This model captures physical effects, such as sharp fronts in fluid pressures and saturations, which are present in more complex models of multiphase flow. The numerical solution of RE is difficult not only because of these physical effects but also because of the mathematical problems that arise in dealing with the nonlinearities. The method of lines has been shown to be very effective for solving RE in one space dimension. We present a theorem on the convergence of inexact Newton methods, and based on this theorem, an adaptive method that selects an appropriate linear tolerance.
Numerical results show the method to be effective compared with an existing approach.