  An exact solution of coarse-grained polymer models with fluctuating internal
friction and hydrodynamic interactions has not been proposed so far due to a
one-to-all coupling between the connector vector velocities that precludes the
formulation of the governing stochastic differential equations. A methodology
for the removal of this coupling is presented, and the governing stochastic
differential equations, obtained by attaching a kinetic interpretation to the
Fokker-Planck equation for the system, are integrated numerically using
Brownian dynamics simulations. The proposed computational route eliminates the
calculation of the divergence of the diffusion tensor which appears in models
with internal friction, and is about an order of magnitude faster than the
recursion-based algorithm for the decoupling of connector-vector velocities
previously developed [J. Rheol., 65, 903 (2021)] for the solution of freely
draining models with internal friction. The effects of the interplay of various
combinations of finite extensibility, internal friction and hydrodynamic
interactions on the steady-shear-viscosity is examined. While finite
extensibility leads solely to shear-thinning, both internal friction and
hydrodynamic interactions result in shear-thinning followed by
shear-thickening. The shear-thickening induced by internal friction effects are
more pronounced than that due to hydrodynamic interactions.
