An efficient and fast adaptive numerical method for a novel phase-field model of crystal growth

In this study, we present an efficient, fast, and fully explicit adaptive numerical scheme for solving a recently developed novel phase-field model of crystal growth in both two-dimensional (2D) and three-dimensional (3D) spaces. The novel phase-field model employed in this research incorporates a term specifically designed to eliminate the artificial curvature effect, thereby facilitating accelerated evolution when compared to traditional models. This enhancement significantly enhances the efficiency and speed of the simulation, leading to more expedited results. The crystal growth model employed in this study incorporates a phase-field equation to accurately represent the crystal interface, in addition to a heat equation that effectively models the distribution of temperature. To effectively solve the phase-field equation, we employ an adaptive numerical algorithm that optimizes the computational process. Our numerical scheme, specifically tailored for simulating dendritic growth, incorporates an adaptive narrow-band domain approach to accurately resolve the interfacial transition layer of the phase field. Furthermore, we enhance computational efficiency by implementing a double-sized grid for the temperature distribution, further improving the overall efficiency of the model. By combining these strategies, we achieve accurate and efficient solutions for the dendritic growth model. To validate the accuracy and efficiency of our proposed adaptive numerical method for solving the phase-field equation of dendritic growth, we conduct a series of numerical experiments in both 2D and 3D spaces. In these experiments, we assess the performance of our algorithm, analyzing its ability to accurately capture the intricate dynamics of dendritic growth while maintaining computational efficiency. By thoroughly evaluating the results obtained from these experiments, we provide strong evidence supporting the reliability and effectiveness of our adaptive numerical algorithm.