A fully decoupled, linear and unconditionally energy stable numerical scheme for a melt-convective phase-field dendritic solidification model
A fully decoupled, linear and unconditionally energy stable numerical scheme for a melt-convective phase-field dendritic solidification model
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DOI：
10.1016/j.cma.2019.112779
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发表时间：
2020-05
影响因子：
7.2
通讯作者：
Jun Zhang;Xiaofeng Yang
中科院分区：
文献类型：
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作者：
Jun Zhang;Xiaofeng Yang
本文考虑熔体-对流相场-枝晶凝固模型的数值逼近。求解该模型的一个具有挑战性的数值问题是，由于该模型是一个高度耦合的非线性系统，如何发展出有效的时间推进格式，不仅是无条件能量稳定的，而且是线性和完全解耦的。我们结合了Navier-Stokes方程的修正投影格式和各向异性相场方程的稳定不变能量二次化方法来解决这个问题。同时，为了获得完全解耦的特性，我们引入了一个辅助的中间温度变量，将温度的计算与相场变量解耦。我们证明了该格式的无条件能量稳定性，并给出了各种二维和三维的数值模拟，以证明该格式的精度和稳定性。
We consider in this paper numerical approximations of a melt-convective phase-field dendritic solidification model. A challenging numerical issue for solving this model is how to develop efficient time marching schemes that are not only unconditionally energy stable, but also linear and totally decoupled since the model is a highly coupled nonlinear system. We solve this issue by combining the modified projection scheme for the Navier–Stokes equations, the stabilized-Invariant Energy Quadratization method for the anisotropic phase field equation. Meanwhile, in order to obtain the fully decoupled feature, we introduce an auxiliary intermediate temperature variable to decouple the computation of the temperature from the phase field variable. We prove the unconditional energy stability of the developed scheme and further present various numerical simulations in 2D and 3D to demonstrate the accuracy and stability of the developed scheme.