Boundary Element Method for 2D Stokes Slip Flow in Porous Medium Composed of a Large Number of Circular Inclusions

A computationally efficient Fourier boundary element method for calculating Stokes flow in a porous medium consisting of a large number of circular inclusions, proposed in R. Mardanov, S. Zaripov, and D. Maklakov, Engineering Analysis with Boundary Elements 113, 204-218 (2020), is extended to the case of nanoscale inclusions (small Knudsen numbers). The sought-after functions on the surface of circular inclusions are approximated by a truncated Fourier series expansion, which reduces the number of unknowns by one to two orders of magnitude compared to the classical boundary elements method while maintaining the accuracy of calculations in the case of high porosity. Formulas for hydrodynamic forces and moments acting on each circular inclusion are obtained. The results of parametric calculations are presented, demonstrating the accuracy of the generalized method.