Hulsen, et al. introduced in [1] the concept of Brownian Configuration Fields for the simulation of stochastic models and flows in complex geometries. Even for homogeneous flows, stochastic models require numerical simulation of either the Fokker-Planck Equation, or their equivalent stochastic differential equations. Brownian configuration fields represented a major advance to CONNFFESSIT methods, allowing excellent variance reduction. We present an alternative argument to show a connection between Fokker-Planck equations in non-homogeneous flows and the Brownian Configuration Fields. Most importantly, the method is used to show how this technique can be generalized to include the effects of center-of-mass diffusion of the polymer chains on stress.

[1] M. A. Hulsen, B. H. A. A. van den Brule, A. P. G. van Heel, Simulation of viscoelastic flows using Brownian configuration fields, J. Non-Newtonian Fluid Mech. 70 (1-2) (1997) 79–101.