A gas-kinetic BGK scheme for gas–water flow

A new one-dimensional gas-kinetic BGK scheme for gas–water flow is developed with the inclusion of the stiffened equation of state for water. The mixture model is considered, where the gas and water inside a computational cell achieve the equilibrium state, with equal pressure, velocity and temperature, within a time step. The splitting method is adopted to calculate the flux of each component at a cell interface individually. The preliminary application of the present newly developed method in different types of shock tube problems, including gas–gas shock tube and gas–water shock tube problems, validates its good performance for gas–water flow.