A fast, accurate, and stable numerical algorithm is proposed to solve the anisotropic phase-field dendritic crystal growth model. The algorithm combines the first-order direction splitting method and the linear stabilization technique, which preserve the energy stability while ensuring fast computing. The related stability analysis is shown. To obtain high accurate solution, the solution of first-order direction splitting method is extrapolated to be fourth-order, and the fourth-order difference method is applied to spatial discretization. To further improve the stability and prevent the blow-up of numerical solution, two post-processing methods, the bound preserving least-distance modification and the cut-off approach, are developed to control the boundedness of numerical solution, and their theoretical proofs are given. The proposed novel algorithm can be performed in parallel in each time step, significantly improving computing efficiency. Several numerical examples demonstrate the effectiveness of the proposed algorithm, including convergence and stability tests, the effectiveness of two post-processing techniques, and a series of 2D and 3D dendritic crystal growth simulations.

提出了一种快速、准确、稳定的数值算法来求解各向异性相场枝晶生长模型。该算法结合一阶方向分裂法和线性稳定技术，在保证快速计算的同时保持能量稳定性。显示了相关的稳定性分析。为获得高精度解，将一阶方向分裂法的解外推为四阶，并将四阶差分法应用于空间离散化。为了进一步提高数值解的稳定性，防止数值解的爆炸，提出了两种后处理方法，即保界最小距离修正法和截断法来控制数值解的有界性，其理论证明如下：给定的。所提出的新算法可以在每个时间步中并行执行，显着提高了计算效率。几个数值例子证明了所提出算法的有效性，包括收敛性和稳定性测试、两种后处理技术的有效性，以及一系列 2D 和 3D 枝晶生长模拟。