Systems analysis of hybrid, multi-scale complex flow simulations using Newton-GMRES

We present a methodology to analyze the stationary states and stability of complex fluid flows by using hybrid, discrete, and/or continuum multi-scale simulations. Building on existing theories, our scheme extracts dynamical and equilibrium characteristics from carefully chosen time integrations of these multi-scale evolution equations. Two canonical problems are presented to demonstrate the ability and accuracy of the formalism. The first is an investigation of flow-induced transitions seen in homogeneous, hard- rod liquid crystal suspensions subjected to a linear shear flow. In the second problem, we study the phenomenon of draw resonance, a dynamical instability in an isothermal fiber-spinning process, by using a multi-scale hybrid simulation that incorporates both stochastic and continuum models.