Numerical simulations by a finite-difference method have been made for viscoelastic flows due to a rotating disc enclosed in a cylindrical casing. The Giesekus model was used as a constitutive equation. We could simulate some typical secondary flow patterns for viscoelastic fluids; e.g., a secondary flow (C.T. Hill, 1972) of which the circulation direction at a low Reynolds number is reversed compared with that for a Newtonian fluid and a double-cell flow structure which Escudier et al. (1996) observed at a relatively high Reynolds number. The secondary flow patterns are characterized by the elasticity number (=Weissenberg number / Reynolds number) from low to high Reynolds numbers.
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