We present a theoretical framework for simulating dynamic processes in polymeric fluids with embedded nanoparticles. The method couples an Eulerian, field-theoretic description of polymer hydrodynamics with a Lagrangian technique for tracking particles of arbitrary shape and size. Results are presented which reproduce nanoparticle localization in diblock nanosphere composites and interfacial jamming in homopolymer blend nanocomposites. Some of the method's unique capabilities are demonstrated by simulating systems containing non-spherical particles, particles of multiple sizes, and surface driven self-assembly. Published by Elsevier Ltd.