P. Broadbridge et Jm. Goard, STEADY UNSATURATED FLOW IN 2-DIMENSIONAL SCALE HETEROGENEOUS POROUS-MEDIA, Mathematical and computer modelling, 26(3), 1997, pp. 45-54
Unsaturated how in scale heterogeneous porous media is described by a
class of nonlinear partial differential equations involving three gene
ral coefficient functions. It is shown that among these, there is a la
rge class of integrable models, being transformable to linear equation
s even when the spatially varying geometric dilation scale factor is a
n arbitrary twice differentiable function. Explicit solutions are cons
tructed for basic boundary value problems that relate to field and lab
oratory measurements. In one of these solutions, the flow pattern is u
naffected by the heterogeneity even though the water concentration is
modified. From another solution, we predict the bulk conductivity of a
heterogeneous soil sample with a constant hydraulic potential differe
nce maintained between the ends.