A New Timestep Criterion for the Simulation of Immiscible Two-Phase Flow with IMPES Solvers

We present an IMplicit Pressure Explicit Saturation (IMPES) solver and a novel timestep criterion for the simulation of immiscible two-phase flow involving compressible fluid phases. The novel timestep criterion uses the Courant-Friedrichs-Lewy (CFL) condition and employs numerically com-puted velocity derivatives to adapt the timestep size, regardless of the dominant flow characteristics. The solver combined with this timestep criterion demonstrates both effi-ciency and robustness across a range of flow scenarios, including pressure drop dominated and capillary dominated flows with compressible and incompressible fluid phases, without the need to adjust any numerical parameters. Furthermore, it successfully reaches the expected stationary states in a case involving discontinuous porous media parameters such as porosity, permeabilities, and capillary pressure function. Comparison with the established Coats timestep criterion reveals that our approach requires fewer time iterations while maintaining comparable accuracy on the Buckley-Leverett problem and a gravity-capillary equaliza-tion example with a known stationary state. Additionally, in an example with air compression, the new timestep criterion leads to a significantly improved non-wetting phase mass conservation compared to the Coats criterion. WHY THIS PAPER MATTERS Accurately simulating how fluids move through complex materials like soil, rock, or battery parts is a major challenge for engineers, as computer mod-els can often become slow or unstable when conditions change. Our work introduces a smart method that automatically adjusts the simulation’s pace, ensuring it remains fast and reliable even when dealing with difficult sce-narios like highly compressible fluid phases or drastically changing porous materials. These findings help experts in fields like carbon storage, ground-water protection, and green energy manufacturing achieve more precise predictions with less computing power, accelerating the development of critical new technologies.