Filtering procedures for flow in heterogeneous porous media: numerical results


Attinger S., Eberhard J., Neuss N., Computing and Visualization in Science, 451, 1-3, 136-140, 2008



This paper focuses on heterogeneous soil permeabilities and on the impact their resolution has on the solution of the piezometric head equation. The method of coarse graining is proposed in order to filter the piezometric head equation on arbitrary support scales: Large scale fluctuations of the permeabilities are resolved, whereas small scale fluctuations are smoothed by a spatial filtering procedure. The filtering procedure is performed in Fourier space with the aid of a low-frequency cut-off function. In the filtered equations, the impact of the small scale variability is modeled by scale dependent effective permeabilities which are determined by additional differential equations. The additional differential equations are equivalent to the piezometric head equation on cells which are solved numerically by using the software toolbox UG. The numerical results are compared with the theoretical results derived in Attinger 2001