A level set simulation of dendritic solidification with combined features of front-tracking and fixed-domain methods
A level set simulation of dendritic solidification with combined features of front-tracking and fixed-domain methods
复制标题
DOI：
10.1016/j.jcp.2005.05.013
复制
发表时间：
2006
影响因子：
4.1
通讯作者：
Lijian Tan;N. Zabaras
中科院分区：
文献类型：
--
作者：
Lijian Tan;N. Zabaras
结合前沿跟踪法和固定域法的特点，提出了一种模拟纯材料枝晶凝固的方法。为了明确地跟踪界面生长和凝固晶体的形状，基于水平集方法的前端跟踪方法。为了方便地模拟热量和动量的传输，一个固定域的方法来实现，假设一个扩散的冻结前的液体分数定义的水平集函数。固定域的方法，通过避免显式应用的基本边界条件上的冻结前，导致能量守恒的方法，是不敏感的网格大小。为了计算冻结锋形态，考虑了一个扩展的Stefan条件。应用到几个经典的斯特凡问题和二维和三维晶体生长的纯材料在过冷熔体，包括熔体流动的影响被认为是。计算结果与现有的解析解以及采用波前跟踪技术和相场法得到的结果吻合得很好。
A method combining features of front-tracking methods and fixed-domain methods is presented to model dendritic solidification of pure materials. To explicitly track the interface growth and shape of the solidifying crystals, a front-tracking approach based on the level set method is implemented. To easily model the heat and momentum transport, a fixed-domain method is implemented assuming a diffused freezing front where the liquid fraction is defined in terms of the level set function. The fixed-domain approach, by avoiding the explicit application of essential boundary conditions on the freezing front, leads to an energy conserving methodology that is not sensitive to the mesh size. To compute the freezing front morphology, an extended Stefan condition is considered. Applications to several classical Stefan problems and two- and three-dimensional crystal growth of pure materials in an undercooled melt including the effects of melt flow are considered. The computed results agree very well with available analytical solutions as well as with results obtained using front-tracking techniques and the phase-field method.