This article is a follow up of our submitted paper (D. Seus et al, Comput Methods Appl Mech Eng 333:331-355, 2018) in which a decomposition of the Richards equation along two soil layers was discussed. A decomposed problem was formulated and a decoupling and linearisation technique was presented to solve the problem in each time step in a fixed point type iteration. This article extends these ideas to the case of two-phase in porous media and the convergence of the proposed domain decomposition method is rigorously shown.
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机译：本文是我们提交文件的后续行动（D.Seus等，计算方法Appl Mech Eng 333：331-355,2018），其中讨论了理查兹方程沿两种土壤层的分解。制定了分解的问题，并提出了一种解耦和线性化技术以解决固定点类型迭代的每次步骤中的问题。本文将这些想法扩展到多孔介质中两相的情况，并且严格地示出了所提出的域分解方法的收敛性。
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