CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   Computational Stochastic Modeling of Two-phase Flow 
         in Fractal Porous Media
 

SPEAKER: Felipe Pereira, LNCC-CNPq, Rio de Janeiro, Brazil 

DATE:    Wednesday, March 6, 1996

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    noon - 1 pm



ABSTRACT

The analysis, through high resolution numerical simulations, of instabilities
(viscous fingering) in oil-water fronts in heterogeneous porous media requires
efficient computations on fast, multi--processor computers. This talk is devoted
to the description of an algorithm for such a computation and to the presentation 
of numerical results that lead to the characterization of the statistical behavior 
of the relative area occupied by fingers, which we call the mixing region.

The computational algorithm combines hybridized mixed finite elements, a new 
version of the modified method of characteristics, and domain decomposition 
iteration and has several distinctive features; it is naturally parallelizable 
in distributed memory machines, it has very low storage requirements, explicit 
upwinding techniques are not necessary to stabilize the solution (thus reducing 
spurious effects of numerical diffusion), the scheme runs very rapidly (large 
linear systems do not have to be constructed and solved), it conserves mass, 
and the implementation at the level of code development is quite simple.   

For physically typical heterogeneity strengths and viscosity ratios it is shown
that the mixing region displays a highly anomalous growth pattern;
the exponent gamma describing the scaling behavior (for large time) of the
mixing region is very close to one, and may depend on the correlation length
of the geological heterogeneities.