Adaptive RBF-FD meshless simulation of two-phase flows with phase-field approach

This work presents a new adaptive strategy for the simulation of incompressible and immiscible two‑phase flows, combining a Radial Basis Function–Finite Difference (RBF‑FD) meshless discretization with a phase-field formulation based on the Cahn–Hilliard model. The method leverages the geometric flexibility of the RBF-FD approach through high-quality dynamic refinement of the node distribution in the vicinity of the interface, thus enhancing accuracy where sharp gradients develop and representing a novelty in the context of the RBF-FD simulation of two‑phase flows. Thorough quantitative assessments are conducted to evaluate both convergence behavior and overall accuracy. Results for three classic 2D benchmark problems, i.e., reversed single vortex test, Rayleigh-Taylor instability and rising bubble problem, are compared against highly resolved reference results obtained both with the same meshless methodology, using a large number of nodes, and with traditional finite‑volume simulations carried out with ANSYS Fluent. In all cases, the proposed adaptive RBF‑FD framework demonstrated excellent agreement with the reference solutions, achieving favorable convergence properties and high overall accuracy. These results highlight the strong potential of coupling meshless discretizations with adaptive node refinement, indicating a promising direction for future developments in multiphase computational modeling.