Fast, accurate, and robust solution of advection dominated transport equations

A grid-based alternative to streamline simulation that is mass-conservative and avoids problems with mapping and choice of representative streamline distribution.

The reordering procedure is applicable to any grid that can be mapped to a directed graph (with directions given by inter-cell fluxes). Based on the reordering, one can formulate a highly efficient Gauss-Seidel type (non)linear solver. Applications studied so far:

The discontinuous Galerkin discretisation:

A fast grid-based alternative to streamline simulation that

Isocontours of time-of-flight define natural timelines in the reservoir, here visualized in a half slice of a 3D quarter five-spot with heterogeneous permeability.

Drainage volumes for the SPE 10 model defined by computing the steady-state solution of a continuous tracer injection.

Localization of nonlinear iteration by use of reordering. The color shows the number of iterations per cell during a typical transport step. Compared with a standard Newton-Raphson method this gives 100 times reduction of runtime for this model.

Published April 21, 2008

A portfolio of strategic research projects funded by the Research Council of Norway

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