Abstract The phase-field method coupling with thermodynamic data has become a trend for predicting the microstructure formation in technical alloys. Nevertheless, the frequent access to thermodynamic database and calculation of local equilibrium conditions can be time intensive. The extrapolation methods, which are derived based on Taylor expansion, can provide approximation results with a high computational efficiency, and have been proven successful in applications. This paper presents a high precision second order extrapolation method for calculating the driving force in phase transformation. To obtain the phase compositions, different methods in solving the quasi-equilibrium condition are tested, and the M-slope approach is chosen for its best accuracy. The developed second order extrapolation method along with the M-slope approach and the first order extrapolation method are applied to simulate dendrite growth in a Ni-Al-Cr ternary alloy. The results of the extrapolation methods are compared with the exact solution with respect to the composition profile and dendrite tip position, which demonstrate the high precision and efficiency of the newly developed algorithm. To accelerate the phase-field and extrapolation computation, the graphic processing unit (GPU) based parallel computing scheme is developed. The application to large-scale simulation of multi-dendrite growth in an isothermal cross-section has demonstrated the ability of the developed GPU-accelerated second order extrapolation approach for multiphase-field model.

中文翻译：

---

一种模拟枝晶生长的多相场模型高精度外推方法

摘要 结合热力学数据的相场法已成为预测工业合金微观结构形成的趋势。然而，频繁访问热力学数据库和计算局部平衡条件可能需要大量时间。基于泰勒展开式推导出的外推方法可以提供具有较高计算效率的近似结果，并且已经在应用中被证明是成功的。本文提出了一种用于计算相变驱动力的高精度二阶外推方法。为了获得相组成，测试了求解准平衡条件的不同方法，并选择了 M 斜率方法以获得最佳精度。所开发的二阶外推法以及 M 斜率法和一阶外推法用于模拟 Ni-Al-Cr 三元合金中的枝晶生长。外推方法的结果与关于成分轮廓和枝晶尖端位置的精确解进行了比较，这证明了新开发算法的高精度和效率。为了加速相场和外推计算，开发了基于图形处理单元（GPU）的并行计算方案。等温截面中多枝晶生长的大规模模拟的应用证明了开发的 GPU 加速二阶外推方法对多相场模型的能力。