Generalized SAV approaches for gradient systems
Generalized SAV approaches for gradient systems
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DOI：
10.1016/j.cam.2021.113532
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Q. Cheng;Chun Liu;Jie Shen
中科院分区：
文献类型：
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作者：
Q. Cheng;Chun Liu;Jie Shen
本文提出了三种广义辅助标量变量（G-SAV）方法来开发梯度系统的高效能量稳定数值格式。前两种G-SAV方法允许SAV变量定义中的一系列函数，此外，第二种G-SAV方法仅需要从下面限制总自由能，而不是要求从下面限制自由能的非线性部分。另一方面，第三种G-SAV方法相对于原始自由能是无条件能量稳定的，而不是修改的能量。各种梯度系统的数值结果验证了所提出的G-SAV方法的有效性和准确性。
We propose in this paper three generalized auxiliary scalar variable (G-SAV) approaches for developing, efficient energy stable numerical schemes for gradient systems. The first two G-SAV approaches allow a range of functions in the definition of the SAV variable, furthermore, the second G-SAV approach only requires the total free energy to be bounded from below as opposed to the requirement that the nonlinear part of the free energy to be bounded from below. On the other hand, the third G-SAV approach is unconditionally energy stable with respect to the original free energy as opposed to a modified energy. Ample numerical results for various gradient systems are presented to validate the effectiveness and accuracy of the proposed G-SAV approaches.