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.