Purpose This study aims to improve the efficiency and accuracy of fully implicit (FI) multiphase flow simulations in highly heterogeneous petroleum reservoirs through advanced multiscale numerical strategies. Design/methodology/approach Two strategies based on the non-uniform algebraic dynamic multilevel (NU-ADM) method are proposed and investigated in new contexts. The first, denoted FINU-ADM, extends the NU-ADM methodology (originally developed for IMPES schemes) to an FI formulation, using NU-ADM as an approximate nonlinear solver within a Newton-based framework. The second, CPR-FINU-ADM, integrates NU-ADM into a constrained pressure residual (CPR) approach, using it as a multilevel preconditioner for the pressure subsystem to accelerate the fine-scale solution. Both strategies rely on adaptive non-uniform multilevel meshes that preserve fine-scale resolution in critical regions, such as high-pressure gradients and saturation fronts. Operator construction follows the original NU-ADM algorithm, reformulated for FI context. Findings The proposed methods enable the use of larger time steps and eliminate post-processing steps required for constructing conservative velocity fields. Numerical results from challenging benchmarks confirm that both FINU-ADM deliver accurate pressure and saturation fields while significantly reducing computational cost compared to classical fine-scale simulations or multiscale methods. The CPR-FINU-ADM improves preconditioning and speeds up the fine-scale solution. Originality/value To the best of the authors’ knowledge, this is the first work to extend the NU-ADM method to the FI flow simulation framework, both as a standalone multiscale solver and as a preconditioner in combination with the CPR approach. These formulations enhance scalability and numerical robustness, offering a promising path for large-scale reservoir simulation with adaptive resolution and reduced overhead.
Santos et al. (Thu,) studied this question.