Numerical approximation of the spectra of Phan-Thien Tanner liquids

Numerical Algorithms

Volumn 38, Issue 1-3, 2005, Pages 133-153

  Palmer, A S ^a   Phillips, T N ^a,b  

^a ABERYSTWYTH UNIVERSITY   (United Kingdom)

^b CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Chebyshev approximation; Generalized eigenvalue problem; Linear stability analysis; Phan Thien Tanner liquid

Indexed keywords

EID: 23944524142     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-004-2862-3     Document Type: Article

References (14)

1. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods in Fluid Dynamics (Springer, Berlin, 1988).
2. A.M. Grillet, A.C.B. Bogaerds, G.W.M. Peters and F.P.T. Baaijens, Stability analysis of constitutive equations for polymer melts in viscometric flows, J. Non-Newtonian Fluid Mech. 103 (2002) 221-250.
3. C.D. Han, Rheology in Polymer Processing (Academic Press, New York, 1976).
4. T.C. Ho and M.M. Denn, Stability of plane Poiseuille flow of a highly elastic liquid, J. Non-Newtonian Fluid Mech. 3 (1977/1978) 179-195.
5. R.A. Keiller, Numerical instability of time-dependant flows, J. Non-Newtonian Fluid Mech. 43 (1992) 229-246.
6. R.G. Larson, Instabilities in viscoelastic flows, Rheol. Acta. 31 (1992) 213-263.
7. C.C. Lin, The Theory of Hydrodynamic Stability (Cambridge Univ. Press, Cambridge, 1955).
8. Maple V 5.1, Waterloo Maple Inc., Ontario, Canada.
9. NAG Library Mark 22, NAG, Oxford, UK.
10. N. Phan-Thien, A nonlinear network viscoelastic model, J. Rheol. 22 (1978) 259-283.
11. N. Phan-Thien and R.I. Tanner, A new constitutive equation derived from network theory, J. Non-Newtonian Fluid Mech. 2 (1977) 353-365.
12. K.C. Porteous and M.M. Denn, Linear stability of plane Poiseuille flow of viscoelastic liquids, Trans. Soc. Rheol. 16 (1972) 295-308.
13. R. Sureshkumar and A.N. Beris, Linear stability analysis of viscoelastic Poiseuille flow using an Arnoldi-based orthogonalization algorithm, J. Non-Newtonian Fluid Mech. 56 (1995) 151-182.
14. H.J. Wilson, M. Renardy and Y. Renardy, Structure of the spectrum in zero Reynolds number shear flow of the UCM and Oldroyd-B liquids, J. Non-Newtonian Fluid Mech. 80 (1999) 251-268.