Geodesic network method for flows between two rough surfaces in contact

A discrete network method based on previous asymptotic analysis for computing fluid flows between confined rough surfaces is proposed. This random heterogeneous geodesic network method could be either applied to surfaces described by a continuous random field or finely discretized on a regular grid. This method tackles the difficult problem of fluid transport between rough surfaces in close contact. We describe the principle of the method as well as detail its numerical implementation and performances. Macroscopic conductances are computed and analyzed far from the geometrical percolation threshold. Numerical results are successfully compared with the effective medium approximation, the application of which is also studied analytically.