Abstract:
We consider a system of nonlinear partial differential equations that arises in the
modeling of two-phase flows in a porous medium. The phase velocities are modeled using a
Brinkman regularization of the classical Darcy's law. We propose a notion of weak solution
for these equations and prove existence of these solutions. A finite difference scheme for 1- and 2-d
is proposed and is shown to converge to the weak solutions of this system. The Darcy limit
of the Brinkman regularization is studied numerically using the convergent finite difference scheme in two space dimensions as well as using both analytical and numerical tools in one
space dimension. |