论文标题
耗散系统的高效和准确的半刻度标量辅助变量（ESI-SAV）方法
A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system
论文作者
论文摘要
标量辅助变量（SAV）方法是一种非常流行和有效的方法，用于模拟各种相位字段模型。为了节省计算成本，通过引入新的变量$θ$给出了一种新的SAV方法。可以证明新的SAV方法可以节省原始SAV方法的近一半CPU时间，同时保留其所有其他优势。在本文中，我们提出了一种新型技术，以构建指数的半密度标量辅助变量（ESI-SAV）方法，而无需引入任何额外的变量。新提出的方法还只需要在每个时间步长以恒定系数求解一个线性方程。此外，构造的ESI-SAV方法不需要以下非线性自由能电位的限制，这对于各种相位场模型更合理且有效。同时，很容易构建一阶，二阶和高阶无条件能量稳定的时间稳定方案。除此之外，可以证明ESI-SAV方法可以有效地解决非梯度但耗散的系统，例如Navier-Stokes方程。提供了几个数值示例，以证明该方法的提高效率和准确性。
The scalar auxiliary variable (SAV) approach is a very popular and efficient method to simulate various phase field models. To save the computational cost, a new SAV approach is given by introducing a new variable $θ$. The new SAV approach can be proved to save nearly half CPU time of the original SAV approach while keeping all its other advantages. In this paper, we propose a novel technique to construct an exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach without introducing any extra variables. The new proposed method also only needs to solve one linear equation with constant coefficients at each time step. Furthermore, the constructed ESI-SAV method does not need the bounded below restriction of nonlinear free energy potential which is more reasonable and effective for various phase field models. Meanwhile it is easy to construct first-order, second-order and higher-order unconditionally energy stable time-stepping schemes. Other than that, the ESI-SAV approach can be proved to be effective to solve the non-gradient but dissipative system such as Navier-Stokes equations. Several numerical examples are provided to demonstrate the improved efficiency and accuracy of the proposed method.
