Fully decoupled energy-stable numerical schemes for two-phase coupled porous media and free flow with different densities and viscosities
Fully decoupled energy-stable numerical schemes for two-phase coupled porous media and free flow with different densities and viscosities
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DOI：
10.1051/m2an/2023012
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发表时间：
2023-02
期刊：
影响因子：
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通讯作者：
Yali Gao;Xiaoming He;Tao Lin;Yanping Lin
中科院分区：
文献类型：
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作者：
Yali Gao;Xiaoming He;Tao Lin;Yanping Lin
本文考虑了多孔介质两相流与两相自由流耦合的不同密度和粘度的相场模型，并进行了相应的数值模拟。该模型由三部分组成：描述基质中多孔介质流动的不同密度/粘度的Cahn-Hilliard-Darcy系统，描述管道中自由流体的不同密度/粘度的Cahn-Hilliard-Navier-Stokes系统，以及耦合基质和管道中流动的七个界面条件。基于多孔介质区和自由流动区的Cahn-Hilliard方程，提出了一个弱模型，该模型包含了两个区域的两相体系和它们之间的7个界面条件，并证明了相应的能量定律。一个完全解耦的数值格式，包括新的解耦的Cahn-Hilliard方程通过四个相界面条件，开发解决这个耦合的非线性相场模型。分析了时间半离散化方案的能量守恒性。在此基础上，提出了一种全离散的Galerkin有限元方法。六个数值例子证明了所提出的完全解耦格式的精度、离散能量定律和适用性。
In this article, we consider a phase field model with different densities and viscosities for the coupled two-phase porous media flow and two-phase free flow, as well as the corresponding numerical simulation. This model consists of three parts: a Cahn-Hilliard-Darcy system with different densities/viscosities describing the porous media flow in matrix, a Cahn-Hilliard-Navier-Stokes system with different densities/viscosities describing the free fluid in conduit, and seven interface conditions coupling the flows in the matrix and the conduit. Based on the separate Cahn-Hilliard equations in the porous media region and the free flow region, a weak formulation is proposed to incorporate the two-phase systems of the two regions and the seven interface conditions between them, and the corresponding energy law is proved for the model. A fully decoupled numerical scheme, including the novel decoupling of the Cahn-Hilliard equations through the four phase interface conditions, is developed to solve this coupled nonlinear phase field model. An energy-law preservation is analyzed for the temporal semi-discretization scheme. Furthermore, a fully discretized Galerkin finite element method is proposed. Six numerical examples are provided to demonstrate the accuracy, discrete energy law, and applicability of the proposed fully decoupled scheme.