A novel phase-field/immersed-boundary algorithm for two-phase fluid–structure interaction simulation

Accurate simulation of multiphase fluid–structure interaction with large density ratios is challenging on non-staggered grids due to spurious pressure oscillations. To address this issue, we present a novel and efficient pressure-oscillation-free projection algorithm, which decouples the incompressible Navier–Stokes equations using an improved incremental pressure correction scheme. The fluid–fluid interface is captured using the Cahn–Hilliard equation, with surface tension forces accurately modeled by a momentum-weighted interpolation scheme that eliminates pressure oscillations. The interaction between fluid and structure is handled through an implicit Eulerian–Lagrangian framework. The validation of the method includes systematic comparisons with established benchmarks such as lid-driven cavity flows and droplet deformations, demonstrating the algorithm's robustness and precision. Additionally, we present a case study of a rising bubble navigating an obstacle, illustrating the method's capability in dynamic fluid–structure interactions. The results confirm that the proposed algorithm not only reduces pressure oscillations but also enhances the accuracy of multiphase simulations.