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 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.