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In this paper, we consider an exponential scalar auxiliary variable (E-SAV)approach to obtain energy stable schemes for a class of phase field models.This novel auxiliary variable method based on exponential form of nonlinearfree energy potential is more effective and applicable than the traditional SAVmethod which is very popular to construct energy stable schemes. The firstcontribution is that the auxiliary variable without square root removes thebounded from below restriction of the nonlinear free energy potential. Then, weprove the unconditional energy stability for the semi-discrete schemescarefully and rigorously. Another contribution is that we can discrete theauxiliary variable combined with the nonlinear term totally explicitly. Suchmodification is very efficient for fast calculation. Furthermore, the positiveproperty of $r$ can be guaranteed which is very important and reasonable forthe models' equivalence. Besides, for complex phase field models with two ormore unknown variables and nonlinear terms, we construct a multiple E-SAV(ME-SAV) approach to enhance the applicability of the proposed E-SAV approach.A comparative study of classical SAV and E-SAV approaches is considered to showthe accuracy and efficiency. Finally, we present various 2D numericalsimulations to demonstrate the stability and accuracy.

The exponential scalar auxiliary variable (E-SAV) approach for phase field models and its explicit computing