A boundary element analysis of multiply connected three-dimensional cavitymixing flow of polymer solutions

The emergence of non-linear dynamics in cavity mixing is examined using the boundary element method (BEM). The method is implemented for the simulatio n of three-dimensional transient creeping flow of Newtonian or linear visco elastic fluids of the Jeffreys type. A boundary only formulation in the tim e domain is proposed for viscoelastic flow. Special emphasis is placed on c avity flow involving multiply connected moving domains. The BEM becomes par ticularly suited for this case, when part of the boundary (stirrer or rotor ) is moving, and the remaining outer part (cavity) is at rest. In contrast to conventional volume methods, the BEM is shown to be much easier to imple ment since the kinematics of the elements bounding the fluid is known (impo sed). It is found that, for a simple cavity flow induced by a rotating vane at constant angular velocity, the tractions at the vane tip and cavity fac e exhibit non-linear periodic dynamical behaviour with time for fluids obey ing linear constitutive equations. Copyright (C) 1999 John Wiley & Sons, Lt d.