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 1 8 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.