Abstract The numerical approximations for the coupled Cahn–Hilliard system describing the phase separation of the copolymer and homopolymer mixtures are considered in this paper. To develop easy to implement time marching schemes with unconditional energy stabilities, we use the Scalar Auxiliary Variable (SAV) approach for achieving two efficient, decoupled, and linear numerical schemes, where a new scalar auxiliary variable is introduced to reformulate the model. The schemes lead to decoupled linear equations with constant coefficients at each time step, and their unique solvability and unconditional energy stabilities are proved rigorously. Numerical examples are performed to demonstrate the accuracy and energy stability of the proposed schemes, and numerous benchmark simulations are also presented to show a variety of morphologies of pattern formations of the copolymer and homopolymer mixtures.

中文翻译：

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共聚物/均聚物混合物中耦合 Cahn-Hilliard 系统的高效、解耦和二阶无条件能量稳定数值方案

摘要 本文考虑了描述共聚物和均聚物混合物相分离的耦合 Cahn-Hilliard 系统的数值近似。为了开发易于实现且具有无条件能量稳定性的时间推进方案，我们使用标量辅助变量 (SAV) 方法来实现两种高效、解耦和线性数值方案，其中引入了新的标量辅助变量来重新制定模型。该方案导致在每个时间步长具有常系数的解耦线性方程，并严格证明了其独特的可解性和无条件能量稳定性。执行数值例子来证明所提出方案的准确性和能量稳定性，