The coupling of different scales and physical processes is important in the study of complex fluids. Indeed, the interaction between these (microscopic) elastic properties and the (macroscopic) fluid motions gives not only the rich and complicated rheological phenomena, but also presents formidable challenges in mathematical analysis and numerical simulations.

           We have undergone systematic development of closure models for the macro-micro FENE models of polymeric fluids. Our approach is featured as an important and effective off-line approach for multiscale modeling. We will be looking into various dynamic and adaptive closure approaches and their numerical implementations.