Parallel fully coupled methods for bound-preserving solution of subsurface flow and transport in porous media

As more powerful supercomputer systems with lots of memory and a large number of computing cores become available, the family of fully coupled algorithms is drawing more attention in scientific and engineering applications, due to its impressive robustness and scalability in extreme-scale simulations. In this work, we introduce and study some parallel domain decomposition preconditioned generalized Newton algorithms for solving the fully coupled and bound-preserving formulation of the subsurface flow and transport problem in porous media. In the approach, we present the active–set reduced–space (ASRS) method to guarantee the nonlinear consistency of the fully coupled system in a monolithic way, and meanwhile ensure the boundedness requirement of the solution. Furthermore, we focus on the application of the overlapping additive Schwarz preconditioning technique to accelerate the linear convergence of Newton iterations and be beneficial to the scalability of the inner linear solver. We present some numerical experiments to demonstrate the parallel scalability of the proposed algorithm on the Shaheen-II supercomputer with thousands of processors. In particular, the numerical results also show that the fully coupled framework has the nature of bound preservation and is efficient for the proposed reservoir flow problems.