Abstract In the current study, Fourier Pseudo-spectral based dealiasing scheme Random Phase Shift Method (RPSM) using the RK4 temporal scheme is implemented for simulating some benchmark problems of Phase Field based pure metal solidification. This high-resolution scheme is capable of resolving the thin solid-liquid interface accurately without using Adaptive Mesh Refinement (AMR) algorithm even using just adequate number of grid points. Both the conservative and non-conservative forms of the Phase Field equations are studied. It is found that the conservative RPSM scheme gives better computational performances as indicated by the lower values of average CPU time and different error norms calculated for the Phase Field variable. The RPSM based Phase Field model is applied for simulating dendritic solidification and it is found that dendrite shape and dimensionless tip velocity agree well with the existing literature. The RK4 based RPSM scheme is also compared with a 10 th order exponential Fourier smoothing Filter in the evolution of four arm dendritic structure and it is observed that the conservative Phase Field equations with filtering scheme display numerical instabilities at later simulation time, while both forms of the RPSM scheme show stable and accurate solutions. Subsequently, the capability of the RPSM based Phase Field model in simulating microstructure evolution consisting of multiple dendrites with random location and orientation is demonstrated. The present study shows that the RPSM based Phase Field model computes dendritic growth accurately and efficiently.

中文翻译：

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一种有效的基于伪光谱的相场方法用于枝晶凝固

摘要 在当前的研究中，采用基于傅立叶伪光谱的去混叠方案随机相移方法（RPSM）使用RK4时间方案来模拟基于相场的纯金属凝固的一些基准问题。即使仅使用足够数量的网格点，这种高分辨率方案也无需使用自适应网格细化 (AMR) 算法即可准确解析薄固液界面。研究了相场方程的保守和非保守形式。发现保守的 RPSM 方案提供更好的计算性能，如平均 CPU 时间的较低值和为相场变量计算的不同误差范数所示。基于RPSM的相场模型用于模拟枝晶凝固，发现枝晶形状和无量纲尖端速度与现有文献非常吻合。基于 RK4 的 RPSM 方案还在四臂树枝状结构的演化过程中与 10 阶指数傅立叶平滑滤波器进行了比较，观察到具有滤波方案的保守相场方程在后期模拟时表现出数值不稳定性，而两种形式的RPSM 方案显示稳定和准确的解决方案。随后，证明了基于 RPSM 的相场模型在模拟由具有随机位置和方向的多个枝晶组成的微观结构演变方面的能力。