Fast Real Space Renormalization for Two-Phase Porous Media Flow

Upscaling of hydraulic conductivity data in space is one of the important problems in hydrological modelling.In this article the basics of Real Space Renormalization (RSR) for up-scaling hydraulic conductivity are introduced. The RSR procedure is described on a 2 — D hydraulic conductivity grid. RSR is chosen because it can cope with correlated and anisotropic media. An up to now unanswered problem is the non-unique relationship between water fluxes and water contents or heads.In special cases analytical solutions for two phase flow systems allow RSR to be as fast as single phase RSR. In the general case, numerical solution of the small scale flow equations are required. A new solution procedure which reduces the amount of computations is described.