  The molecular constitutive models, like FENE-P for polymer solutions, are
known to have convergence issues at relatively larger flow rates. In this
study, we investigate the possibility of a numerically efficient GNF-based
approximation of FENE-P, which would closely approximate the flow field.
Firstly, we compare the flow fields predicted by FENE-P and an equivalent GNF
model. For these studies, we considered the flow around a sphere and selected
the Carreau-Yasuda model as the representative GNF. This is made equivalent to
the FENE-P by selecting parameters to equalize the viscosity-shear rate
dependence. Our results show severe deficiencies of the GNF model, owing to its
inability to account for chain stretching, particularly near the stagnation
points. Next, the effect of extensional components on the local viscosity was
added by formulating an equivalent GNF-X [Journal of Rheology 64, 493 (2020)]
model. Even this failed to capture the asymmetry in the stress and flow
profiles and predicted very large stresses at both stagnation points, relative
to FENE-P. Hence, we proposed a novel modified formalism (denoted as GNF-XM)
that was able to capture all trends successfully. The drag coefficients from
GNF-XM agreed well with FENE-P predictions for all flow rates considered.
Significantly, the computational times required to solve the flow field with
GNF-XM is about an order of magnitude lower than that of FENE-P, especially at
higher flow rates. Thus, we have successfully formulated a highly efficient
GNF-based approximation to the FENE-P, whose formalism can be extended to other
similarly complicated constitutive models.
