastic flow: Stress interpolation

Journal of Non-Newtonian Fluid Mechanics

Volumn 146, Issue 1-3, 2007, Pages 59-78

  Belblidia, F ^a   Matallah, H ^a   Puangkird, B ^a,b   Webster, M F ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b KING MONGKUT'S INSTITUTE OF TECHNOLOGY LADKRABANG   (Thailand)

Author keywords

High order pressure correction; Stability; Subcell approximations; Upwinding; Viscoelastic

Indexed keywords

APPROXIMATION THEORY; CONSTITUTIVE EQUATIONS; FINITE ELEMENT METHOD; FLUID MECHANICS; INTERPOLATION; PRESSURE; PRESSURE MEASUREMENT; STRESSES; VISCOELASTICITY;

FINITE ELEMENT DISCRETISATION; STRESS INTERPOLATION; SUBCELL APPROXIMATIONS; VISCOELASTIC FLOW;

VISCOUS FLOW;

APPROXIMATION THEORY; CONSTITUTIVE EQUATIONS; FINITE ELEMENT METHOD; FLUID MECHANICS; INTERPOLATION; PRESSURE; PRESSURE MEASUREMENT; STRESSES; VISCOELASTICITY; VISCOUS FLOW;

EID: 34548453982     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2006.12.009     Document Type: Article

References (36)

1. Wapperom P., and Webster M.F. A second-order hybrid finite-element/volume method for viscoelastic flows. J. Non-Newtonian Fluid Mech. 79 (1998) 405-431
2. Aboubacar M., and Webster M.F. A cell-vertex finite volume/element method on triangles for abrupt contraction viscoelastic flows. J. Non-Newtonian Fluid Mech. 98 (2001) 83-106
3. Aboubacar M., Matallah H., and Webster M.F. Highly elastic solutions for Oldroyd-B and Phan-Thien/Tanner fluids with a finite volume/element method: planar contraction flows. J. Non-Newtonian Fluid Mech. 103 (2002) 65-103
4. Keshtiban I.J., Belblidia F., and Webster M.F. Numerical simulation of compressible viscoelastic liquids. Non-Newtonian Fluid Mech. 122 (2004) 131-146
5. Belblidia F., Keshtiban I.J., and Webster M.F. Stabilised computations for viscoelastic flows under compressible implementations. J. Non-Newtonian Fluid Mech. 134 (2006) 56-76
6. Marchal J.M., and Crochet M.J. A new mixed finite element for calculating viscoelastic flow. J. Non-Newtonian Fluid Mech. 26 (1987) 77-114
7. Basombrio F.G., Buscaglia G.C., and Dari E.A. Simulation of highly elastic fluid flows without additional numerical diffusivity. J. Non-Newtonian Fluid Mech. 39 (1991) 189-206
8. Baaijens F.P.T. Numerical analysis of unsteady viscoelastic flow. Comp. Meth. Appl. Mech. Eng. 94 (1992) 285-299
9. Carew E.O.A., Townsend P., and Webster M.F. On a discontinuity capturing technique for Oldroyd-B fluids. J. Non-Newtonian Fluid Mech. 51 (1994) 231
10. F. Shakib, Finite Element Analysis of the Compressible Euler and Navier-Stokes Equations, Ph.D. Dissertation, Stanford University, Department of Mechanical Engineering, 1988.
11. Guénette R., and Fortin M. A new mixed finite element method for computing viscoelastic flows. J. Non-Newtonian Fluid Mech. 60 (1995) 27-52
12. Sun J., Phan-Thien N., and Tanner R.I. An adaptive viscoelastic stress splitting scheme and its applications: AVSS/SI and AVSS/SUPG. J. Non-Newtonian Fluid Mech. 65 (1996) 75-91
13. Matallah H., Nithiarasu P., and Webster M.F. Stabilisation techniques for viscoelastic flows. ECCOMAS Conf. (2001)
14. Fortin M., and Fortin A. A new approach for the FEM simulation of viscoelastic flows. J. Non-Newtonian Fluid Mech. 32 (1989) 295-310
15. Matallah H., Townsend P., and Webster M.F. Recovery and stress-splitting schemes for viscoelastic flows. J. Non-Newtonian Fluid Mech. 75 (1998) 139-166
16. Oliveira P.J., and Pinho F.T. Plane contraction flows of upper convected Maxwell and Phan-Thien-Tanner fluids as predicted by a finite-volume method. J. Non-Newtonian Fluid Mech. 88 (1999) 63-88
17. Alves M.A., Oliveira P.J., and Pinho F.T. Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions. J. Non-Newtonian Fluid Mech. 110 (2003) 45-75
18. Ghia U., Ghia K.N., and Shin C. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comp. Phys. 48 (1982) 387-411
19. Shankar P.N., and Deshpande M.D. Fluid mechanics in the driven cavity. Annu. Rev. Fluid Mech. 32 (2000) 93-136
20. Peyret R., and Taylor T.D. Computational Methods for Fluid Flow (1983), Springer-Verlag, New York
21. Renardy M. Stress integration for the constitutive law of the upper convected Maxwell fluid near the corners in a driven cavity. J. Non-Newtonian Fluid Mech. 112 (2003) 77-84
22. Fattal R., and Kupferman R. Constitutive laws for the matrix-logarithm of the conformation tensor. J. Non-Newtonian Fluid Mech. 123 (2004) 281
23. Fattal R., and Kupferman R. Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation. J. Non-Newtonian Fluid Mech. 126 (2005) 23-37
24. Afonso A., Alves M.A., Pinho F.T., and Oliveira P.J. Benchmark calculations of viscoelastic flows with a finite-volume method using the log-conformation approach. Proceeding of the Third Annual European Rheology Conference, AERC (2006) 197
25. Evans R.E., and Walters K. Flow characteristics associated with abrupt changes in geometry in the case of highly elastic liquids. J. Non-Newtonian Fluid Mech. 20 (1986) 11-29
26. Evans R.E., and Walters K. Further remarks on the lip-vortex mechanism of vortex enhancement in planar-contraction flows. Non-Newtonian Fluid Mech. 32 (1989) 95-105
27. Boger D.V. Viscoelastic flows through contractions. Annual Rev. Fluid Mech. 19 (1987) 157-182
28. Rothstein J.P., and McKinley G.H. Extensional flow of a polystyrene Boger fluid through a 4:1:4 axisymmetric contraction/expansion. J. Non-Newtonian Fluid Mech. 86 (1999) 61-88
29. Rodd L.E., Scott T.P., Boger D.V., Cooper-White J.J., and McKinley G.H. The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries. J. Non-Newtonian Fluid Mech. 129 (2005) 1-22
30. Renardy M. Current issues in non-Newtonian flows: a mathematical perspective. J. Non-Newtonian Fluid Mech. 90 (2000) 243-259
31. Waters N.D., and King M.J. Unsteady flow of an elasto-viscous liquid. Rheol. Acta 9 (1970) 11-29
32. Webster M.F., Tamaddon-Jahromi H.R., and Aboubacar M. Time-dependent algorithm for viscoelastic flow-finite element/volume schemes. Num. Meth. Partial Diff. Equ. 21 (2005) 272-296
33. Hubbard M.E., and Roe P.L. Multidimensional upwind fluctuation distribution schemes for scalar dependent problems. Int. J. Num. Meth. Fluids 33 (2000) 711-736
34. Deconinck H., Roe P.L., and Struijs R. A multidimensional generalization of Roe's flux difference splitter for the Euler equations. Comput. Fluids 22 (1993) 215-222
35. Jameson A., and Mavriplis D. Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh. AIAA 24 (1986) 611-618
36. Morton K.W., Crumpton P.I., and Mackenzie J.A. Cell vertex methods for inviscid and viscous flows. Comput. Fluids 22 (1993) 91-102