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

TL;DR

This paper extends a domain decomposition method for Richards equation to two-phase flow in porous media, providing a linear, decoupled iterative solution with proven convergence.

Contribution

It introduces a linear domain decomposition approach for two-phase flow in porous media, with a rigorous proof of convergence, advancing previous work on Richards equation.

Findings

Convergence of the proposed method is rigorously demonstrated.

The method effectively decouples the two-phase flow problem.

The approach improves computational efficiency for porous media simulations.

Abstract

This article is a follow up of our submitted paper [11] 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.