A deformed scalar auxiliary variable approach without bounded below restriction for gradient flows
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Recently developed scalar auxiliary variable (SAV) approach has been proven to be a very efficient and powerful way to construct energy stable schemes for gradient flows. In this paper, we consider a deformed scalar auxiliary variable (DSAV) approach to obtain energy stable schemes for gradient flows. The deformed scheme gives a fixed and efficient constant E_0 in energy functional to replace C in square root before calculation. We proved the unconditional energy stability for all the semi-discrete schemes carefully and rigorously. The novelty of the proposed schemes is that we do not need to choose different constant C for different phase filed models. It means that the DSAV approach does not need the assumption that E_1(ϕ) is bounded from below which is essential in SAV approach. A comparative study of classical SAV and DSAV 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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