A novel relaxed scalar auxiliary variable approach for gradient flows

In this paper, we propose a novel relaxed scalar auxiliary variable (nRSAV) approach to solve a series of gradient flow problems. The proposed nRSAV approach inherits all the advantages of the traditional SAV and RSAV method. Meanwhile, it preserves a quite close original energy dissipative law and provides an improved accuracy than the baseline SAV method. Besides, compared with the RSAV approach, we do not need to solve a quadratic equation with one unknown to obtain the relaxation. All the semi-discrete schemes are proved to be unconditionally energy stable. Several numerical examples are provided to demonstrate the improved efficiency and accuracy of the proposed method.(c) 2023 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, a novel relaxed scalar auxiliary variable (nRSAV) approach is proposed to solve gradient flow problems. The method inherits the advantages of the traditional SAV and RSAV methods, while maintaining a close original energy dissipative law and improved accuracy compared to the baseline SAV method. Furthermore, it eliminates the need to solve a quadratic equation with one unknown to obtain the relaxation, as required by the RSAV approach. All the semi-discrete schemes are proven to be unconditionally energy stable. Numerical examples are provided to demonstrate the improved efficiency and accuracy of the proposed method.