Comparative Analysis of Scaling Techniques for AIM Matrices in Reservoir Flow Equations

Scaling improves the performance of iterative solvers for large, sparse linear systems by enhancing conditioning and balancing row and column magnitudes. This work highlights a tailored scaling approach for linear systems arising from Adaptive Implicit Method (AIM) discretization in multiphase porous media flow equations. The method focuses on conditioning implicit equations to reduce computational costs and improve solver efficiency. We compare this approach with general algorithms, such as Sinkhorn-Knopp and Ruiz, using the GMRES solver. Results show that the tailored method enhances convergence and outperforms general-purpose techniques in reservoir simulation,  highlighting the benefits of problem-specific scaling strategies in large-scale simulations.