A Schur-Consistent GPU CPRW–AMG Preconditioner for Well-Coupled Fully Implicit Multiphase Flow Simulation

Fully implicit simulation of multiphase flow in porous media requires repeated solution of large, sparse, nonsymmetric Jacobian systems, where linear solvers and preconditioners often dominate the computational cost. In field-scale models with strong well controls and well–reservoir coupling, bottom-hole pressure (BHP) constraints may introduce slowly converging pressure-related error modes that are not fully represented by pressure-only constrained pressure residual (CPR) preconditioning. This paper develops a Schur-consistent graphics processing unit (GPU) implementation of constrained pressure residual with wells and algebraic multigrid (CPRW-AMG) for the Open Porous Media (OPM) Flow simulator. The method augments the pressure coarse space with one auxiliary BHP unknown per active well while preserving a reservoir-only fine-level Krylov system. The pressure–BHP coarse operator is constructed from the same assembled effective reservoir Jacobian used by the Krylov matrix–vector product and the GPU diagonal incomplete lower–upper (DILU) smoother, avoiding inconsistent treatment of well contributions between fine and coarse levels. A GPU-resident sparse update strategy refreshes well-related coarse entries, and the NVIDIA AMGX library is used for the scalar coarse solve. Benchmarks on SPE9, SPE10, Sleipner, and Norne cover small well-coupled, highly heterogeneous carbon dioxide storage and field-realistic reservoir models. Compared with CPU CPRW-AMG, the GPU implementation reduces total runtime by factors of 1.69–8.78 and achieves linear-solve speedups of up to 17.96×. Compared with GPU CPR-AMG, the performance benefit is case-dependent, indicating that CPRW-AMG is most effective when the reduction in well-induced slow error modes compensates for the additional coarse-level cost.