Development and evaluation of a micro-macro algorithm for the simulation of polymer flow

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A micro-macro algorithm for the calculation of polymer flow is developed and numerically evaluated. The system being solved consists of the momentum and mass conservation equations from continuum mechanics coupled with a microscopic-based rheological model for polymer stress. Standard finite element techniques are used to solve the conservation equations for velocity and pressure, while stochastic simulation techniques are used to compute polymer stress from the simulated polymer dynamics in the rheological model. The rheological model considered combines aspects of reptation, network and continuum models. Two types of spatial approximation are considered for the configuration fields defining the dynamics in the model: piecewise constant and piecewise linear. The micro-macro algorithm is evaluated by simulating the abrupt planar die entry flow of a polyisobutylene solution described in the literature. The computed velocity and stress fields are found to be essentially independent of mesh size and ensemble size, while there is some dependence of the results on the order of spatial approximation to the configuration fields close to the die entry. Comparison with experimental data shows that the piecewise linear approximation leads to better predictions of the centerline first normal stress difference. Finally, the computational time associated with the piecewise constant spatial approximation is found to be about 2.5 times lower than that associated with the piecewise linear approximation. This is the result of the more efficient time integration scheme that is possible with the former type of approximation due to the pointwise incompressibility guaranteed by the choice of velocity-pressure finite element. © 2005 Elsevier Inc. All rights reserved.

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Journal of Computational Physics