UNIVERSITY OF COLORADO AT DENVER

PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St., Denver

TIME: NOON (Refreshments served at 11:45 am)

DATE: Nov. 20, 2000

Title:
         An ELLAM-MFEM Solution Technique for Subsurface Flows
                   with Point Sources and Sinks


Speaker:
    Hong Wang                                                           |
    Department of Mathematics                                           |
    University of South Carolina                                        |
    Columbia, South Carolina 29208




Abstract:

We present an ELLAM-MFEM solution procedure for the numerical simulation
of compressible fluid flows in porous media with point sources and sinks.
An Eulerian-Lagrangian localized adjoint method (ELLAM), which was
originally proposed by Celia, Russell, Herrera, and Ewing and was
previously shown to outperform many widely used and well regarded methods
in the context of linear transport partial differential equations, is
presented to solve the transport equation for concentration. Since
accurate fluid velocities are crucial in numerical simulations, a mixed
finite element method (MFEM) is used to simultaneously solve the pressure
equation as a system of first-order partial differential equations for
the pressure and mass flow rate. This minimizes the numerical
difficulties occurring in standard methods caused by differentiation
of the pressure and then multiplication by rough coefficients.

Computational experiments show that the ELLAM-MFEM solution procedure
can accurately simulate compressible fluid flows in porous media with
coarse spatial grids and very large time steps. The ELLAM-MFEM solution
technique symmetrizes the governing partial
differential equations, greatly reduces or eliminates non-physical
oscillation and/or excessive numerical dispersion present in many
large-scale simulators that are widely used in industrial applications.
It conserves mass and treats boundary conditions in a natural manner.
It can treat large adverse mobility ratios, discontinuous permeabilities
and porosities, anisotropic dispersion in tensor form, compressible
fluid, heterogeneous media, and point sources and sinks.