Effects of Multi-Scale Heterogeneity

Abstract

It is generally agreed that problems with multi-scale heterogeneity present the biggest challenge to computation and understanding. A few such problems may be easily understood using percolation theory. It is not clear at this time whether such treatments will prove particularly useful in the general case; however, as always, they will be superior to simple averaging techniques. Three problems will be dealt with, one at the pore scale, in which the effects of soil structure on hydraulic properties are discussed, the second treats a two-scale upscaling problem, where the percolation variable is different at the two scales, the third was only meant to be a schematic treatment of a geologic scale hierarchical problem, but appears to have captured the essence of a “scale effect” on the hydraulic conductivity.