Asymptotic Preserving Property of a Semi-implicit Method

This work focuses on the study of the asymptotic preserving property of a semi-implicit method. The semi-implicit method, which is a pressure-based method, has been successfully used to simulate two-phase flows in numerous industrial applications. This method is used in our studies due to the fact that pressure-based methods generally perform well at low Mach numbers. The semi-implicit method is applied to the homogeneous equilibrium model (HEM) in this work to simulate two-phase flows. We show that the semi-implicit method is asymptotic preserving, i.e. the discretization for a compressible model tends to a consistent discretization for the related incompressible model at the low Mach number limit. Finally, test cases are performed to show that the numerical method is able to deal with low Mach number flows, as well as flows with a wide range of Mach numbers.