We introduce a mesoscale method for simulating hydrodynamic transport andself assembly of inhomogeneous polymer melts in pressure driven and draginduced flows. This method extends dynamic self consistent field theory (DSCFT)into the hydrodynamic regime where bulk material transport and viscoelasticeffects play a significant role. The method combines four distinct componentsas a single coupled system, including (1) non-equilibrium self consistent fieldtheory describing block copolymer self-assembly, (2) multi-fluid Navier-Stokestype hydrodynamics for tracking material transport, (3) constitutive equationsmodeling viscoelastic phase separation, and (4) rigid wall fields whichrepresent moving channel boundaries, machine components, and nano-particulatefillers. We also present an efficient, pseudospectral implementation for thisset of coupled equations which enables practical application of the model inperiodic domains. We validate the model by reproducing well known phenomenaincluding equilibrium diblock meso-phases, analytic Stokes flows, andviscoelastic phase separation of glassy/elastic polymer melts. We alsodemonstrate the stability and accuracy of the numerical implementation byexamining its convergence under grid-size refinement.
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