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Institut für Wasserbau - IWS

Selected Topics and International Network Lectures

16:00 Uhr
Haakon Haegland
University of Bergen (Norway), Department of Mathematics

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.