  We derive 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
modeling 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 one needs to properly sample the space of kinematic
parameters. In particular, we highlight the importance of extensional rheology
in simulating generic flows of polymeric fluids.
