Efficient phase field simulation using an adaptive finite volume method is presented for two-dimensional dendritic growth in a forced flow. The extremely large domain (over 2(18) in the ratio of cell size), while keeping very small cell size at the interface, makes the simulation at low supercooling possible. With a strong forced flow, the upstream tip speed reaches a steady state quickly even at low supercooling. The upstream arm develops side branches easily, but remains similar after rescaling, i.e., self-affine, as the diffusive one at steady state. (C) 2002 Elsevier Science B.V. All rights reserved.