A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flow

Abstract Domain decomposition methods are widely used as preconditioners for Krylov subspace linear solvers. In the simulation of porous media flow there has recently been a growing interest in nonlinear preconditioning Newton’s method. this work, we perform numerical study spatial additive Schwarz preconditioned exact Newton (ASPEN) method preconditioner applied to both fully implicit or sequential schemes simulating immiscible and compositional multiphase flow. We first review ASPEN discuss how resulting linearized global equations can be recast so that one use standard developed underlying model equations. observe local updates efficiently handle nonlinearities, whereas long-range interactions resolved by update. The combination two leads very competitive algorithm. illustrate behavior algorithm conceptual two-dimensional cases, well realistic three dimensional models. A complexity analysis demonstrates with scheme is robust scalable alternative well-established schemes.