This research will consider numerical methods for highly advective flow problems with particular application to simulation of flows in porous media and incompressible flows modeled by the Navier-Stokes equations. Discretization by operator splitting methods will be emphasized. The advection operator will be approximated using the modified of characteristics, and diffusion-dispersion or viscosity and the Stokes problem will be dealt with using finite element methods. This work should provide new insight into flows in unsaturated zones and flows in fractured media.
