  We simulate complex fluids by means of an on-the-fly coupling of the bulk
rheology to the underlying microstructure dynamics. In particular, a
macroscopic continuum model of polymeric fluids is constructed without a
pre-specified constitutive relation, but instead it is actively learned from
mesoscopic simulations where the dynamics of polymer chains is explicitly
computed. To couple the macroscopic rheology of polymeric fluids and the
microscale dynamics of polymer chains, the continuum approach (based on the
finite volume method) provides the transient flow field as inputs for the
(mesoscopic) dissipative particle dynamics (DPD), and in turn DPD returns an
effective constitutive relation to close the continuum equations. In this
multiscale modeling procedure, we employ an active learning strategy based on
Gaussian process regression (GPR) to minimize the number of expensive DPD
simulations, where adaptively selected DPD simulations are performed only as
necessary. Numerical experiments are carried out for flow past a circular
cylinder of a non-Newtonian fluid, modeled at the mesoscopic level by
bead-spring chains. The results show that only five DPD simulations are
required to achieve an effective closure of the continuum equations at Reynolds
number Re=10. Furthermore, when Re is increased to 100, only one additional DPD
simulation is required for constructing an extended GPR-informed model closure.
Compared to traditional message-passing multiscale approaches, applying an
active learning scheme to multiscale modeling of non-Newtonian fluids can
significantly increase the computational efficiency. Although the method
demonstrated here obtains only a local viscosity from the mesoscopic model, it
can be extended to other multiscale models of complex fluids whose
macro-rheology is unknown.
