Second order linear decoupled energy dissipation rate preserving schemes for the Cahn-Hilliard-extended-Darcy model
Second order linear decoupled energy dissipation rate preserving schemes for the Cahn-Hilliard-extended-Darcy model
复制标题
Cahn-Hilliard-extend-Darcy 模型的二阶线性解耦能量耗散率保持方案
DOI：
10.1016/j.jcp.2021.110561
复制
发表时间：
2021
影响因子：
4.1
通讯作者：
Wang, Qi
中科院分区：
文献类型：
--
作者：
Li, Yakun;Yu, Wenkai;Zhao, Jia;Wang, Qi
热力学一致的卡恩-希利亚德-扩展-达西 (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，我们基于能量二次化策略，为 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 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，我们设计了一些投影形式的线性、二阶、解耦、半离散、时间算法和能量二次化（EQ）方法。利用空间交错网格上的二阶有限差分法得到了全离散算法。我们从理论上证明，所获得的数值算法在任何时间步长上都遵循离散水平上的能量耗散率和体积守恒性质，从而使它们无条件能量稳定。对网格细化测试、二元流体的粗化动力学以及多孔介质中浮力驱动的二元流体运动进行了数值研究。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很好地比较。
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.