Direct numerical simulation for air–water two-phase flow with a ghost-pressure method in a fully staggered curvilinear grid

A ghost-pressure method for two phase flows using a fully staggered curvilinear grid is implemented to solve the incompressible Navier–Stokes equation based on a direct numerical simulation. Without any turbulent model, dam-break simulations are conducted, and the result is compared with the experimental study. The results exhibit reasonable agreement in both the time history of the pressure and the air–water interface. The hybrid convection scheme provides enhanced interface resolution compared to the implicit convection scheme, while effectively avoiding numerical instability following the pressure impact of the dam breaking. Two-phase flow simulations over a half-cylinder bump are also performed with the hybrid convection scheme with Froude numbers ranging from 1 to 3 and the order of Reynolds numbers varying from 106 to 108. When the Froude number is over 2, the intensity of large-scale vortices from the bump increases, indicating the onset of significant interaction with the free surface. The vortex core sustains low pressure in the downstream region, where pressure recovery occurs, creating a substantial pressure gradient at the vortex ring boundary that accelerates velocity and potentially enhances upward rotational motion of the flow. Reynolds stress terms indicate negative signs in most of the flow field when it does not include lateral velocity fluctuations. Turbulent dissipation rates directly calculate including Taylor microscales for the entire flow field in which the result shows comparably small-scale values near the no-slip wall and at the air–water interface. Finally, componential contours for turbulent anisotropy behaviors show near two-component fluctuations at the air–water interface.