ENVIRONMENTAL ENGINEERING - Introduction to Soft Soil Geotechnique: Content, Context and Application - page 229

The use of analytic elements for numerical studies of the phenomenon of
macroscopic dispersion has advanced significantly in the last years. By applying
the principle of superposition, computational performance could be increased by
special solvers and parallel processing. Supercomputer clusters analyze ground
water flow and transport through hundreds of thousands of particles, allowing
stochastic experiments to examine effective conductivity and dispersion
coefficients for heterogeneous formations, describing detailed variations at various
levels. One peculiar result of such analysis is the additional effect of microscopic
torque flow on dispersion in three-dimensional simulations, which is not observed
in two-dimensional flow (Jankovic).
Figure 14.3 Dispersion by groundwater flow at meso-level
At a larger scale, at mesoscopic level, the velocity field itself is non-uniform
(Fig 14.3) and the concentration may change accordingly with a dispersion
coefficient of a different scale and the dispersivity should attain a value according
to the length scale of the flow field characteristics.
If one considers regional differences, the megascopic scale, i.e. soil layers with
different permeability and usually with horizontal dimensions significantly larger
than vertical ones, the transport process could be characterised with a dispersivity
of a regional length scale. (Fig 14.4).
Figure 14.4 Mega-dispersion
The transport of a concentration of a solute of suspended material in a plane
uniform groundwater flow at velocity v (convection) is described by the so-called
transport equation at macroscopic level, according to