This paper aims to enhance the performance of Newton–Krylov solvers for coupled poromechanical problems with two-phase flow. In particular, we investigate the impact of capillary pressure on preconditioning strategies. Capillarity complicates the coupling between the solid deformation and fluid pressure degrees of freedom, as well as increases the nonlinearity of the system. Depending on the capillary pressure relation used in the constitutive formulation, the flow equations may exhibit a spectrum of advection-dominated to diffusion-dominated behavior. We propose preconditioning approaches that account for this behavior and lead to robust numerical performance within a broad range of regimes.

中文翻译：

---

具有强毛细作用的多相多孔力学预调节剂

本文旨在提高 Newton-Krylov 求解器对两相流耦合多孔力学问题的性能。特别是，我们研究了毛细管压力对预处理策略的影响。毛细作用使固体变形和流体压力自由度之间的耦合复杂化，并增加了系统的非线性。根据本构公式中使用的毛细管压力关系，流动方程可能表现出一系列对流主导到扩散主导的行为。我们提出了解释这种行为的预处理方法，并在广泛的范围内产生强大的数值性能。