A stable immersed boundary method for suppressing interface penetration into immersed solids in two-phase flows

Conventional immersed boundary (IB) method, when coupled with interface-capturing schemes for multiphase flows, often suffers from unphysical penetration of the gas–liquid interface into immersed solids. This failure mode originates from velocity errors at fluid–solid interface nodes induced by strong temporal pressure gradients, which become particularly severe when the interior of the immersed body is initially filled with a light phase. Increasing the density of the virtual fluid inside the solid region can reduce this velocity error and suppress interface penetration. However, this strategy simultaneously amplifies the spurious pressure oscillations when the IB moves across the grid. These oscillations arise from geometric non-conservation of the inertial and body-force integrals associated with fresh and dead cells generated by immersed-boundary motion. To resolve this issue, a conservative cut-cell-based momentum forcing formulation is developed to restore discrete geometric conservation near the IB. The resulting framework naturally leads to a density-weighted hybrid velocity reconstruction and a modified velocity corrector. The performance and accuracy of the methodology are assessed using three test cases involving fluid–structure interaction in surface-piercing configurations, which demonstrate its capability to eliminate free-surface penetration into the structure and accurately predict hydrodynamic forces. Finally, the proposed method is applied to simulate the propulsion of a manta ray swimmer.