A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows.

We propose a new numerical technique to deal with nonlinear terms in gradient ows. By introducing a scalar auxiliary variable (SAV), we construct effcient and robust energy stable schemes for a large class of gradient ows. The SAV approach is not restricted to specific forms of the nonlinear part of the free energy and only requires solving decoupled linear equations with constant coeffcients. We use this technique to deal with several challenging applications which cannot be easily handled by existing approaches, and we present convincing numerical results to show that our schemes are not only much more effcient and easy to implement, but can also better capture the physical properties in these models. Based on this SAV approach, we can construct unconditionally second-order energy stable schemes, and we can easily construct even third- or fourth-order BDF schemes which, although not unconditionally stable, are very robust in practice. In particular, when coupled with an adaptive time stepping strategy, the SAV approach can be extremely effcient and accurate. [ABSTRACT FROM AUTHOR]