The exponential scalar auxiliary variable (E-SAV) approach for phase field models and its explicit computing
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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 nonlinear free energy potential is more effective and applicable than the classical SAV method which is very popular to construct energy stable schemes for phase field models. The first contribution is that we remove the bounded below restriction of nonlinear free energy potential by using the positive property of the exponential functions. Then, we prove the unconditional energy stability for the semi-discrete schemes carefully and rigorously. Another contribution is that the computations of ϕ and the auxiliary variable r are totally decoupled in the discrete scheme based on E-SAV approach. Such modification is very efficient for fast calculation. Besides, for complex phase field models with two or more 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 show the accuracy and efficiency. Finally, we present various 2D numerical simulations to demonstrate the stability and accuracy.
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