We applied a phase field model to compute the evolution of two grains during the solidification of silicon. Simulations have been performed in two-dimensional domains of about 50 x 50 mu m(2) size. The situation in the groove between the two grains is analyzed in detail. For certain cases we found that the overgrowing is defined by equilibrium angle at the three phase junction between the two grains and melt. Because of the limits of applying a phase field model to this problem we propose a hybrid scheme which will allow to go to larger domains. (C) 2013 Elsevier B.V. All rights reserved.