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We introduce a new heterogeneous multi-scale method for the simulation offlows of non-Newtonian fluids in general geometries and present its applicationto paradigmatic two-dimensional flows of polymeric fluids. Our method combinesmicro-scale data from non-equilibrium molecular dynamics (NEMD) withmacro-scale continuum equations to achieve a data-driven prediction of complexflows. At the continuum level, the method is model-free, since the Cauchystress tensor is determined locally in space and time from NEMD data. Themodelling effort is thus limited to the identification of suitable interactionpotentials at the micro-scale. Compared to previous proposals, our approachtakes into account the fact that the material response can depend strongly onthe local flow type and we show that this is a necessary feature to correctlycapture the macroscopic dynamics. In particular, we highlight the importance ofextensional rheology in simulating generic flows of polymeric fluids.

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