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

作者：Gomez Hector^*; Nogueira Xesus

来源：Computer Methods in Applied Mechanics and Engineering, 2012, 249: 52-61.

DOI：10.1016/j.cma.2012.03.002

• Isogeometric Analysis
• Time-integration
• Unconditionally stable
• Phase-field crystal

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.

• 出版日期2012-12-1