In this article, we first establish a new flow-coupled binary phase-field crystal model and prove its energy law. Then by using some newly introduced variables, we reformulate this three-phase model into an equivalent form, which makes it possible to construct a fully discrete linearized decoupling scheme with unconditional energy stability and second-order time accuracy to solve this model for the first time. The energy law of the reformulated model is also proved. Then we incorporate the explicit-IEQ (invariant energy quadratization) method for the nonlinear potentials, the projection method for the Navier-Stokes equations, the Crank-Nicolson method for time marching, and the finite element method for spatial discretization together to develop the fully discrete scheme for the reformulated and equivalent system. By using the nonlocal splitting technique, at each time step, only a few decoupled constant-coefficient elliptic equations are required to be solved, even though the original and reformulated models are much more complicated in the form. The developed algorithm is further proved to be unconditionally energy stable, and a detailed implementation process is also provided. Various numerical experiments in 2D and 3D are carried out to verify the effectiveness of the developed scheme, including the binary crystal growth under the action of shear flow and the sedimentation process of many binary particles.

在本文中，我们首先建立了一种新的流耦合二元相场晶体模型，并证明了它的能量定律。然后通过使用一些新引入的变量，我们将这个三相模型重新构造成等价形式，这使得第一次有可能构造一个具有无条件能量稳定性和二阶时间精度的全离散线性化解耦方案来求解这个模型. 重新制定模型的能量定律也得到了证明。然后，我们将非线性势的显式 IEQ（不变能量二次化）方法、Navier-Stokes 方程的投影方法、时间推进的 Crank-Nicolson 方法和空间离散化的有限元方法结合在一起，以开发完全重新制定和等效系统的离散方案。通过使用非局部分裂技术，在每个时间步，即使原始模型和重构模型在形式上要复杂得多，也只需要求解几个解耦的常数系数椭圆方程。进一步证明了所开发的算法是无条件能量稳定的，并提供了详细的实现过程。为验证所开发方案的有效性，进行了各种 2D 和 3D 数值实验，包括剪切流作用下的二元晶体生长和许多二元颗粒的沉降过程。进一步证明了所开发的算法是无条件能量稳定的，并提供了详细的实现过程。为验证所开发方案的有效性，进行了各种 2D 和 3D 数值实验，包括剪切流作用下的二元晶体生长和许多二元颗粒的沉降过程。进一步证明了所开发的算法是无条件能量稳定的，并提供了详细的实现过程。为验证所开发方案的有效性，进行了各种 2D 和 3D 数值实验，包括剪切流作用下的二元晶体生长和许多二元颗粒的沉降过程。