### Numerical investigation of the dipole type solution for the problem of unsteady groundwater flow with capillary absorption and forced drainage

##### Eugene Ingerman, University of California, Berkeley

A few problems related to groundwater flow are considered. One particular problem concerns groundwater mound formation and extension following a flood. A flood, which can follow a break-through of a dam, can have a very significant environmental impact if contaminated floodwater enters and then extends far into the soil.

The mathematical model for groundwater flow, which is described by the porous medium equation, has many interesting properties. For the case when the pores do not retain water, it can be shown analytically that there exist special self-similar solutions. The graphs of such solutions at different times are related by a similarity transformation. Such solutions are not simply special analytic solution, but they also provide asymptotics for a class of initial and boundary value problems. However, for a porous medium with capillary retention, the existence of self-similar solutions cannot be established analytically. My co-author and I performed numerical computations that showed that special self-similar solution exists for this problem too.

We also considered the problem of controlling the groundwater mound extension after the flood by using forced drainage. It has been shown analytically that the porous medium equation with forced drainage also has self-similar solutions for some special forced drainage rates. However, there are no self-similar solutions that model the constant forced drainage rate. Numerically, we computed non self-similar solutions with constant drainage and showed that, in this case, it is possible to extinguish completely the water mound that appeared after the flood.

We also analyzed the problem of flooding and forced drainage for the case of porous medium with cracks. In many practical cases, this is a more realistic model than a homogeneous porous medium. The groundwater moves much faster in cracks than in the pores. However, also the volume of cracks is very small compared to the volume of pores. Thus, the inclusion of the cracks in the model significantly changes the results obtained above.

Abstract Author(s): Eugene Ingerman