Scaling-up of groundwater flow equations via Butterworth filtering.

Abstract

Water flow and solute transport in porous media evolve over many different length scales. The numerical simulation of the dynamics of all scales would require excessively large computational resources. Whereas it may never be possible to develop models to resolve all significant scales, it may be feasible to develop models of the large scale dynamics. These large scale models would not require the explicit description of the small scales, but should include the effect of the small scales on the large scale dynamics. The incorporation of such effects requires the solution of a problem of closure. Through the use of Butterworth filters, an exact solution of the closure problem for highly heterogeneous groundwater flow is developed. Numerical tests that validate the theoretical results are included.