Modeling of viscoelastic lid driven cavity flow using finite element simulations Anne M. Grillet a , Bin Yang b , Bamin Khomami b,* , Eric S.G. Shaqfeh a a Department of Chemical Engineering, Stanford University, Stanford, CA 94305-5025, USA b Department of Chemical Engineering, Washington University, St. Louis, MO 63130, USA Received 16 September 1998; received in revised form 27 January 1999 Abstract In this study we have used a convergent and highly accurate mixed finite element technique to model the effect of fluid elasticity on the flow kinematics and the stress distribution in lid driven cavity flow. Our work is motivated by the desire to capture the important physical aspects of the basic flow and thus to better understand the purely elastic instability in recirculating flows which has been reported in the literature elsewhere [A.M. Grillet, E.S.G. Shaqfeh, Observations of viscoelastic instabilities in recirculation flows of Boger fluids, J. Non-Newtonian Fluid Mech. 64 (1996) 141±155; P. Pakdel, G.H. McKinley, Cavity flows of elastic liquids: purely elastic instablities, Phys. Fluids 10 (5) (1998) 1058±1070]. In our numerical investigations we have treated the corner singularities by incorporating a controlled amount of leakage which allows the computation of fully elastic mesh converged solutions. We begin by validating our Newtonian cavity results against previous work to show that the introduction of leakage does not appreciably modify the cavity recirculation flow. Then we examine the polymer stresses to understand how elasticity changes the flow kinematics, slowing the primary recirculation vortex and causing the vortex center to shift opposite of the direction of lid motion. Variations of the cavity aspect ratio are also explored. Focusing on the corners we find that the leakage relieves the corner singularities and moreover, finite leakage helps explain the unusual behavior seen in the radial velocity in experiments. Finally, we have reexamined the previously proposed mechanisms for elastic instability in this flow and put forth a new instability mechanism. Together, these mechanisms may better explain the complex aspect ratio dependence of the onset of elastic instability in lid driven cavity flow. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Viscoelastic cavity flow; Finite element; Elastic instability; FENE-CR constitutive equation; Corner singularities; Recirculation flow 1. Introduction Lid driven cavity flows are important in many industrial processing applications such as short-dwell and flexible blade coaters [1]. They also provide a model for understanding more complex flows with J. Non-Newtonian Fluid Mech. 88 (1999) 99±131 ÐÐÐÐ *Corresponding author. Tel.: +1-314-935-6065; fax: +1-314-935-7211 E-mail address: bam@poly1.wustl.edu (B. Khomami) 0377-0257/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S0377-0257(99)00015-4