Efficient adaptive phase field simulation is carried out for a non-isothermal free dendritic growth in a nickel/copper system under a forced flow. The adaptive nature of the present scheme allows the simulation to be performed in an extremely large domain for viscous and thermal boundary layers, while keeping fine mesh for the solutal boundary layer and the diffusive interface. To suppress the solutal trapping due to the "thick" interface, an anti-trapping current is introduced. For isothermal growth, a steady-state growth can be obtained quickly and the calculated solution agrees quite well with the Oseen-Ivontsov solution. For non-isothermal growth, due to side-arm effect, caused by the large thermal spreading from the side arms and side branching, a steady state is not possible. With a forced flow, the upstream tip grows faster and its side branching is easily induced; the amplitude and frequency of the side branching increase with the flow speed. More importantly, with the anti-solute trapping, the difference in the grown morphology between isothermal and non-isothermal growth is much smaller than that without the anti-trapping current. (C) 2004 Elsevier B.V. All rights reserved.