Adaptive Nonlinear Domain-Decomposition for Scalable Reservoir Simulation

We recently proposed a method to accelerate convergence in nonlinearly stiff reservoir simulations by prepending local subdomain solves to each global Newton iteration, improving initial guesses and reducing the need for global corrections. Our implementation in the open-source, operational OPM Flow simulator employs MPI/OpenMP parallelization of the resulting two-level partitioning: the global Newton step is distributed across MPI ranks, each managing multiple subdomains. Nonlinear stiffness leads to highly localized computational cost for subdomain solves, many of which can be bypassed adaptively based on convergence history and solution changes. This approach has demonstrated significant speedup for industry-grade CO₂ storage and oil recovery models. Through examples, we highlight the resulting challenges in load balancing and partitioning, as the cost of the global solve depends on the number of cells per rank, while local solve costs vary spatially due to nonlinear stiffness.