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Institut für Wasserbau - IWS

Selected Topics and International Network Lectures

16:00 Uhr
Birgitte Eikemo
Haakon Haegland
Department of Mathematics
University of Bergen

A Discontinuous Galerkin Method for Computing Transport Flow in Porous Media" und "Streamline tracing on irregular grids

We consider a discontinuous Galerkin scheme for flow in heterogeneous media. By applying an optimal reordering algorithm, one does not need to assemble the full linear system and may compute the solution in an element-by-element fashion. We demonstrate the discontinuos Galerkin method and the prior reordering on a boundary value problem for time-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's method to obtain streamlines and time-of-flight coordinates (TOF). The usual way of handling irregular grids is by trilinear transformation of each grid cell to a unit cube together with a linear flux interpolation scaled by the Jacobian. The flux interpolation allows for fast integration of streamlines, but is inaccurate even for uniform flow. To improve the tracing accuracy, we introduce a new interpolation method, which we call corner velocity interpolation. Instead of interpolating the velocity field based on discrete fluxes at cell edges, the new method interpolates directly from reconstructed point velocities given at the corner points in the grid. This allows for reproduction of uniform flow, and eliminates the influence of cell geometries on the velocity field. Numerical examples demonstrate that the new method is more accurate than the standard tracing methods.