This paper considers the numerical approximation of a two-component phase-field crystal model consisting of two coupled nonlinear Cahn–Hilliard equations of binary alloys. We develop a highly efficient time-marching scheme with second-order accuracy based on the SAV approach, in which two additional stabilization terms are introduced to improve stability, thus allowing large time steps. Unconditional energy stability is then proved strictly. By simulating a large number of numerical simulations in 2D and 3D, including binary crystal growth and phase separation with vacancies, we then verify the stability and accuracy of the scheme.

中文翻译：

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二元合金两组分相场晶体模型的高效稳定数值算法

本文考虑了由二元合金的两个耦合的非线性Cahn-Hilliard方程组成的两组分相场晶体模型的数值近似。我们基于SAV方法开发了一种具有二阶精度的高效时间行进方案，其中引入了两个附加的稳定项以提高稳定性，从而允许较大的时间步长。然后严格证明了无条件的能量稳定性。通过在2D和3D中模拟大量数值模拟，包括二元晶体生长和具有空位的相分离，我们然后验证了该方案的稳定性和准确性。