Speaker
Description
Simulating two-phase flow in porous media requires solving large nonlinear systems, commonly via Newton–Krylov methods such as GMRES. These methods rely on Jacobian–vector products, which can be efficiently computed using automatic differentiation (AD), avoiding explicit Jacobian assembly. However, the lack of an assembled Jacobian complicates preconditioner design.
This work presents a sparsity-aware preconditioning strategy that constructs a sparsified Jacobian approximation using AD and graph coloring. The method exploits Jacobian sparsity to achieve scalable and memory-efficient preconditioning without forming or storing the full Jacobian matrix.
Results show that solver performance improves as the preconditioner better approximates the Jacobian, though gains diminish at higher sparsity due to memory costs. Despite minor deviations in saturation, overall accuracy, particularly in pressure, is preserved. The study demonstrates that semi-matrix-free methods combined with AD-based sparse preconditioning substantially reduce memory requirements while maintaining convergence, enabling scalable two-phase flow simulations in large reservoir models.