Abstract
This paper presents the application of spectral element methods to simulate the time-dependent flow of viscoelastic fluids in non-trivial geometries using a closed-form differential constitutive equation. As an example, results relative to the flow of a FENE-CR fluid in a two-dimensional four-to-one contraction are given.
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REFERENCES
Bodart, C., and Crochet, M. J. (1993). Time-dependent numerical simulation of viscoelastic flow and stability. Theoret. Comput. Fluid Dynamics 5, 57–75.
Chauvière, C., and Owens, R. G. (2000). How accurate is your solution? Error indicators for viscoelastic flow calculations. J. Non-Newtonian Fluid Mech. 95, 1–33.
Chilcott, M. D., and Rallison, J. M. (1988). Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newtonian Fluid Mech. 29, 381–432. 4._ Couzy, W. (1995). Spectral Element Discretization of the Unsteady Navier–Stokes Equations and its Iterative Solution on Parallel Computers, Ph.D. thesis, No. 1380, Ecole Polytechnique Fédérale de Lausanne.
Couzy, W.(1995). Spectral Element Discretization of the Unsteady Navier–Stokes Equations and its Iterative Solution on Parallel Computers ,Ph.D. thesis, No.1380, Ecole Polytechnique Fédérale de Lausanne.
Deville, M. O., Fischer, P. F., and Mund, E. H. (2002). High-Order Methods for Incompressible Fluid Flow, Cambridge University Press, New York.
Dubois-Pèlerin, Y., Van Kemenade, V., and Deville, M. O. (1999). An object-oriented toolbox for spectral element analysis. J. Sci. Comput. 14, 1–29.
Fiétier, N., and Deville, M. O. (2000). Spectral Element Methods for Unsteady Viscoelastic Flows, Proc. of the 16th IMACS World Congress, Session 129–3B, Swiss Federal Institute of Technology, Lausanne, Switzerland.
Fiétier, N., and Deville, M. O. Time-dependent algorithms for the simulation of viscoelastic flows with spectral element methods: Applications and stability. Submitted to J. Comput. Phys.
Fiétier, N., and Deville, M. O. Linear stability analysis of time-dependent algorithms with spectral element methods for the simulation of viscoelastic flows (in preparation).
El Hadj, M., and Tanguy, P. A. (1990). A finite element procedure coupled with the method of characteristics for simulation of viscoelastic fluid flow. J. Non-Newtonian Fluid Mech. 36, 333–349.
Van Kemenade, V., and Deville, M. O. (1994). Application of spectral elements to viscoelastic creeping flows. J. Non-Newtonian Fluid Mech. 51, 277–308.
McKinley, G. H., Raiford, W. P., Brown, R. A., and Armstrong, R. C. (1991). Nonlinear dynamics of viscoelastic flow in axisymmetric abrupt contractions. J. Fluid Mech. 223, 411–456.
Mullen, J. S., and Fischer, P. F. (1999). Filtering techniques for complex geometry fluid flows. Commun. Numer. Meth. Engng. 15, 9–18.
Smith, M. D., Armstrong, R. C., Brown, R. A., and Sureshkumar, R. (2000). Finite element analysis of stability of two-dimensional viscoelastic flows to three-dimensional perturbations. J. Non-Newtonian Fluid Mech. 93, 203–244.
Weill, D., and Deville, M. O. (2002). Steady gap flows by spectral and mortar element methods. J. Sci. Comput. 17, 639–648.
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Fiétier, N., Deville, M.O. Simulations of Time-Dependent Flows of Viscoelastic Fluids with Spectral Element Methods. Journal of Scientific Computing 17, 649–657 (2002). https://doi.org/10.1023/A:1015135016765
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DOI: https://doi.org/10.1023/A:1015135016765