A Mixed Finite Volume Element Method for Flow Calculations in
                                 Porous Media

                                 Jim E. Jones
       Institute for Computer Applications in Science and Engineering 
                         NASA Langley Research Center

                                   ABSTRACT

A key ingredient in the simulation of flow in porous media is the accurate
determination of the velocities that drive the flow.  The large scale
irregularities of the geology, such as faults, fractures, and layers suggest
the use of irregular grids in the simulation.  Work has been done in applying
the finite volume element (FVE) methodology as developed by McCormick in
conjunction with mixed methods which were developed by Raviart and Thomas.
The resulting mixed finite volume element discretization scheme has the
potential to generate more accurate solutions that standard approaches.  The
focus of this paper is on a multilevel algorithm for solving the discrete
mixed FVE equations.  The algorithm uses a standard cell centered finite
difference scheme as the `coarse' level and the more accurate mixed FVE scheme
as the `fine' level.  The algorithm appears to have potential as a fast solver
for large size simulations of flow in porous media.