Abstract
Domain decomposition methods as preconditioners for Krylov methods are widely used for linear problems. There have been recently a growing interest into nonlinear preconditioning methods for Newton’s method applied to porous media flow. In this work, we study a spatial Additive Schwarz Preconditioned Exact Newton (ASPEN) method as a nonlinear preconditioner to the Newton’s method with fully implicit scheme in the context of immiscible and compositional multiphase flow. We first describe the method and how it can be implemented in a reservoir simulation package. We then study the nonlinearities addressed by the different components of the method. We observe that the local fully implicit updates are tackling well all the local nonlinearities and that the global ASPEN updates are tackling well the long range interactions. The combination of the two updates leads to a very competitive algorithm. We illustrate the behavior of the algorithm for conceptual one and two-dimensional cases, as well as realistic three dimensional models. We perform a complexity analysis and demonstrate that the Newton’s method with fully implicit scheme preconditioned by ASPEN is a very robust and scalable alternative to the well-established Newton’s method for fully implicit schemes.