论文标题
梯度流的广义标量辅助变量方法（G-SAV）
The generalized scalar auxiliary variable approach (G-SAV) for gradient flows
论文作者
论文摘要
我们建立了一个通用框架，用于开发有效的能量稳定的数值方案，以用于梯度流，并开发三类的广义标量辅助变量方法（G-SAV）。基于G-SAV方法的数值方案与原始SAV方案\ cite {sxy19，cheng2018multiple}的原始SAV方案一样有效，即梯度流量，即仅需要在每个时间步骤中均具有恒定系数的求解线性方程，可以无条件地稳定。但是G-SAV方法删除了辅助变量只能是平方根函数的定义限制。辅助变量的定义形式适用于G-SAV方法的任何可逆函数。给出了相位场模型的足够数值结果，以验证所提出的G-SAV数值方案的有效性和准确性。
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.
