Numerical Simulation of Viscoelastic Flows using BrownianConfiguration Fields and Spectral Element Methods

The stress in any polymeric liquid depends on the conformations of the polymer molecules, viz., the orientation and degree of stretch of a molecule. Kinetic theory provides a description of the polymer conformations based on coarse-grained molecular models of polymers. The method of Brownian configuration fields avoids the necessity of having to track individual particles. Instead the polymer dynamics is described by the evolution of an ensemble of configuration fields governed by a stochastic differential equation. The configuration fields serve to determine the polymeric contribution to the extra-stress tensor, which is required as a source term in the conservation equation. Spectral methods are used for the spatial discretization. The application of the technique to the start-up of Couette flow and flow between eccentrically rotating cylinders will be described for various dumbbell model fluids. Finally the technique will be applied to a journal bearing simulator (JBS). The performance of the method will be discussed.