Efficient quantitative phase field simulation using an adaptive finite volume method with an antisolutal trapping scheme is presented for a binary dendritic growth in a forced flow. For the case of no convection, the calculated results with different interface thickness are examined. It is found that with a proper antisolutal trapping flux, a thick interface, but smaller than the diffusion boundary layer, could be used and the solution could approach to the sharp-interface Gibbs-Thompson equation limit in almost all aspects quantitatively. Based on the concentration driving force obtained from the sharp-interface limit of the Wheeler-Boettinger-McFadden (WBM) model, the calculated results are in good agreement with the classic Oseen-Ivantsov solution for the concentration-driven growth in a forced flow. And the selection scaling factor also increases with the external flow as the theoretical prediction.