**Inclusion of transverse diffusion/dispersion in streamline
methods using normal lines**
Streamline methods have shown great potential for advection dominated
problems in porous media. Diffusion dominated problems are however not
as well suited for streamline methods since they involve flow transverse
to the streamlines. The common way of including diffusion and dispersion
is to use an operator splitting combined with a mapping of
saturation/concentration from streamlines to the 2D/3D grid used for the
pressure solution. Hence, diffusion is not directly incorporated along
the streamlines, but must be solved on the pressure grid. If an explicit
method is used there may be an efficiency problem due to the
CFL-condition, and also the full 2D/3D solution is more time consuming
than a set of 1D solutions along streamlines. In addition, the mapping
from streamlines to the pressure grid may generate unwanted numerical
diffusion.
We propose a new method to handle diffusion in streamline methods for 2D
problems. Our method uses 1D normal lines, which are orthogonal to the
streamlines. Transverse diffusion can then be handled using a
one-dimensional diffusion equation on the normal lines, whereas the
longitudinal diffusion and advection is handled by an
advection-diffusion equation along the streamlines. |