A multiscale simulation method for polymeric flow has been developed 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 . Case (c) is particularly difficult since is necessarily to keep track of polymer conformation exactly on the streamline.
In our multiscale method, the local stress of each fluid element is calculated directly by performing (microscopic or mesoscopic) particle-based simulations according to the local flow profiles instead of using any constitutive relations. The grovel flow profile is then updated using (macroscopic) continuum fluid dynamics according to the local stress obtained by the particle-based simulations. S. Yasuda and R. Yamamoto, "Rheological properties of polymer melt between rapidly oscillating plates: an application of multiscale modeling", EPL 86, 18002 (2009).
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