A multi-scale method for complex flows of non-Newtonian fluids

We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines micro-scale data from non-equilibrium molecular dynamics (NEMD) with macro-scale continuum equations to achieve a data-driven prediction of complex flows. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modelling effort is thus limited to the identification of suitable interaction potentials at the micro-scale. Compared to previous proposals, our approach takes into account the fact that the material response can depend strongly on the local flow type and we show that this is a necessary feature to correctly capture the macroscopic dynamics. In particular, we highlight the importance of extensional rheology in simulating generic flows of polymeric fluids.