TITLE:

Two-stage preconditioners for inexact Newton methods in
 multi-phase reservoir simulation

ABSTRACT:

We discuss two-stage preconditioners for solving systems of coupled 
nonlinear partial differential equations in the modeling of underground 
multiphase flow phenomena. The linear systems arising from the 
discretization and Newton linearization are nonsymmetric and indefinite 
but coefficient blocks associated with a particular type of unknown 
possess properties that can be exploited to improve the conditioning 
of the coupled system. We show through theoretical discussion and 
numerical experiments that decoupling strategies combined with two-stage 
preconditioners are more effective to accelerate Krylov subspace methods 
such as GMRES\ and BiCGSTAB than standard ones which ``blindly''  
precondition the entire coupled linear system.  We also show a 
distributed memory parallel implementation of some of the iterative 
schemes proposed in this work.