Abstract
In this study, we propose a hybrid numerical method for the predictions of the solidification patterns formed through the growth of multiples dendrites under melt convection. The proposed method is a combination of the multi-phase-field method for dendrite growth and the lattice Boltzmann method for predicting the melt flow. Important aspects such as the no-slip boundary conditions at the liquid-solid interface and the movement of the solid phase are taken into account by appropriately including additional terms in the formulation of the method. The effects of the solid motion and the melt flow on the solidification patterns are investigated in some detail.
