Towards Hybrid Two-Phase Modelling Using Linear Domain Decomposition

TL;DR

This paper proposes a hybrid two-phase modeling approach for porous media flow, combining full two-phase and simplified Richards models with a linear domain decomposition scheme, validated through theoretical proof and numerical experiments.

Contribution

It introduces a novel coupling strategy for hybrid modeling of porous media flow and proves the convergence of the associated linear iterative scheme.

Findings

The hybrid model reduces computational effort compared to full two-phase simulations.

The proposed domain decomposition scheme is proven to be convergent.

Numerical results confirm the efficiency and accuracy of the hybrid approach.

Abstract

The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g. in soil layers in contact with the atmosphere) the system can be substituted by the scalar Richards model. Thus, the domain of the porous medium may be partitioned into disjoint subdomains with either the full two-phase or the simplified Richards model dynamics. Extending the one-model approach from [1, 2] we suggest coupling conditions for this hybrid model approach. Based on an Euler implicit discretisation, a linear iterative (-type) domain decomposition scheme is proposed, and proven to be convergent. The theoretical findings are verified by a comparative numerical study that in particular confirms the efficiency of the hybrid ansatz as compared to full two-phase model computations.