Adaptively Coupled Domain Decomposition Method for Multiphase and Multicomponent Porous Media Flows

Numerical simulation of large-scale multiphase and multicomponent flow in porous media is a significant field of interest in the petroleum industry. The fully implicit approach is favored in reservoir simulation due to its numerical stability and relaxed constraints on time-step sizes. However, this method requires solving a large nonlinear system at each time step, making the development of efficient and convergent numerical methods crucial for accelerating the nonlinear solvers. In this paper, we present an adaptively coupled subdomain framework based on the domain decomposition method. The solution methods developed within this framework effectively handle strong nonlinearities in global problems by addressing subproblems in the coupled regions. Furthermore, we propose several adaptive coupling strategies and develop a method for leveraging initial guesses to accelerate the solution of nonlinear problems, thereby improving the convergence and parallel performance of nonlinear solvers. A series of numerical experiments validate the effectiveness of the proposed framework. Additionally, by utilizing tens of thousands of processors, we demonstrate the scalability of this approach through a large-scale reservoir simulation with over 2 billion degrees of freedom.