An Algebraic Dynamic Non-Uniform Multilevel Preconditioner for CPR Pressure Systems in Reservoir Simulation
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The numerical simulation of multiphase flow in highly heterogeneous petroleum reservoirs poses severe computational challenges due to the large number of degrees of freedom and the ill-conditioning of the discrete systems. These challenges are particularly critical in industrial settings, where multiple scenarios must be evaluated for reservoir management optimization and uncertainty quantification, requiring robust and scalable numerical solvers. This work presents the Dynamic Non-Uniform Multiscale Restricted Smoothed Basis (DNU-MsRSB) method applied as a preconditioner for two-phase flow simulations of petroleum reservoirs in the context of the Constrained Pressure Residual (CPR) method. Multilevel operators are built using the Multiscale Restricted Smoothed Basis (MsRSB) approach and dynamically adapted according to normalized pressure gradients, enabling selective refinement in regions with strong flow variations. The pressure subsystem is obtained with the CPR technique, and the resulting linear systems are solved using GMRES, with the proposed algebraic multilevel operators acting as preconditioners. The performance of the NU-ADM approach is evaluated against standard industrial preconditioners, including Incomplete LU (ILU) and Algebraic Multigrid (AMG), applied to the CPR pressure system. Numerical results demonstrate that the proposed method significantly improves convergence and robustness in highly heterogeneous reservoirs, where traditional preconditioners often exhibit slow convergence or scalability limitations. The approach preserves fine-scale accuracy while reducing computational costs. Ongoing work investigates the use of multi-stage preconditioning strategies to further enhancing performance and robustness. Future developments will extend the method to more complex physical models and large-scale reservoir simulations.
