  In this paper we establish a new efficient method for simulating
polymer-solvent systems which combines a lattice Boltzmann approach for the
fluid with a continuum molecular dynamics (MD) model for the polymer chain. The
two parts are coupled by a simple dissipative force while the system is driven
by stochastic forces added to both the fluid and the polymer. Extensive tests
of the new method for the case of a single polymer chain in a solvent are
performed. The dynamic and static scaling properties predicted by analytical
theory are validated. In this context, the influence of the finite size of the
simulation box is discussed. While usually the finite size corrections scale as
L^{-1} (L denoting the linear dimension of the box), the decay rate of the
Rouse modes is only subject to an L^{-3} finite size effect. Furthermore, the
mapping to an existing MD simulation of the same system is done so that all
physical input values for the new method can be derived from pure MD
simulation. Both methods can thus be compared quantitatively, showing that the
new method allows for much larger time steps. Comparison of the results for
both methods indicates systematic deviations due to non-perfect match of the
static chain conformations.
