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An efficient finite volume method is developed for the phase-field simulation of two-dimensional dendritic growth in a forced flow at various supercoolings. The adaptive nature of the method allows the dendrite in a large domain to evolve secondary structures, even at low supercoolings. In addition to good agreement with previous calculations on the tip shape and speed, the effects of forced flow at various supercoolings are investigated and compared with the Oseen-Ivantsov solution and good agreement is found. The steady dendrite shape in all cases continues to have a self-affine nature and the invariant scaling parameters are in good agreement with the estimation.

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