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Fully implicit non-uniform algebraic dynamic multilevel method as an approximate solver and as a preconditioner for the numerical simulation of two-phase fluid flow in highly heterogeneous petroleum reservoir
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DOI：10.1108/hff-10-2025-0828.png)
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Abstract
En 中文
<jats:sec>
<jats:title>Purpose</jats:title>
<jats:p>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.</jats:p>
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<jats:title>Design/methodology/approach</jats:title>
<jats:p>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.</jats:p>
</jats:sec>
<jats:sec>
<jats:title>Findings</jats:title>
<jats:p>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.</jats:p>
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<jats:title>Originality/value</jats:title>
<jats:p>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.</jats:p>
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