A multitude of substances exist as mixtures comprising multiple chemical components in the natural world. These substances undergo morphological changes under external influences. the phase field model coupled with fluid flow, the dynamic movement and evolution of the phase interface intricately interact with the fluid motion. This article focuses on the N-component models that couple the conservative Allen-Cahn equation with two types of incompressible fluid flow systems: the Navier-Stokes equation and the Darcy equation. By utilizing the scalar auxiliary variable method and the projection method, we innovatively construct two types of structure-preserving weighted implicit-explicit schemes for the coupled models, resulting in fully decoupled linear systems and second-order accuracy in time. The schemes are proved to be mass-conservative. In addition, with the application of $G$-norm inspired by the idea of $G$-stability, we rigorously establish its unconditional energy stability. Finally, the performance of the proposed scheme is verified by some numerical simulations.

翻译：自然界中大量物质以多化学组分混合物的形式存在。这些物质在外界影响下会发生形态变化。对于与流体流动耦合的相场模型，相界面的动态运动与演化与流体运动存在复杂交互作用。本文聚焦于将守恒型Allen-Cahn方程与两类不可压流体流动系统（Navier-Stokes方程与Darcy方程）耦合的N组分模型。通过采用标量辅助变量法与投影法，我们创新性地为耦合模型构建了两类结构保持的加权隐式-显式格式，从而实现了完全解耦的线性系统与时间二阶精度。这些格式被证明具有质量守恒性。此外，基于$G$-稳定性思想引入$G$-范数后，我们严格建立了格式的无条件能量稳定性。最后，通过数值模拟验证了所提格式的性能。