  For the past few years, scalar auxiliary variable (SAV) and SAV-type
approaches became very hot and efficient methods to simulate various gradient
flows. Inspired by the new SAV approach in \cite{huang2020highly}, we propose a
novel technique to construct a new exponential scalar auxiliary variable
(E-SAV) approach to construct high-order numerical energy stable schemes for
gradient flows. To improve its accuracy and consistency noticeably, we propose
an E-SAV approach with relaxation, which we named the relaxed E-SAV (RE-SAV)
method for gradient flows. The RE-SAV approach preserves all the advantages of
the traditional SAV approach. In addition, we do not need any the
bounded-from-below assumptions for the free energy potential or nonlinear term.
Besides, the first-order, second-order and higher-order unconditionally energy
stable time-stepping schemes are easy to construct. Several numerical examples
are provided to demonstrate the improved efficiency and accuracy of the
proposed method.
