 
Summary: 1
On Gravity Currents in Heterogeneous Porous Media
Daniel M. Andersona
, Richard M. McLaughlinb
, and Cass T. Millerc
a
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030
b
Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599
c
Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill,
NC, 27599
We examine the case of densitydependent flow in heterogeneous porous medium systems bounded by
a free surface using homogenization methods for leadingorder approximations. Specifically we consider
the twodimensional case in which variations occur in both the horizontal and vertical directions. Such
problems lead to the need to solve cell problems to compute the solution, which is generally done using
numerical approaches. We review the general homogenization results for general topology and aspect
ratio. We derive an analytical solution for a case with twodimensional variability in the slender limit
for certain assumed scaling of the permeability, and we find excellent agreement with the numerical
solution. We also consider the case of two miscible fluids with an assumed sharp interface and contrasting
