A linear domain decomposition method for two-phase flow in porous media

Abstract

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.