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A phase-field method is presented that can be used for direct numerical simulation of microstructure formation in solidifying alloys. Notable new features are a simple derivation of the governing phase-field and species conservation equations and the inclusion of convection in the liquid phase. Particular attention is given to the interfacial forces in the smeared interface region, in order to accurately calculate the velocities and stresses at the interface. Numerical results are presented for the interface. Numerical results are presented for the coarsening of a binary solid/liquid mixture with and without flow and compared to available theories.