An unconditionally energy-stable method for the phase field crystal equation

Hector Gomez; Xesus Nogueira

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An unconditionally energy-stable method for the phase field crystal equation

机译：相场晶体方程的无条件能量稳定方法

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The phase field crystal equation has been recently put forward as a model for microstructure evolution of two-phase systems on atomic length and diffusive time scales. The theory is cast in terms of an evolutive nonlinear sixth-order partial differential equation for the interatomic density that locally minimizes an energy functional with the constraint of mass conservation. Here we propose a new numerical algorithm for the phase field crystal equation that is second-order time-accurate and unconditionally stable with respect to the energy functional. We present several numerical examples in two and three dimensions dealing with crystal growth in a supercooled liquid and crack propagation in a ductile material. These examples show the effectiveness of our new algorithm.

机译：最近提出了相场晶体方程，作为在原子长度和扩散时间尺度上两相系统微观结构演化的模型。该理论是根据用于原子间密度的演化非线性六阶偏微分方程建立的，该方程在质量守恒的约束下局部最小化能量函数。在这里，我们为相场晶体方程式提出了一种新的数值算法，该算法是二阶时间精确的并且相对于能量函数是无条件稳定的。我们在二维和三维中提供了几个数值示例，这些示例涉及过冷液体中的晶体生长和韧性材料中的裂纹扩展。这些示例说明了我们新算法的有效性。

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来源
《Computer Methods in Applied Mechanics and Engineering》 |2012年第1期|52-61|共10页
作者
Hector Gomez; Xesus Nogueira;
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作者单位

Group of Numerical Methods in Engineering, University of A Coruna, Department of Mathematical Methods, Campus de Elviiia, s, 15192 A CoruHa, Spain;

Group of Numerical Methods in Engineering, University of A Coruna, Department of Mathematical Methods, Campus de Elviiia, s, 15192 A CoruHa, Spain;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
isogeometric analysis; time-integration; unconditionally stable; phase-field crystal;

机译：等几何分析时间整合无条件稳定;相场晶体;

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An unconditionally energy-stable method for the phase field crystal equation

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