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Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification with two-sided diffusion

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タイトル: Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification with two-sided diffusion
著者: Ohno, Munekazu 著作を一覧する
Takaki, Tomohiro 著作を一覧する
Shibuta, Yasushi 著作を一覧する
発行日: 2016年 1月20日
出版者: American Physical Society (APS)
誌名: Physical Review E
巻: 93
号: 1
開始ページ: 012802-1
終了ページ: 012802-20
出版社 DOI: 10.1103/PhysRevE.93.012802
抄録: We present the variational formulation of a quantitative phase-field model for isothermal low-speed solidification in a binary dilute alloy with diffusion in the solid. In the present formulation, cross-coupling terms between the phase field and composition field, including the so-called antitrapping current, naturally arise in the time evolution equations. One of the essential ingredients in the present formulation is the utilization of tensor diffusivity instead of scalar diffusivity. In an asymptotic analysis, it is shown that the correct mapping between the present variational model and a free-boundary problem for alloy solidification with an arbitrary value of solid diffusivity is successfully achieved in the thin-interface limit due to the cross-coupling terms and tensor diffusivity. Furthermore, we investigate the numerical performance of the variational model and also its nonvariational versions by carrying out two-dimensional simulations of free dendritic growth. The nonvariational model with tensor diffusivity shows excellent convergence of results with respect to the interface thickness.
Rights: ©2016 American Physical Society
資料タイプ: article
URI: http://hdl.handle.net/2115/60739
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 大野宗一

 

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