Modified formulation of the interfacial boundary condition for the coupled Stokes–Darcy problem

Abstract

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.