A modified formulation of the interfacial boundary condition for the coupling of the Stokes and Darcy models describing the incompressible fluid flow in the free space and porous medium domains is proposed using the dimension analysis procedure. The case is considered for the porous media formed by circular or square cylinders located in the centers of rectangular cells. The vorticity is derived as a linear combination of the tangential velocity components in the free space and porous medium. The proposed condition is potentially directly applicable for a class of 2D problems with an arbitrary shaped boundary for the boundary element method. The fluid flow problems are solved numerically using the Stokes flow model and analytically for the Stokes–Darcy flow model to determine the coefficients in the introduced linear dependence for the vorticity. As a result, the corresponding coefficients in the boundary condition are found as a porosity function for two types of the porous medium configuration. The approximate analytical estimation of the coefficients confirms the numerical dependencies. The verifications of the found coefficients were made by solving two 2D fluid flow problems. It is shown that the fluid flow calculated on the basis of the Stokes–Darcy flow model with modified boundary condition agrees well with the results of the microscopic Stokes flow model. The advantages of the proposed boundary condition are discussed.

使用尺寸分析程序，提出了一种用于描述斯托克斯和达西模型耦合的界面边界条件的改进公式，该模型描述了自由空间和多孔介质域中的不可压缩流体流动。考虑到由位于矩形单元中心的圆形或方形圆柱体形成的多孔介质的情况。涡度是自由空间和多孔介质中切向速度分量的线性组合得出的。所提出的条件可能直接适用于边界元素方法具有任意形状边界的一类二维问题。使用Stokes流动模型以数值方式解决了流体流动问题，并通过Stokes-Darcy流动模型进行了分析，从而确定了引入的线性相关性（用于涡度）中的系数。结果，对于两种类型的多孔介质构造，边界条件下的相应系数被发现为孔隙率函数。系数的近似分析估计确认了数值依赖性。通过解决两个二维流体流动问题，对找到的系数进行了验证。结果表明，基于Stokes–Darcy流动模型的边界条件被修改的流体流动与微观Stokes流动模型的结果非常吻合。讨论了提出的边界条件的优点。通过解决两个二维流体流动问题，对找到的系数进行了验证。结果表明，基于Stokes–Darcy流动模型的边界条件被修改的流体流动与微观Stokes流动模型的结果非常吻合。讨论了提出的边界条件的优点。通过解决两个二维流体流动问题，对找到的系数进行了验证。结果表明，基于Stokes–Darcy流动模型的边界条件被修改的流体流动与微观Stokes流动模型的结果非常吻合。讨论了提出的边界条件的优点。