A Discontinuous Galerkin Method for Computing Transport Flow inPorous Media und Streamline tracing on irregular grids

December 5, 2006, 4:00 p.m. (CET)

Time: 12/5/06, 4:00 p.m. – 5:30 p.m.
Lecturer: Birgitte Eikemo
Haakon Haegland
Department of Mathematics
University of Bergen
Venue: Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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We consider a discontinuous Galerkin scheme for flow in heterogeneousmedia. By applying an optimal reordering algorithm, one does not need toassemble the full linear system and may compute the solution in anelement-by-element fashion. We demonstrate the discontinuos Galerkinmethod and the prior reordering on a boundary value problem fortime-of-flight. Streamline methods have shown to be effective for reservoir simulation. For a regular grid, it is common to use the semi-analytical Pollock'smethod to obtain streamlines and time-of-flight coordinates (TOF). Theusual way of handling irregular grids is by trilinear transformation ofeach grid cell to a unit cube together with a linear flux interpolationscaled by the Jacobian. The flux interpolation allows for fastintegration of streamlines, but is inaccurate even for uniform flow. Toimprove the tracing accuracy, we introduce a new interpolation method,which we call corner velocity interpolation. Instead of interpolatingthe velocity field based on discrete fluxes at cell edges, the newmethod interpolates directly from reconstructed point velocities givenat the corner points in the grid. This allows for reproduction ofuniform flow, and eliminates the influence of cell geometries on thevelocity field. Numerical examples demonstrate that the new method is more accurate than the standard tracing methods.
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