  We present a hybrid numerical method to introduce hydrodynamics in dynamic
self-consistent field (SCF) studies of inhomogeneous polymer systems. It solves
a set of coupled dynamical equations: The Navier-Stokes equations for the fluid
flow, and SCF-based convection-diffusion equations for the evolution of the
local monomer compositions. The Navier-Stokes equaitons are simulated by the
lattice Boltzmann method and the dynamic self-consistent equations are solved
by a finite difference scheme. Two applications are presented: First, we study
microphase separation in symmetric and asymmetric block copolymer melts with
various values of shear and bulk viscosities, comparing the results to those
obtaiuned with purely diffusive dynamics. Second, we investigate the effect of
hydrodynamics on vesicle formation in amphiphilic block copolymer solutions. In
agreement with previous studies, hydrodynamic interactions are found to have
little effect on the microphase separation at early times, buty they
substantially accelerate the process of structure formation at later times.
Furthermore, they also contribute to selecting the pathway of vesicle
formation, favoring spherical intermediates over aspherical (disklike) ones.
