基于能量上界的新型辅助变量的梯度流能量稳定格式
Energy stable schemes for gradient flows based on novel auxiliary variable with energy bounded above
摘要：
本文考虑一种新的辅助变量方法来获得梯度流的能量稳定格式。基于能量有界的辅助变量不限于以前方法中采用的假设条件。我们仔细而严格地证明了所有半离散格式的无条件能量稳定性。所提出的计划的新颖性是，平方根的功能的计算值被保证是积极的。这种方法，称为新的辅助能量变量（NAEV）方法不再考虑任何有界下的限制。然而，这些限制是必要的不变能量二次化（IEQ）和标量辅助变量（SAV）的方法，这是非常流行的方法，最近。这种保证正性的性质在以前的方法中是不可用的。经典的SAV和NAEV方法的比较研究被认为是显示的准确性和效率。最后，我们提出了各种二维数值模拟，以证明稳定性和准确性。
英文摘要：
In this paper, we consider a novel auxiliary variable method to obtain energy stable schemes for gradient flows. The auxiliary variable based on energy bounded above does not limited to the hypothetical conditions adopted in previous approaches. We proved the unconditional energy stability for all the semi-discrete schemes carefully and rigorously. The novelty of the proposed schemes is that the computed values for the functional in square root are guaranteed to be positive. This method, termed novel auxiliary energy variable (NAEV) method does not consider any bounded below restrictions any longer. However, these restrictions are necessary in invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches which are very popular methods recently. This property of guaranteed positivity is not available in previous approaches. A comparative study of classical SAV and NAEV approaches is considered to show the accuracy and efficiency. Finally, we present various 2D numerical simulations to demonstrate the stability and accuracy.
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