| Abstract: | In the present work the viscous (low Reynolds) flow in plane ducts confined by permeable walls has been studied. A simple model of the filtrating walls has been used, with the normal velocity component proportional to the pressure jump across the wall, resulting in a non-standard boundary value Navier-Stokes problem. A critical analysis of the appropriate boundary condition and pressure problem has led to the conclusions of employing a simple explicit finite volume approach, and of avoiding the use of higher order finite difference schemes. In this paper a special emphasis on the structure of the involved computational matrices has been given to illustrate the chosen algorithm. The latter yields a steady state solution that is second order accurate in space, and it has an accuracy in time of order ≤ Δt (the time step), due to the explicit treatment of the velocity boundary conditions along the membrane. The model has been tested to study the effects of the inlet/outlet conditions, Reynolds number and filtrating wall constant. |
