An Adaptive Subdomain Coupling Approach in Domain Decomposition for Multiphase Porous Media Flow

TL;DR

This paper introduces an adaptive subdomain coupling framework for domain decomposition in multiphase porous media flow, enhancing convergence and scalability in large-scale reservoir simulations.

Contribution

It proposes a novel adaptive coupling strategy and initial guess calculation method to improve nonlinear solver performance in complex heterogeneous media.

Findings

Effective handling of strong local nonlinearities

Improved convergence and scalability of nonlinear solvers

Competitive parallel performance in large-scale simulations

Abstract

The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations owing to its superior numerical stability and more relaxed time step constraints. However, this method requires solving a large nonlinear system, which becomes highly nonlinear in complex heterogeneous media with small grid scales, emphasizing the need for efficient and convergent numerical methods to accelerate nonlinear solvers on parallel computing systems. In this paper, we present an adaptively coupled subdomain framework based on domain decomposition methods. This framework effectively handles strong local nonlinearities in global problems by solving subproblems within the coupled regions. Furthermore, we propose several adaptive coupling strategies and present a novel method for calculating initial guesses, aimed at improving the convergence and scalability of nonlinear solvers. A series of numerical experiments validate the effectiveness and robustness of the proposed framework. Additionally, large-scale reservoir simulations demonstrate that the proposed method achieves competitive parallel performance.