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A novel mesoscopic simulation technique is under development to describe the non-steady growth of several equiaxed dendritic grains into a supercooled melt of a pure substance. Simulation results are in good agreement with experiments for the growth of a single dendritic grain of the model substance succinonitrile. In the mesoscopic model the calculation of the temperature field in the supercooled liquid is coupled with a modified stagnant film model for dendritic growth, so that without resolving the microstructure the internal solid fraction inside the grain envelopes can be predicted. The model is applied to the transient growth of up to 15 strongly interacting grains.