CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM
UNIVERSITY OF COLORADO AT DENVER
TITLE: Fluid Mixing Regimes for Nonlinear Flow in Multiscale
Heterogeneous Porous Media
SPEAKER: Fred Furtado, Department of Mathematics,
University of Wyoming, Laramie, Wyoming
DATE: Monday, October 20, 1997
PLACE: Math Conference Room 626
UCD Building, 1250 14th St., Denver
TIME: noon (Refreshments served at 11:45 am)
ABSTRACT
Fluid mixing and nonlinear fluid flow are important in a number
of scientific and technological contexts. In this talk we discuss
some results of our numerical study of the complex fluid mixing
(fingering) in nonlinear porous media flows that results from
the combined effect of nonlinearities in the flow equations and
geological heterogeneities.
Spatial variations of geological formations (aquifers, petroleum
reservoirs) occur at several scales, but only the variations at
the largest length scales are reliably reconstructed from the
data available. The heterogeneities occurring on the smaller
length scales have to be incorporated stochastically, on the
basis of random fields. As a consequence, the resulting flows
through such formations are stochastic and require statistical
descriptions.
We focus on stochastic theories for a description of the size
of the region where the fluid mixing takes place. We investigate
explicitly the scaling behavior of this mixing region in the
asymptotic limit of large times. As we shall see, this scaling,
or growth law, is a signature of the leading mechanism governing
the asymptotic dynamics of the mixing process.