The development of accurate coarse-grained models for macromolecular solutions has been an area of active research as the non-Newtonian flow characteristics of polymeric fluids strongly impact the vast majority of processing operations used to manufacture diverse products. To date, macroscopic models have been conventionally used to relate the applied deformation to the macroscopic stress but have displayed several deficiencies either due to the lack of microstructural information or due to approximations that are applied to the moments of the distribution function in order to obtain a constitutive model. On the other hand, mesoscopic models that describe the microstructure of the molecule, such as bead-rod and bead-spring models have been successful in predicting macroscopic stresses and other properties such as the radius of gyration and tumbling frequency of molecules in standard benchmark flow types. Multi-scale simulations that couple these mesoscopic models with macroscopic flow equations have however had limited success in predicting complex macroscopic flows due to the computational overhead involved. Despite the explosion of computational resources such as the development of Beowulf clusters, and simulation methodologies such as parallel programming, multi-scale simulation of complex flows using molecules with over a few segments is still a challenge. Therefore, there is a need to develop reduced order models that retain microstructural information while being capable of simulating complex flows.

We present a novel approach to coarse-graining the microstructural representation of molecules by the partitioning of phase space into a few configuration classes namely folds, half dumbbells, kinks, dumbbells, coils and stretched states. Each individual configuration class is described using a dumbbell model but is unique in its representation due to a modified drag that is assigned to each configuration class. Configuration dependent drag is calculated by studying the drag force on the molecules via a constant extension ensemble simulation. We also develop a configuration map for the probability of occurrence of different configurations as a function of the end-to-end distance of the molecules which guides the evolution of the populations of configuration classes under flow. These two concepts coupled together form the basis of the reduced order model wherein microstructural information is incorporated via the partitioning of phase space into configuration classes and the development of a configuration dependent drag, while the dumbbell based representation allows for the implementation of this model in complex flows. We study the performance of this reduced order model by studying the start up of steady shear, uniaxial elongational flow as well as a few mixed kinematics flows.