Reduced-stress method for efficient computation of time-dependent viscoelastic flow with stress equations of FENE-P type

Most calculation procedures for time-dependent viscoelastic flows require iteration within the time step used to advance the solution, in order to satisfy simultaneously the momentum and the constitutive equations for each stress component. We have devised a way of reformulating the constitutive equation for the FENE-P model, or models described by similar equations expressed in terms of the stress tensor, which enables iterative methods for simulating time-dependent viscoelastic flows to become much more efficient: the number of iterations to obtain a solution with the reformulated stress equations is substantially smaller (by a factor of 5-10) than with a comparable method applied to the original, non-reformulated, constitutive equations. The proposed reformulation is rather simple and consists in considering as dependent variables the reduced stresses obtained by dividing the stress components by the extensibility function of the model. It is tested with three problems of increasing complexity, start-up of channel and square-duct flows, and start-up of a rotating duct flow.