23. Oktober 2007, 17:00 Uhr

Inclusion of transverse diffusion-dispersion in streamlinemethods using normal lines

23.10.07, 17:00 – 18:30 Uhr
Haakon Haegland
University of Bergen (Norway),Department of Mathematics
Streamline methods have shown great potential for advection dominatedproblems in porous media. Diffusion dominated problems are however notas well suited for streamline methods since they involve flow transverseto the streamlines. The common way of including diffusion and dispersionis to use an operator splitting combined with a mapping ofsaturation/concentration from streamlines to the 2D/3D grid used for thepressure solution. Hence, diffusion is not directly incorporated alongthe streamlines, but must be solved on the pressure grid. If an explicitmethod is used there may be an efficiency problem due to theCFL-condition, and also the full 2D/3D solution is more time consumingthan a set of 1D solutions along streamlines. In addition, the mappingfrom streamlines to the pressure grid may generate unwanted numericaldiffusion.

We propose a new method to handle diffusion in streamline methods for 2Dproblems. Our method uses 1D normal lines, which are orthogonal to thestreamlines. Transverse diffusion can then be handled using aone-dimensional diffusion equation on the normal lines, whereas thelongitudinal diffusion and advection is handled by anadvection-diffusion equation along the streamlines.

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