ABSTRACT Typical solidification microstructures consist of equiaxed and columnar structures. During solidification, convection of liquid plays a crucial role on both solidification structures. Here, the growth direction of columnar structures is changed by the convection [1], and free dendrites flowing within the melt form the equiaxed structure

M Ohno

R Rojas

T Takaki

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Coupling Simulations of Growth and Motion of Dendrite by  
Phase-field Lattice Boltzmann Method 
T. Takaki*, R. Rojas† and M. Ohno†† 
* Mechanical and System Engineering, Kyoto Institute of Technology 
Matsugasaki, Sakyo, Kyoto 606-8585, Japan 
e-mail: takaki@kit.ac.jp, web page: http://www.cis.kit.ac.jp/~takaki/ 
 
† Mechanical and System Engineering, Kyoto Institute of Technology 
Matsugasaki, Sakyo, Kyoto 606-8585, Japan 
e-mail: rojas@kit.ac.jp 
 
†† Faculty of Engineering, Hokkaido University 
Kita 13 Nishi 8, Kita, Sapporo, 060-8628 Hokkaido, Japan 
e-mail: mohno@eng.hokudai.ac.jp 
 
ABSTRACT 
Typical solidification microstructures consist of equiaxed and columnar structures. During 
solidification, convection of liquid plays a crucial role on both solidification structures. Here, the 
growth direction of columnar structures is changed by the convection [1], and free dendrites flowing 
within the melt form the equiaxed structures [2]. 
Due to some computational advantages over other numerical techniques, the phase-field method (PFM) 
has emerged as the most powerful numerical tool to simulate dendritic solidification [3]. The PFM has 
been also applied to dendritic growth in fluid flow [4]. However, almost all simulations have been 
carried out for fixed dendrites in fluid flow, and only few phase-field studies have been done for 
moving dendrites [5]. Recently, we have developed a phase-field lattice Boltzmann method (PFLBM) 
which can simultaneously simulate dendritic growth, and translation and rotation of the solid phase in 
fluid flow [6].  
In this study, by using the PFLBM, we simulate dendritic growth with motion induced by fluid flow at 
various conditions, such as in forced flow, rising and sinking due to gravity, multiple dendrites, and so 
on. To accelerate those simulations, we perform parallel computing using multiple graphics processing 
units (GPUs) [7].  
REFERENCES 
[1] K. Murakami, T. Fujiyama, A. Koike and T. Okamoto, “Influence of melt flow on the growth 
directions of columnar grains and columnar dendrites”, Acta Metall., 31, pp. 1425-1432, (1983). 
[2] H. Yasuda, Y. Yamamoto, N. Nakatsuka, M. Yoshiya, T. Nagira, A. Sugiyama, I. Ohnaka, K. 
Uesugi and K. Umetani, “In situ observation of solidification phenomena in Al-Cu and Fe-Si-Al 
alloys”, Int. J. Cast Met. Res., 22, pp.15-21, (2009). 
[3] T. Takaki, “Phase-field Modeling and Simulations of Dendrite Growth”, ISIJ Int., 54, 437-444, 
(2014). 
[4] C. Beckermann, H.J. Diepers, I. Steinbach, A. Karma and X. Tong, “Modeling Melt Convection 
in Phase-Field Simulations of Solidification”, J. Comput. Phys., 154, 468-496, (1999). 
[5] M. Do-Quang, G. Amberg, “Simulation of free dendritic crystal growth in a gravity environment”, 
J. Comput. Phys., 227, 1772-1789, (2008). 
[6] R. Rojas, T. Takaki and M. Ohno, submitting. 
[7] T. Takaki, T. Shimokawabe, M. Ohno, A. Yamanaka and T. Aoki, “Unexpected selection of 
growing dendrites by very-large-scale phase-field simulation”, J. Cryst. Growth, 382, 21-25, 
(2013). 


Coupling Simulations of Growth and Motion of Dendrite by Phase-field Lattice Boltzmann Method

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Coupling Simulations of Growth and Motion of Dendrite by Phase-field Lattice Boltzmann Method

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