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首页> 外文期刊>Journal of Crystal Growth >A multiphase-field model f sharp interface asymptotics and numerical simulations of moving phase boundaries and multjunctions
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A multiphase-field model f sharp interface asymptotics and numerical simulations of moving phase boundaries and multjunctions

机译：尖锐界面渐近性的多相场模型和运动相边界和多结的数值模拟

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In this paper we bring together, compare and extend two recent developments in a special formulation of an anisotropic multiphase-field model; namely the results of sharp interface asymptotic analysis by Nestler and Wheeler [B. Nestler, A.A. Wheeler, Phys. Rev. E 57 (3) (1998) 2602.] and numerical simulations of moving phase boundaries and multjunctions by Garcke et al. [H. Garcke, B. Nestler, B. Stoth, Physica D 115 (1998) 87, SIAM J. Appl. Math., in press]. First, we present the formulation of the multiphase-field model, which includes surface energy anisotropy. Then we state, how the leading order conditions at both interfaces and junctions can succinctly be derived in the sharp interface limit by introducing a generalized Cahn-Hoffman ξ-vector formalism and by using the motion of a stress tensor. These analytical results contain that the force balance at multi junctions is recovered, which comprises Young's law and, in the anisotropic case, additional shear forces. Next, we present numerical simulations of evolving phase boundaries and junctions, concentrating on the case of isotropic phases. We find that our numerical solutions of the multiphase-field model compare favorably with the exact solutions of the sharp interface analytical results. We observe that the classical angle conditions at trijunctions are obtained numerically. Finally, we perform simulations of grain growth evolution and numerically verify the validity of the qualitative features of the von Neumann law.
机译：在本文中，我们将各向异性多相场模型的特殊公式汇总，比较和扩展了两个最新进展。即由Nestler和Wheeler [B.提出的清晰的界面渐近分析结果。雀巢公司惠勒，物理学。 Rev. E 57（3）（1998）2602.]和Garcke等人的运动相边界和多结的数值模拟。 [H。 Garcke，B.Nestler，B.Stoth，Physica D 115（1998）87，SIAM J.Appl。数学，印刷中]。首先，我们提出了包含表面能各向异性的多相场模型。然后我们说明，如何通过引入广义的Cahn-Hoffmanξ-向量形式主义并利用应力张量的运动，在尖锐的界面极限中简洁地导出界面和结点处的先导条件。这些分析结果包含恢复了多结点处的力平衡，这包括杨氏定律，并且在各向异性情况下还包括附加的剪力。接下来，我们将重点介绍各向同性相的情况，对演化的相界和结进行数值模拟。我们发现，我们的多相场模型的数值解与尖锐的界面分析结果的精确解相比具有优势。我们观察到三点的经典角度条件是通过数值获得的。最后，我们进行晶粒长大演化的模拟，并数值验证冯·诺依曼定律的定性特征的有效性。

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