A novel Grand-Potential Phase-Field Lattice-Boltzmann model for multi-phase solidification with convection

Abstract: Melt convection plays a critical role in microstructure evolution during alloy solidification, yet accurately capturing its interaction with moving solid-liquid interfaces remains a significant computational challenge, particularly in multi-phase, multi-component systems. In this work, we develop a computational framework that couples a Grand-Potential phase-field model with the Lattice Boltzmann method (LBM) to simulate convection-driven solidification within a unified and thermodynamically consistent formulation. The proposed approach rigorously enforces no-slip conditions at evolving solid-liquid interfaces, while fluid transport is solved using the standard single-relaxation-time Bhatnagar-Gross-Krook collision operator. The framework provides an efficient and robust methodology for resolving the coupled evolution of interfaces, solute transport, and fluid flow. The versatility of the proposed framework is demonstrated through simulations of dendritic and eutectic solidification under natural convection. The results show that convection significantly modifies solute segregation, destabilizes growth fronts, and induces oscillatory growth modes in both systems. These examples illustrate the capability of the proposed method to capture complex flow-induced morphological instabilities and provide new insights into the mechanisms governing convection-driven microstructure evolution in alloy solidification.