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 methods for Newton’s method. In this work, we perform a numerical study of a spatial additive Schwarz preconditioned exact Newton (ASPEN) method as a nonlinear preconditioner for Newton’s method applied to both fully implicit or sequential implicit schemes for simulating immiscible and compositional multiphase flow. We first review the ASPEN method and discuss how the resulting linearized global equations can be recast so that one can use standard preconditioners developed for the underlying model equations. We observe that the local fully implicit or sequential implicit updates efficiently handle the local nonlinearities, whereas long-range interactions are resolved by the global ASPEN update. 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. A complexity analysis demonstrates that Newton’s method with a fully implicit scheme preconditioned by ASPEN is a very robust and scalable alternative to the well-established Newton’s method for fully implicit schemes.

域分解方法被广泛用作 Krylov 子空间线性求解器的预处理器。在多孔介质流动的模拟中，最近人们对牛顿法的非线性预处理方法越来越感兴趣。在这项工作中，我们对空间加性施瓦茨预处理精确牛顿 (ASPEN) 方法进行了数值研究，该方法作为牛顿方法的非线性预处理器，适用于全隐式或顺序隐式方案，用于模拟不混溶和成分多相流。我们首先回顾 ASPEN 方法并讨论如何重铸所得的线性化全局方程，以便可以使用为基础模型方程开发的标准预处理器。我们观察到局部完全隐式或顺序隐式更新有效地处理了局部非线性，而远程交互由全局 ASPEN 更新解决。这两个更新的结合导致了一个非常有竞争力的算法。我们针对概念性的一维和二维情况以及现实的三维模型说明了算法的行为。复杂性分析表明，具有由 ASPEN 预处理的完全隐式方案的牛顿方法对于完全隐式方案的成熟牛顿方法是一种非常稳健且可扩展的替代方法。