Abstract
This paper reports a numerical study of coupling two-phase fluid flow in a free fluid region with two-phase Darcy flow in a homogeneous and anisotropic porous medium region. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Obtained results have shown the anisotropic properties effect on the velocity and pressure of the two-phase flow.
Highlights
Fluid flows in coupled free flow and porous media regions are of great interest and have several important applications, such as ground water systems [1], well-reservoir coupling in petroleum engineering [2], fluid-organ interactions, and industrial filtering where fluid passes through a filter to remove unwanted particles [3]
A transmission condition for the two-phase flow is imposed at the interface boundary of the free flow region and the porous media region
The two-phase flow crossing the interface between free flow region and anisotropic porous media region is considered
Summary
Fluid flows in coupled free flow and porous media regions are of great interest and have several important applications, such as ground water systems [1], well-reservoir coupling in petroleum engineering [2], fluid-organ interactions, and industrial filtering where fluid passes through a filter to remove unwanted particles [3]. Research of the two-phase flow in coupled free flow and porous media regions is still at a primary stage. The authors raise a numerical method for a model of two-phase flow in a coupled free flow and porous media system [11]. As far as we know, that paper is the first work on the two-phase flow in coupled free fluid and porous media regions. We use a coupled Cahn-Hilliard and Navier-Stokes system to describe the two-phase fluid flow in the free flow region and two-phase Darcy equations to depict the Darcy flow in porous media region. A transmission condition for the two-phase flow is imposed at the interface boundary of the free flow region and the porous media region. For the single-phase flow, the Beavers-Joseph-Saffman (BJS) [12,13,14] condition states that the tangential slip velocity at the interface is proportional to the shear stress at the interface: L−p1u
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