Shizhe Li, Li Zhao, Chen-Song Zhang
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.