Title:         New optimization approach to multiphase flow

Authors:       T. Kearsley, L. C. Cowsar, R. Glowinski, M. F. Wheeler, 
               and I. Yotov

Source:        J. Optim. Theory Appl. 111 (2001) 473-488.

Status:        Published

Abstract: A new optimization formulation for multiphase flow in porous
media is introduced. A locally mass conservative mixed finite element
method is used for the spatial discretization.  An unconditionally
stable, fully implicit time discretization is also used and leads to a
coupled system of nonlinear equations that must be solved at each time
step.  We reformulate this system as a least squares problem with
simple bounds involving only one of the phase saturations.  Both a
Gauss-Newton method and a BFGS secant method are considered as
potential solvers for the optimization problem.  Each evaluation of
the least squares objective function and gradient requires solving two
single-phase self-adjoint, linear, uniformly elliptic partial
differential equations for which very efficient solution techniques
have been developed.  However, numerical experiments suggest that the
new formulation may not be computationally competitive with existing
methods.