Stabilised computations for viscoelastic flows under compressible implementations

Journal of Non-Newtonian Fluid Mechanics

Volumn 134, Issue 1-3 SPEC. ISS., 2006, Pages 56-76

  Belblidia, F ^a   Keshtiban, I J ^a   Webster, M F ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Compressible; Critical Weissenberg number; High order incremental pressure correction; Low Mach number; Oldroyd B; Planar contraction; Strain rate stabilisation; Vortex activity

Indexed keywords

COMPRESSIBLE FLOW; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; MATHEMATICAL MODELS; STRAIN RATE; STRESS ANALYSIS; VISCOELASTICITY; VORTEX FLOW;

CRITICAL WEISSENBERG NUMBER; PLANAR CONTRACTION; STRAIN RATE STABILISATION; VORTEX ACTIVITY;

FLUID MECHANICS;

COMPRESSIBLE FLOW; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; FLUID MECHANICS; MATHEMATICAL MODELS; STRAIN RATE; STRESS ANALYSIS; VISCOELASTICITY; VORTEX FLOW;

EID: 33645109504     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2005.12.003     Document Type: Article

References (43)

1. K. Walters M.F. Webster The distinctive CFD challenges of computational rheology Int. J. Numer. Meth. Fluids 43 2003 577-596
2. I.J. Keshtiban F. Belblidia M.F. Webster Numerical simulation of compressible viscoelastic liquids J. Non-Newtonian Fluid Mech. 122 2004 131-146
3. M.F. Webster I.J. Keshtiban F. Belblidia Computation of weakly-compressible highly-viscous liquid flows Eng. Comput. 21 2004 777-804
4. M.F. Webster H.R. Tamaddon-Jahromi M. Aboubacar Time-dependent algorithm for viscoelastic flow-finite element/volume schemes Numer. Meth. Partial Diff. Eqn. 21 2005 272-296
5. R. Keunings Simulation of viscoelastic flow C.L. Tucker Proceedings of the Computer Modeling for Polymer Processing Conference 1989 404-469
6. F.P.T. Baaijens Mixed finite element methods for viscoelastic flow analysis: A review J. Non-Newtonian Fluid Mech. 79 1998 361-385
7. R. Codina O.C. Zienkiewicz CBS versus GLS stabilization of the incompressible Navier-Stokes equations and the role of the time step as stabilization parameter Comm. Numer. Meth. Eng. 18 2002 99-112
8. J.L. Guermond L. Quartapelle On stability and convergence of projection methods based on pressure Poisson equation Int. J. Numer. Meth. Fluids 26 1998 1039-1054
9. M. Aboubacar M.F. Webster A cell-vertex finite volume/element method on triangles for abrupt contraction viscoelastic flows J. Non-Newtonian Fluid Mech. 98 2001 83-106
10. T. De Mulder The role of bulk viscosity in stabilized finite element formulations for incompressible flow: A review Comp. Meth. Appl. Mech. Eng. 163 1998 1-10
11. F. Belblidia, I.J. Keshtiban, M.F. Webster, Stabilised computations for incompressible and mildly compressible viscoelastic flows, Report No. CSR 01-2005, Computer Science Department, University of Wales Swansea, UK. http://www-compsci.swan.ac.uk/reports/.
12. H. Matallah P. Townsend M.F. Webster Recovery and stress-splitting schemes for viscoelastic flows J. Non-Newtonian Fluid Mech. 75 1998 139-166
13. E.O.A. Carew P. Townsend M.F. Webster A Taylor-Petrov-Galerkin algorithm for viscoelastic flow J. Non-Newtonian Fluid Mech. 50 1993 253-287
14. P. Wapperom M.F. Webster Simulation for viscoelastic flow by a finite volume/element method Comp. Meth. Appl. Mech. Eng. 180 1999 281-304
15. J.M. Marchal M.J. Crochet A new mixed finite element for calculating viscoelastic flow J. Non-Newtonian Fluid Mech. 26 1987 77-114
16. F.G. Basombrio G.C. Buscaglia E.A. Dari Simulation of highly elastic fluid flows without additional numerical diffusivity J. Non-Newtonian Fluid Mech. 39 1991 189-206
17. F. Brezzi M. Fortin Mixed and Hybrid Finite Elements Methods 1991 Springer-Verlag New York
18. M. Fortin A. Fortin A new approach for the FEM simulation of viscoelastic flows J. Non-Newtonian Fluid Mech. 32 1989 295-310
19. F.P.T. Baaijens An iterative solver for the DEVSS/DG method with application to smooth and non-smooth flows of the upper convected Maxwell fluid J. Non-Newtonian Fluid Mech. 75 1998 119-138
20. O.C. Zienkiewicz J.Z. Zhu The superconvergent patch recovery and a posteriori error estimates. Part 1. The recovery technique Int. J. Numer. Meth. Eng. 33 1992 1331-1364
21. J. Sun N. Phan-Thien R.I. Tanner An adaptive viscoelastic stress splitting scheme and its applications: AVSS/SI and AVSS/SUPG J. Non-Newtonian Fluid Mech. 65 1996 75-91
22. H. Matallah P. Nithiarasu M.F. Webster Stabilisation techniques for viscoelastic flows Proceedings of the ECCOMAS Conference 2001
23. M. Aboubacar T.N. Phillips H.R. Tamaddon-Jahromi B.A. Snigerev M.F. Webster High-order finite volume methods for viscoelastic flow problems J. Comput. Phys. 199 2004 16-40
24. R. Guénette M. Fortin A new mixed finite element method for computing viscoelastic flows J. Non-Newtonian Fluid Mech. 60 1995 27-52
25. W.M.H. Verbeeten G.W.M. Peters F.P.T. Baaijens Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model J. Non-Newtonian Fluid Mech. 117 2004 73-84
26. I.J. Keshtiban F. Belblidia M.F. Webster Computation of incompressible and weakly-compressible viscoelastic liquids flow: Finite element/volume schemes J. Non-Newtonian Fluid Mech. 126 2005 123-143
27. M.F. Webster H.R. Tamaddon-Jahromi M. Aboubacar Transient viscoelastic flows in planar contractions J. Non-Newtonian Fluid Mech. 118 2004 83-101
28. M.A. Alves P.J. Oliveira F.T. Pinho Benchmark solutions for the flow of Oldroyd-B and PTT fluids in planar contractions J. Non-Newtonian Fluid Mech. 110 2003 45-75
29. M. Renardy Current issues in non-Newtonian flows: A mathematical perspective J. Non-Newtonian Fluid Mech. 90 2000 243-259
30. E.O.A. Carew P. Townsend M.F. Webster On a discontinuity capturing technique for Oldroyd-B fluids J. Non-Newtonian Fluid Mech. 51 1994 231
31. A. Jameson W. Schmidt E. Turkel Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes AIAA, Proceedings of the 14th Fluid and Plasma Dynamic Conference 1981 1259-1276
32. J.M. Rallison E.J. Hinch The flow of an Oldroyd fluid past a re-entrant corner: The downstream boundary layer J. Non-Newtonian Fluid Mech. 116 2004 141-162
33. T. Hagen M. Renardy Boundary layer analysis of the Phan-Thien-Tanner and Giesekus model in high Weissenberg number flow J. Non-Newtonian Fluid Mech. 73 1997 181-189
34. M. Aboubacar H. Matallah M.F. Webster 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
35. S.S. Edussuriya A.J. Williams C. Bailey A cell-centred finite volume method for modelling viscoelastic flow J. Non-Newtonian Fluid Mech. 117 2004 47-61
36. P.J. Oliveira F.T. Pinho 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
37. R.E. Evans K. Walters Flow characteristics associated with abrupt changes in geometry in the case of highly elastic liquids J. Non-Newtonian Fluid Mech. 20 1986 11-29
38. R.E. Evans K. Walters Further remarks on the lip-vortex mechanism of vortex enhancement in planar-contraction flows J. Non-Newtonian Fluid Mech. 32 1989 95-105
39. G.H. McKinley W.P. Raiford R.A. Brown R.C. Armstrong Nonlinear dynamics of viscoelastic flow in axisymmetric abrupt contractions J. Fluid Mech. 223 1991 411-456
40. D.V. Boger Viscoelastic flows through contractions Annu. Rev. Fluid Mech. 19 1987 157-182
41. S.-C. Xue N. Phan-Thien R.I. Tanner Three dimensional numerical simulations of viscoelastic flows through planar contractions J. Non-Newtonian Fluid Mech. 74 1998 195-245
42. M.A. Alves F.T. Pinho P.J. Oliveira Effect of a high-resolution differencing scheme on finite-volume predictions of viscoelastic flows J. Non-Newtonian Fluid Mech. 93 2000 287-314
43. M. Aboubacar H. Matallah H.R. Tamaddon-Jahromi M.F. Webster Numerical prediction of extensional flows in contraction geometries: Hybrid finite volume/element method J. Non-Newtonian Fluid Mech. 104 2002 125-164