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 flows. By introducing a scalar auxiliary variable (SAV), we construct efficient and robust energy stable schemes for a large class of gradient flows. The SAV approach is not restricted to specific forms of the nonlinear part of the free energy, and only requires to solve {\it decoupled} linear equations with {\it constant coefficients}. We use this technique to deal with several challenging applications which can not be easily handled by existing approaches, and present convincing numerical results to show that our schemes are not only much more efficient and easy to implement, but can also better capture the physical properties in…

• NS
  National Science Foundation

  Awards: DMS-1620262, DMS-1720442
• NN
  National Natural Science Foundation of China

  Awards: 51661135011, 91630204
• AF
  Air Force Office of Scientific Research

  Award: FA9550-16-1-0102