Most numerical approaches for coupling fluid flow with porous media flow rely either on Stokes equations in the fluid part of the domain and Darcy’s law in the porous part, or on Brinkman’s equation. In both cases, difficulties arise at the boundary between the two parts because the equations used in the porous part are not of Stokes type. In this paper, an alternative to Darcy’s law is proposed for modeling flows in porous media. This alternative relies on equations of Stokes type where the permeability tensor is replaced by force and stress derivative tensors. Numerical procedures are presented to compute these tensors from simulations at pore scale. Simulations in domains containing both fluid and porous parts are finally conducted simply assuming continuity of velocity and pressure and hence without imposing any condition at the boundary between the two parts. Results show that the proposed method is accurate and hence a promising alternative to Darcy’s law for problems involving both fluid and porous parts.

中文翻译：

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耦合流体流动与多孔介质流动的纯斯托克斯方法

大多数将流体流动与多孔介质流动耦合的数值方法依赖于域流体部分中的斯托克斯方程和多孔部分中的达西定律，或者依赖于布林克曼方程。在这两种情况下，由于多孔部分中使用的方程不是斯托克斯类型，因此在两个部分之间的边界处都会出现困难。在本文中，提出了达西定律的替代方法来模拟多孔介质中的流动。这种替代方案依赖于斯托克斯类型的方程，其中渗透率张量被力和应力导数张量代替。提出了数值程序来通过孔隙尺度的模拟来计算这些张量。最终在包含流体和多孔部件的域中进行模拟，简单地假设速度和压力的连续性，因此不在两个部件之间的边界施加任何条件。结果表明，所提出的方法是准确的，因此对于涉及流体和多孔部件的问题来说，是达西定律的有希望的替代方案。