Truncated Newton's method for multiphase flow

A system of nonlinear transient partial differential equations coupled with nonlinear algebraic constitutive relationships are employed to model the flow of two immiscible fluids. A fully stable implicit time stepping and a spatial finite element discretization results in a large stiff nonlinear system of algebraic equations to be solved at each time step. The differential operators involved are self-adjoint, but the use of Newton-type solution methods requires the solution of a system of non-symmetric linear equations to calculate each Newton step. This paper describes an inexact solution to the problem of calculating the Newton step.