The thermodynamically consistent Cahn-Hilliard-Extended-Darcy (CHED) model has been used to describe transient motion of a binary incompressible fluid flow in porous media. In this paper, we develop a series of linear, second-order, energy-dissipation-rate preserving numerical algorithms for the CHED model based on the energy quadratization strategy. We first extend the incompressible CHED model into a weakly compressible, thermodynamically consistent one using the generalized Onsager principle. Guided by the weakly compressible model, we then devise a couple of linear, second-order, decoupled, semi-discrete, temporal algorithms in the form of projection and the energy quadratization (EQ) method. The fully discrete algorithms are obtained by the use of the second-order finite difference method on staggered grids in space. We show theoretically that the obtained numerical algorithms respect the energy-dissipation-rate and the volume conservation property at the discrete level for any time steps, making them unconditionally energy stable. Mesh refinement tests, coarsening dynamics of binary fluids, and the buoyancy-driven binary fluid motion in porous media are investigated numerically. In buoyancy-driven flow simulations, a new set of inflow and outflow boundary conditions are devised using the model. The numerical results compare well with the results in the literature.

热力学一致的 Cahn-Hilliard-Extended-Darcy (CHED) 模型已用于描述多孔介质中二元不可压缩流体流动的瞬态运动。在本文中，我们为基于能量二次化策略的​​ CHED 模型开发了一系列线性、二阶、能量耗散率保持数值算法。我们首先使用广义 Onsager 原理将不可压缩的 CHED 模型扩展为弱可压缩、热力学一致的模型。在弱可压缩模型的指导下，我们设计了一些线性的、二阶的、解耦的、半离散的、投影形式的时间算法和能量二次方化 (EQ) 方法。完全离散算法是通过在空间交错网格上使用二阶有限差分方法获得的。我们从理论上表明，所获得的数值算法在任何时间步长的离散水平上都尊重能量耗散率和体积守恒性质，使它们无条件地能量稳定。数值研究了网格细化测试、二元流体的粗化动力学和浮力驱动的二元流体在多孔介质中的运动。在浮力驱动的流动模拟中，使用该模型设计了一组新的流入和流出边界条件。数值结果与文献中的结果比较良好。数值研究了多孔介质中浮力驱动的二元流体运动。在浮力驱动的流动模拟中，使用该模型设计了一组新的流入和流出边界条件。数值结果与文献中的结果比较良好。数值研究了多孔介质中浮力驱动的二元流体运动。在浮力驱动的流动模拟中，使用该模型设计了一组新的流入和流出边界条件。数值结果与文献中的结果比较良好。