  This paper presents our work on developing parallel computational methods for
two-phase flow on modern parallel computers, where techniques for linear
solvers and nonlinear methods are studied and the standard and inexact Newton
methods are investigated. A multi-stage preconditioner for two-phase flow is
applied and advanced matrix processing strategies are studied. A local
reordering method is developed to speed the solution of linear systems.
Numerical experiments show that these computational methods are effective and
scalable, and are capable of computing large-scale reservoir simulation
problems using thousands of CPU cores on parallel computers. The nonlinear
techniques, preconditioner and matrix processing strategies can also be applied
to three-phase black oil, compositional and thermal models.
