Locally Conservative Algorithms for Flow and Transport

Thursday, March 14, 2002 - 11:00am - 12:00pm
Keller 3-180
Mary Wheeler (The University of Texas at Austin)
Joint with Beatrice Riviere.

In the numerical modeling of fluid flow and transport problems, it is necessary for the velocities to be locally conservative on the transport grid. Lack of local mass conservation results in spurious sources and sinks to the transport equation. Local mass conservation can be accomplished through a projection algorithm, but this can be expensive and is generally only first order. It is generally better to use a locally conservative approach from the beginning.

Here we discuss the formulation, analysis and application of several numerical locally conservative algorithms: Discontinuous Galerkin methods, mixed finite element methods, and control volume. We discuss advantages and disadvantages of each of these methods. Numerical results from subsurface and surface flow problems are presented.