Non-facetted crystal growth from an undercooled melt in the presence of an external flow is simulated using a phase-field lattice-Boltzmann scheme. The selection parameter a as a function of the Peclet number Pe is found to fall approximately on a single curve for dendritic and doublonic growth patterns, respectively. This has interesting implications for the availability of current selection theories as predictors of growth characteristics under flow. The morphology diagram in the plane undercooling versus anisotropy is studied as a function of the imposed flow. We find that when the flow speed is increased, the transition line from dendrites to doublons moves so as to favour dendritic patterns, becoming faster than cloublons. Moreover, the growth of a single finger in a narrow channel is studied. With increasing flow velocity, the finger width at steady state becomes larger. Our results suggest that stationary growth is impossible in sufficiently fast flows. (C) 2006 Published by Elsevier B.V.