In this paper, we consider numerical approximations for solving the Cahn-Hilliard phase-field model with the Flory-Huggins-de Gennes free energy for homopolymer blends. We develop an efficient, second-order accurate, and unconditionally energy stable scheme that combines the SAV approach with the stabilization technique, in which the H¹ norm is split from the total free energy and two extra linear stabilization terms are added to enhance the stability and keeping the required accuracy while using large time steps. The scheme is very easy to implement and non-iterative where one only needs to solve two decoupled fourth-order biharmonic equations with constant coefficients at each time step. We further prove the unconditional energy stability of the scheme rigorously. Through the comparisons with some other prevalent schemes like the non-stabilized-SAV and MSAV schemes for some benchmark numerical examples in 2D and 3D, we demonstrate the stability and the accuracy of the developed scheme numerically.

中文翻译：

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具有Flory-Huggins-de Gennes自由能的Cahn-Hilliard相场模型的非迭代，无条件能量稳定和大时步方法

在本文中，我们考虑了数值近似，用于用均聚物共混物的Flory-Huggins-de Gennes自由能求解Cahn-Hilliard相场模型。我们开发了一种有效的，二阶准确且无条件的能量稳定方案，该方案将SAV方法与稳定技术相结合，其中H ¹将规范从总自由能中分离出来，并添加了两个额外的线性稳定项，以增强稳定性并在使用较大时间步长的同时保持所需的精度。该方案非常容易实现，并且不需要迭代，只需在每个时间步求解两个常数系数解耦的四阶双调和方程即可。我们进一步严格证明了该方案的无条件能量稳定性。通过与2D和3D中一些基准数值示例的非稳定SAV和MSAV方案等其他流行方案的比较，我们以数值方式证明了所开发方案的稳定性和准确性。