Conservative ghost fluid method with an interface cell for compressible two-phase fluid simulations

Numerical methods developed for simulating compressible two-phase flows present a significant challenge due to discontinuities in variables at interfaces. The ghost fluid method (GFM) is a well-known sharp-interface approach that introduces ghost fluids with estimated liquid–gas interactions near the interface, thereby preventing the numerical diffusion of discontinuities. However, this method does not conserve mass, momentum, and energy. This drawback arises because cells that are intersected by the interface are treated as single-phase cells, complicating the development of a conservative algorithm. To address this issue, we propose a conservative ghost fluid method with an interface cell (CGFM-IC), which integrates the volume of fluid (VOF) method with GFM. In the CGFM-IC, ICs that contain both gas and liquid phases are represented using the VOF function. Mass, momentum, energy, and VOF values in the computational cells near the interface are updated based on fluxes across cell surfaces, thereby ensuring conservation. Fluxes in the CGFM-IC are computed using ghost fluids to avoid numerical dissipation near the interface. Several one-dimensional and two-dimensional numerical problems were examined to evaluate the applicability of the CGFM-IC for compressible two-phase flow simulations. The results showed good agreement with exact solutions and prior numerical studies, demonstrating that the proposed method can almost completely ensure conservation. These findings indicate that the CGFM-IC is an effective method for simulating compressible two-phase flows with conservation of mass, momentum, and energy.