The generalized scalar auxiliary variable approach (G-SAV) for gradient flows

Abstract: We establish a general framework for developing, efficient energy stable numerical schemes for gradient flows and develop three classes of generalized scalar auxiliary variable approaches (G-SAV). Numerical schemes based on the G-SAV approaches are as efficient as the original SAV schemes \cite{SXY19,cheng2018multiple} for gradient flows, i.e., only require solving linear equations with constant coefficients at each time step, can be unconditionally energy stable. But G-SAV approaches remove the definition restriction that auxiliary variables can only be square root function. The definition form of auxiliary variable is applicable to any reversible function for G-SAV approaches . Ample numerical results for phase field models are presented to validate the effectiveness and accuracy of the proposed G-SAV numerical schemes.