Preconditioned iterative methods for unsteady non-Newtonian flow between eccentrically rotating cylinders

SIAM Journal on Scientific Computing

Volumn 17, Issue 6, 1996, Pages 1369-1394

  Gwynllyw, D Rh ^a   Phillips, T N ^a  

^a ABERYSTWYTH UNIVERSITY   (United Kingdom)

Author keywords

Eccentrically rotating cylinders; Non Newtonian fluid; Preconditioned conjugate gradient method; Spectral element method

Indexed keywords

EID: 0000512839     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827594271044     Document Type: Article

References (21)

1. H. A. BARNES, J. F. HUTTON, AND K. WALTERS, An Introduction to Rheology, Elsevier, Amsterdam, 1989.
2. T. W. BATES, B. WILLIAMSON, J. A. SPEAROT, AND C. K. MURPHY, A Correlation Between Engine Oil Rheology and Oil Film Thickness in Engine Journal Bearing, Paper 860376, Society of Automotive Engineers, Warrendale, PA, 1986.
3. C. BERNARDI AND Y. MADAY, A collocation method over staggered grids for the Stokes problem, Internat. J. Numer. Methods Fluids, 8 (1988), pp. 537-557.
4. C. BERNARDI, C. CANUTO, AND Y. MADAY, Generalized inf-sup condition for Chebyshev spectral approximation of the Stokes problem, SIAM J. Numer. Anal., 25 (1988), pp. 1237-1271.
5. C. BERNARDI, Y. MADAY, AND B. METIVET, Calcul de la pression dans la résolution spectrale du problème de Stokes, La Researche Aérospatiale, 1 (1987), pp. 1-21.
6. G. BIRKHOFF AND R. E. LYNCH, Numerical Solution of Elliptic Problems, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1984.
7. J. CAHOUET AND J.-P. CHABARD, Some fast 3D finite element solvers for the generalized Stokes problem, Internat. J. Numer. Methods Fluids, 8 (1988), pp. 869-895.
8. M. J. DAVIES AND K. WALTERS, The behaviour of non-Newtonian lubricants in journal bearings - a theoretical study, in Rheology of Lubricants, T. C. Davenport, ed., Applied Science Publishers, Barking, UK, 1972, pp. 65-80.
9. G. GOLUB AND C. VAN LOAN, Matrix Computations, The Johns Hopkins Press, Baltimore, MD, 1989.
10. W. J. GORDON AND C. A. HALL, Construction of curvilinear coordinate systems and application to mesh generation, Internat. J. Numer. Methods Engrg., 7 (1973), pp. 461-477.
11. K. Z. KORCZAK AND A. T. PATERA, Isoparametric spectral element method for solution of the Navier-Stokes equations in complex geometry, J. Comput. Phys., 62 (1986), pp. 361-382.
12. P. F. FISCHER AND A. T. PATERA, Parallel spectral element solution of the Stokes problem, J. Comput. Phys., 92 (1991), pp. 380-421.
13. X. K. LI AND A. R. DAVIES, Numerical modelling of nonisothermal viscoelastic flow between eccentrically rotating cylinders, in Proc. IUTAM Symposium on Numerical Simulation of Nonisothermal Viscoelastic Flows, Kluwer, The Netherlands, 1995, pp. 159-177.
14. Y. MADAY, D. MEIRON, A. T. PATERA, AND E. M. RØNQUIST, Analysis of iterative methods for the steady and unsteady Stokes problem: Application to spectral element discretizations, SIAM J. Sci. Comput., 14 (1993), pp. 310-337.
15. Y. MADAY AND A. T. PATERA, Spectral element methods for the incompressible Navier-Stokes equations, in State of the Art Surveys in Computational Mechanics, A. K. Noor and J. T. Oden, eds., American Society of Mechanical Engineers, New York, 1989, pp. 71-143.
16. Y. MADAY, A. T. PATERA, AND E. M. RØNQUIST, An operator-integration-factor splitting method for time-dependent problems. Application to incompressible fluid flow, J. Sci. Comput., 5 (1990), pp. 263-292.
17. N-2 method for the approximation of the Stokes problem, Numer. Math., (1996), to appear.
18. T. N. PHILLIPS AND G. W. ROBERTS, The treatment of spurious pressure modes in spectral incompressible flow calculations, J. Comput. Phys., 105 (1993), pp. 150-164.
19. G. W. ROBERTS, A. R. DAVIES, AND T. N. PHILLIPS, Three-dimensional spectral approximations to Stokes flow between eccentrically rotating cylinders, Internat. J. Numer. Methods Fluids, 13 (1991), pp. 217-233.
20. G. W. ROBERTS AND K. WALTERS, On viscoelastic effects in journal-bearing lubrication, Rheol. Acta, 31 (1992), pp. 55-62.
21. G. SAACHI LANDRIANI AND H. VANDEVEN, A multidomain spectral collocation method for the Stokes problem, Numer. Math., 58 (1990), pp. 441-464.