Mathematical manipulation of the interface region of multilayer flows

In this paper, an accurate and fast algorithm is proposed to numerically solve for the velocity profile of fluid flow through multilayer porous media. We consider a finite width two-porous-layer problem, where the layers have different permeabilities, which introduces a discontinuity in the permeability at the interface region. At the interface, the continuity of the velocity and shear stress are imposed. The proposed algorithm is based on the nonlinear shooting method and the two-dimensional Newton's method. The accuracy of the proposed algorithm is validated by applying it to examples of known exact solutions. A comparison between the proposed algorithm and a finite difference approach is made, and it shows that the proposed algorithm is more accurate and more efficient.