Multiscale Simulations for Polymeric Flow
  Multiscale simulation methods have been developed based on the local stress sampling strategy and applied to three flow problems with different difficulty levels: (a) general flow problems of simple fluids, (b) parallel (one-dimensional) flow problems of polymeric liquids, and (c) general (two- or three-dimensional) flow problems of polymeric liquids. In our multiscale methods, the local stress of each fluid element is calculated directly by performing microscopic or mesoscopic simulations according to the local flow quantities instead of using any constitutive relations. For simple fluids (a), such as the Lenard-Jones liquid, a multiscale method combining MD and CFD simulations is developed based on the local equilibrium assumption without memories of the flow history. (b), the multiscale method is extended to take into account the memory effects that arise in hydrodynamic stress due to the slow relaxation of polymer-chain conformations. The memory of polymer dynamics on each fluid element is thus resolved by performing MD simulations in which cells are fixed at the mesh nodes of the CFD simulations.For general (two- or three-dimensional) flow problems of polymeric liquids (c), it is necessary to trace the history of microscopic information such as polymer-chain conformation, which carries the memories of past flow history, along the streamline of each fluid element. A Lagrangian-based CFD is thus implemented to correctly advect the polymer-chain conformation consistently with the flow. On each fluid element, coarse-grained polymer simulations are carried out to consider the dynamics of entangled polymer chains that show extremely slow relaxation compared to microscopic time scales. 
Takahiro Murashima, Takashi Taniguchi, Ryoichi Yamamoto, and Shugo   Yasuda
cond-mat.soft