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
elementbyelement fashion. We demonstrate the discontinuos Galerkin
method and the prior reordering on a boundary value problem for
timeofflight.
Streamline methods have shown to be effective for reservoir simulation.
For a regular grid, it is common to use the semianalytical Pollock's
method to obtain streamlines and timeofflight 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.
