We present results of simulations of solutions of flexible polymers molecules during flow in slit and grooved channels. A self-consistent coarse-grained Langevin description of the polymer dynamics is adopted in which hydrodynamic effects are included through a Green's function formalism. The O(N) General Geometry Ewald-like Method is used to calculate the confined Stokeslet and concentrations in the range from ultra-dilute to semi-dilute (near the overlap concentration). As concentration increases, the hydrodynamic migration effects observed in dilute solution unidirectional flows become less prominent, virtually vanishing as the overlap concentration is approached. However, the lower concentration in the near-wall region increases the shear rate, giving rise to an apparent-slip layer. In a grooved channel, the groove is almost completely depleted of polymer chains at high Weissenberg number in the dilute limit, but at finite concentration this depletion effect is dramatically reduced. Only upon inclusion of hydrodynamic interactions can these phenomena be properly captured.