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Volumn 82, Issue 1, 1999, Pages 57-104

Linear stability and dynamics of viscoelastic flows using time-dependent numerical simulations

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; CYLINDERS (SHAPES); EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; INTEGRATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; SHEAR FLOW; VISCOELASTICITY; VORTEX FLOW;

EID: 0033117138     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0257(98)00129-3     Document Type: Article
Times cited : (66)

References (52)
  • 1
    • 84985609786 scopus 로고
    • Instabilities in polymer processing
    • C.J.S. Petrie, M.M. Denn, Instabilities in polymer processing, AIChE J. 22 (1976) 209-236.
    • (1976) AIChE J. , vol.22 , pp. 209-236
    • Petrie, C.J.S.1    Denn, M.M.2
  • 2
    • 33751371137 scopus 로고
    • Instabilities in viscoelastic flows
    • R.G. Larson, Instabilities in viscoelastic flows, Rheol. Acta 31 (1992) 213-263.
    • (1992) Rheol. Acta , vol.31 , pp. 213-263
    • Larson, R.G.1
  • 3
    • 0344936448 scopus 로고    scopus 로고
    • Purely elastic instabilities in viscometric flows
    • E.S.G. Shaqfeh, Purely elastic instabilities in viscometric flows, Ann. Rev. Fluid Mech. 28 (1996) 129-185.
    • (1996) Ann. Rev. Fluid Mech. , vol.28 , pp. 129-185
    • Shaqfeh, E.S.G.1
  • 4
    • 0002807741 scopus 로고
    • The principle of minimized iteration in the solution of matrix eigenvalue problems
    • W.E. Arnoldi, The principle of minimized iteration in the solution of matrix eigenvalue problems, Quart. Appl. Math. 9 (1951) 17-29.
    • (1951) Quart. Appl. Math. , vol.9 , pp. 17-29
    • Arnoldi, W.E.1
  • 5
    • 49149143501 scopus 로고
    • Variations on Arnoldi's methods for computing eigenelements of large non-symmetric matrices
    • Y. Saad, Variations on Arnoldi's methods for computing eigenelements of large non-symmetric matrices, Linear Algebra Appl. 34 (1980) 269-295.
    • (1980) Linear Algebra Appl. , vol.34 , pp. 269-295
    • Saad, Y.1
  • 6
    • 0000386060 scopus 로고
    • An Arnoldi-based iterative scheme for non-symmetric matrix pencils arising in finite element stability problems
    • R. Natarajan, An Arnoldi-based iterative scheme for non-symmetric matrix pencils arising in finite element stability problems, J. Comput. Phys. 100 (1992) 128-142.
    • (1992) J. Comput. Phys. , vol.100 , pp. 128-142
    • Natarajan, R.1
  • 7
    • 0027396797 scopus 로고
    • The instability of the flow past spheres and discs
    • R. Natarajan, A. Acrivos, The instability of the flow past spheres and discs, J. Fluid Mech. 254 (1993) 323-344.
    • (1993) J. Fluid Mech. , vol.254 , pp. 323-344
    • Natarajan, R.1    Acrivos, A.2
  • 8
    • 0029239963 scopus 로고
    • Linear stability analysis of viscoelastic Poiseuille flow using an Arnoldi-based orthogonalization algorithm
    • R. Sureshkumar, 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.
    • (1995) J. Non-Newtonian Fluid Mech. , vol.56 , pp. 151-182
    • Sureshkumar, R.1    Beris, A.N.2
  • 9
    • 0000094594 scopus 로고
    • An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
    • C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Natl. Bur. Stand. 45 (1950) 255-280.
    • (1950) J. Res. Natl. Bur. Stand. , vol.45 , pp. 255-280
    • Lanczos, C.1
  • 11
    • 0030111626 scopus 로고    scopus 로고
    • Stability of viscoelastic flows between eccentric rotating cylinders
    • A. Chawda, M. Avgousti, Stability of viscoelastic flows between eccentric rotating cylinders, J. Non-Newtonian Fluid Mech. 63 (1996) 97.
    • (1996) J. Non-Newtonian Fluid Mech. , vol.63 , pp. 97
    • Chawda, A.1    Avgousti, M.2
  • 12
    • 0026838278 scopus 로고
    • Finite amplitude time-periodic states in viscoelastic Taylor-Couette flow of a UCM fluid
    • P. Northey, R.C. Armstrong, R.A. Brown, Finite amplitude time-periodic states in viscoelastic Taylor-Couette flow of a UCM fluid, J. Non-Newtonian Fluid Mech. 42 (1992) 117-140.
    • (1992) J. Non-Newtonian Fluid Mech. , vol.42 , pp. 117-140
    • Northey, P.1    Armstrong, R.C.2    Brown, R.A.3
  • 13
    • 0027627138 scopus 로고
    • Spectral methods for the viscoelastic time-dependent flow equations with applications to Taylor-Couette flow
    • M. Avgousti, B. Liu, A.N. Beris, Spectral methods for the viscoelastic time-dependent flow equations with applications to Taylor-Couette flow, Int. J. Numer. Methods Fluids. 17 (1993) 49-74.
    • (1993) Int. J. Numer. Methods Fluids. , vol.17 , pp. 49-74
    • Avgousti, M.1    Liu, B.2    Beris, A.N.3
  • 14
    • 34250073348 scopus 로고
    • On the numerical stability of mixed finite-element methods for viscoelastic flows governed by differential constitutive equations
    • R.A. Brown, M.J. Szady, P.J. Northey, R.C. Armstrong, On the numerical stability of mixed finite-element methods for viscoelastic flows governed by differential constitutive equations, Theoret. Comput. Fluid Dyn. 6 (1993) 77-106.
    • (1993) Theoret. Comput. Fluid Dyn. , vol.6 , pp. 77-106
    • Brown, R.A.1    Szady, M.J.2    Northey, P.J.3    Armstrong, R.C.4
  • 17
    • 0027392527 scopus 로고
    • Energy growth in viscous channels
    • S.C. Reddy, D.S. Henningson, Energy growth in viscous channels, J. Fluid Mech. 252 (1993) 209-238.
    • (1993) J. Fluid Mech. , vol.252 , pp. 209-238
    • Reddy, S.C.1    Henningson, D.S.2
  • 18
    • 0026223132 scopus 로고
    • Observations on the elastic instability in cone-and-plate and parallel-plate flows of a polyisobutylene Boger fluid
    • G.H. McKinley, J.A. Byars, R.A. Brown, R.C. Armstrong, Observations on the elastic instability in cone-and-plate and parallel-plate flows of a polyisobutylene Boger fluid, J. Non-Newtonian Fluid Mech. 40 (1991) 201-229.
    • (1991) J. Non-Newtonian Fluid Mech. , vol.40 , pp. 201-229
    • McKinley, G.H.1    Byars, J.A.2    Brown, R.A.3    Armstrong, R.C.4
  • 19
    • 0028768562 scopus 로고
    • Non-axisymmetric, subcritical bifurcations in viscoelastic Taylor-Couette Flow
    • R. Sureshkumar, A.N. Beris, M. Avgousti, Non-axisymmetric, subcritical bifurcations in viscoelastic Taylor-Couette Flow, Proc. R. Soc. London Series A. 447 (1994) 135-153.
    • (1994) Proc. R. Soc. London Series A , vol.447 , pp. 135-153
    • Sureshkumar, R.1    Beris, A.N.2    Avgousti, M.3
  • 20
    • 0030088274 scopus 로고    scopus 로고
    • Hopf-Hopf and steady-Hopf mode interactions in Taylor-Couette flow of an upper convected Maxwell liquid
    • M. Renardy, Y. Renardy, R. Sureshkumar, A.N. Beris, Hopf-Hopf and steady-Hopf mode interactions in Taylor-Couette flow of an upper convected Maxwell liquid, J. Non-Newtonian Fluid Mech. 63 (1996) 1-31.
    • (1996) J. Non-Newtonian Fluid Mech. , vol.63 , pp. 1-31
    • Renardy, M.1    Renardy, Y.2    Sureshkumar, R.3    Beris, A.N.4
  • 21
    • 0000064075 scopus 로고
    • On a linear instability of a plane parallel Couette flow of viscoelastic fluid
    • V.A. Gorodtsov, A.I. Leonov, On a linear instability of a plane parallel Couette flow of viscoelastic fluid, J. Appl. Math. Mech. 31 (1967) 310-319.
    • (1967) J. Appl. Math. Mech. , vol.31 , pp. 310-319
    • Gorodtsov, V.A.1    Leonov, A.I.2
  • 22
    • 0022795184 scopus 로고
    • Linear stability of plane couette flow of an upper convected Maxwell fluid
    • M. Renardy, Y. Renardy, Linear stability of plane couette flow of an upper convected Maxwell fluid, J. Non-Newtonian Fluid Mech. 22 (1986) 23-33.
    • (1986) J. Non-Newtonian Fluid Mech. , vol.22 , pp. 23-33
    • Renardy, M.1    Renardy, Y.2
  • 23
    • 0026465763 scopus 로고
    • A rigorous stability proof for plane Couette flow of an upper convected Maxwell fluid at zero Reynolds number
    • M. Renardy, A rigorous stability proof for plane Couette flow of an upper convected Maxwell fluid at zero Reynolds number, Eur. J. Mech., B/Fluids. 11 (1992) 511-516.
    • (1992) Eur. J. Mech., B/Fluids. , vol.11 , pp. 511-516
    • Renardy, M.1
  • 24
    • 0026801646 scopus 로고
    • Finite element methods for Navier-Stokes equations
    • R. Glowinski, O. Pironneau, Finite element methods for Navier-Stokes equations, Ann. Rev. Fluid Mech. 24 (1989) 167-204.
    • (1989) Ann. Rev. Fluid Mech. , vol.24 , pp. 167-204
    • Glowinski, R.1    Pironneau, O.2
  • 25
    • 0002166066 scopus 로고
    • A new θ-scheme algorithm and incompressible FEM for viscoelastic fluid flows
    • P. Saramito, A new θ-scheme algorithm and incompressible FEM for viscoelastic fluid flows, Math. Modelling and Numer. Anal. 28 (1994) 1-35.
    • (1994) Math. Modelling and Numer. Anal. , vol.28 , pp. 1-35
    • Saramito, P.1
  • 26
    • 0028431277 scopus 로고
    • Flow characteristics of viscoelastic fluids in an abrupt contraction by using numerical modeling
    • P. Saramito, J.M. Piau, Flow characteristics of viscoelastic fluids in an abrupt contraction by using numerical modeling, J. Non-Newtonian Fluid Mech. 52 (1994) 263-288.
    • (1994) J. Non-Newtonian Fluid Mech. , vol.52 , pp. 263-288
    • Saramito, P.1    Piau, J.M.2
  • 27
    • 0002058827 scopus 로고
    • The numerical solution of parabolic and elliptic differential equations
    • D. Peaceman, H. Rachford, The numerical solution of parabolic and elliptic differential equations, J. Siam 3 (1955) 28-41.
    • (1955) J. Siam , vol.3 , pp. 28-41
    • Peaceman, D.1    Rachford, H.2
  • 29
    • 0003709643 scopus 로고
    • Prentice-Hall, Englewood-Cliffs, NJ
    • G.F. Carey, J.T. Oden, Finite Elements, vol. 6, Prentice-Hall, Englewood-Cliffs, NJ, 1986.
    • (1986) Finite Elements , vol.6
    • Carey, G.F.1    Oden, J.T.2
  • 30
    • 0024068483 scopus 로고
    • Creeping flow of dilute polymer solutions past cylinders and spheres
    • M.D. Chilcott, J.M. Rallison, Creeping flow of dilute polymer solutions past cylinders and spheres, J. Non-Newtonian Fluid Mech. 29 (1988) 381-432.
    • (1988) J. Non-Newtonian Fluid Mech. , vol.29 , pp. 381-432
    • Chilcott, M.D.1    Rallison, J.M.2
  • 31
    • 0024714622 scopus 로고
    • On the non-Newtonian flow past a cylinder in a confined flow
    • S.A. Dhahir, K. Walters, On the non-Newtonian flow past a cylinder in a confined flow, J. Rheol. 33 (1989) 781-804.
    • (1989) J. Rheol. , vol.33 , pp. 781-804
    • Dhahir, S.A.1    Walters, K.2
  • 32
    • 0018984093 scopus 로고
    • A numerical simulation of Newtonian and viscoelastic flow past stationary and rotating cylinders
    • P. Townsend, A numerical simulation of Newtonian and viscoelastic flow past stationary and rotating cylinders, J. Non-Newtonian Fluid Mech. 6 (1980) 219-243.
    • (1980) J. Non-Newtonian Fluid Mech. , vol.6 , pp. 219-243
    • Townsend, P.1
  • 33
    • 0008466694 scopus 로고
    • Slow viscoelastic flow past a cylinder in a rectangular channel
    • E.O.A. Carew, P. Townsend, Slow viscoelastic flow past a cylinder in a rectangular channel, Rheologica Acta 30 (1991) 58-64.
    • (1991) Rheologica Acta , vol.30 , pp. 58-64
    • Carew, E.O.A.1    Townsend, P.2
  • 34
    • 0001321120 scopus 로고
    • Polymeric flow through fibrous media
    • L. Skartsis, B. Khomami, J.L. Kardos, Polymeric flow through fibrous media, J. Rheol 36 (1992) 589-620.
    • (1992) J. Rheol , vol.36 , pp. 589-620
    • Skartsis, L.1    Khomami, B.2    Kardos, J.L.3
  • 35
    • 84914970971 scopus 로고
    • Applications of domain decomposition spectral collocation methods in viscoelastic flows through model porous media
    • A. Souvaliotis, A.N. Beris, Applications of domain decomposition spectral collocation methods in viscoelastic flows through model porous media, J. Rheol. 36 (1992) 1417-1453.
    • (1992) J. Rheol. , vol.36 , pp. 1417-1453
    • Souvaliotis, A.1    Beris, A.N.2
  • 36
    • 84955042128 scopus 로고
    • Application of higher order finite element methods to viscoelastic flow in porous media
    • K. Talwar, B. Khomami, Application of higher order finite element methods to viscoelastic flow in porous media, J. Rheol. 36 (1992) 1377-1416.
    • (1992) J. Rheol. , vol.36 , pp. 1377-1416
    • Talwar, K.1    Khomami, B.2
  • 37
    • 0028404040 scopus 로고
    • An experimental and numerical investigation of a viscoelastic flow around a cylinder
    • F.P.T. Baaijens, H.P.W. Baaijens, G.W.M. Peters, H.E.H. Meijer, An experimental and numerical investigation of a viscoelastic flow around a cylinder, J. Rheol. 38 (1994) 351-376.
    • (1994) J. Rheol. , vol.38 , pp. 351-376
    • Baaijens, F.P.T.1    Baaijens, H.P.W.2    Peters, G.W.M.3    Meijer, H.E.H.4
  • 38
    • 0001304924 scopus 로고
    • Viscoelastic flow past a confined cylinder of polyisobutylene solution
    • H.P.W. Baaijens, G.W.M. Peters, F.P.T. Baaijens, H.E.H. Meijer, Viscoelastic flow past a confined cylinder of polyisobutylene solution, J. Rheol. 39 (1995) 1243-1278.
    • (1995) J. Rheol. , vol.39 , pp. 1243-1278
    • Baaijens, H.P.W.1    Peters, G.W.M.2    Baaijens, F.P.T.3    Meijer, H.E.H.4
  • 39
    • 0001271271 scopus 로고
    • Numerical simulation of viscoelastic flow around a cylinder using an integral constitutive equation
    • G. Barakos, E. Mitsoulis, Numerical simulation of viscoelastic flow around a cylinder using an integral constitutive equation, J. Rheol. 39 (1995) 1279-1292.
    • (1995) J. Rheol. , vol.39 , pp. 1279-1292
    • Barakos, G.1    Mitsoulis, E.2
  • 40
    • 11144309217 scopus 로고    scopus 로고
    • Viscoelastic flow of polymer solutions around a periodic, linear array of cylinders: Comparison of predictions for microstructure and flow fields
    • in press
    • A.W. Liu, D.E. Bornside, D.E.R.C. Armstrong, R.A. Brown, Viscoelastic flow of polymer solutions around a periodic, linear array of cylinders: Comparison of predictions for microstructure and flow fields, J. Non-Newtonian Fluid Mech. 1997, in press.
    • (1997) J. Non-Newtonian Fluid Mech.
    • Liu, A.W.1    Bornside, D.E.2    Armstrong, D.E.R.C.3    Brown, R.A.4
  • 41
    • 0027524062 scopus 로고
    • The wake instability in viscoelastic flow past confined circular cylinders
    • G.H. McKinley, R.C. Armstrong, R.A. Brown, The wake instability in viscoelastic flow past confined circular cylinders, Phil. Trans. R. Soc. Lond. A. 344 (1993) 265-304.
    • (1993) Phil. Trans. R. Soc. Lond. A , vol.344 , pp. 265-304
    • McKinley, G.H.1    Armstrong, R.C.2    Brown, R.A.3
  • 42
    • 0028461866 scopus 로고
    • Spiral instabilities in the flow of highly elastic fluids between rotating parallel disks
    • J.A. Byars, A. Öztekin, R.A. Brown, R.C. Armstrong, Spiral instabilities in the flow of highly elastic fluids between rotating parallel disks, J. Fluid Mech. 271 (1994) 173-218.
    • (1994) J. Fluid Mech. , vol.271 , pp. 173-218
    • Byars, J.A.1    Öztekin, A.2    Brown, R.A.3    Armstrong, R.C.4
  • 43
    • 11144325900 scopus 로고    scopus 로고
    • Three-dimensional wake instability in viscoelastic flow past a cylinder: Theory and experiment
    • in press
    • A. Öztekin, J.A. Byars, A.W. Liu, R.C. Armstrong, R.A., Brown, Three-dimensional wake instability in viscoelastic flow past a cylinder: Theory and experiment, J. Fluid Mech. 1997, in press.
    • (1997) J. Fluid Mech.
    • Öztekin, A.1    Byars, J.A.2    Liu, A.W.3    Armstrong, R.C.4    Brown, R.A.5
  • 45
    • 0027643603 scopus 로고
    • Elastic instability in crossflow of polymer solutions through periodic array of cylinders
    • C. Chmielewski, C. A. Petty, K. Jayaraman, Elastic instability in crossflow of polymer solutions through periodic array of cylinders, J. Non-Newtonian Fluid Mech. 48 (1993) 285-301.
    • (1993) J. Non-Newtonian Fluid Mech. , vol.48 , pp. 285-301
    • Chmielewski, C.1    Petty, C.A.2    Jayaraman, K.3
  • 48
    • 0026890783 scopus 로고
    • Numerical instability of time-dependent flows
    • R.A. Keiller, Numerical instability of time-dependent flows, J. Non-Newtonian Fluid Mech. 43 (1992) 229-246.
    • (1992) J. Non-Newtonian Fluid Mech. , vol.43 , pp. 229-246
    • Keiller, R.A.1
  • 49
    • 11144309054 scopus 로고    scopus 로고
    • in press
    • M.D. Graham, 1997, in press.
    • (1997)
    • Graham, M.D.1
  • 50
    • 0029273201 scopus 로고
    • Parallel implementation of finite element/Newton method for solution of steady state and transient non-linear partial differential equations
    • M.R. Mehrabi, R.A. Brown, Parallel implementation of finite element/Newton method for solution of steady state and transient non-linear partial differential equations, J. Sci. Comput. 10 (1995) 93-137.
    • (1995) J. Sci. Comput. , vol.10 , pp. 93-137
    • Mehrabi, M.R.1    Brown, R.A.2
  • 51
    • 11144264818 scopus 로고    scopus 로고
    • Parallel block preconditioning techniques for Stokes-type flow problems and applications to the non-linear buoyancy-driven natural convection flow in a cavity
    • in press
    • Y. Cai, R.A. Brown, Parallel block preconditioning techniques for Stokes-type flow problems and applications to the non-linear buoyancy-driven natural convection flow in a cavity, Comp. Meth. Appl. Mech. and Eng. 1997, in press.
    • (1997) Comp. Meth. Appl. Mech. and Eng.
    • Cai, Y.1    Brown, R.A.2
  • 52
    • 0022659813 scopus 로고
    • Numerical investigation of incompressible flow in grooved channels: Part I. stability and self-sustained oscillations
    • N.K. Ghaddar, K.Z. Korczak, B.B. Mikic, A.T. Patera, Numerical investigation of incompressible flow in grooved channels: Part I. stability and self-sustained oscillations, J. Fluid Mech. 163 (1986) 99-127.
    • (1986) J. Fluid Mech. , vol.163 , pp. 99-127
    • Ghaddar, N.K.1    Korczak, K.Z.2    Mikic, B.B.3    Patera, A.T.4


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