A pressure-based method for solving low Mach number two-phase flows with surface tension

We develop a pressure-based method using a mixture model for solving low Mach number compressible two-phase flows which contain surface tension, viscous stress, and heat conduction. We utilize the inviscid mixture model with isobaric-one velocity conditions imposed at the interface, and simply append viscous dissipation and heat conduction, where an isothermal condition is assumed. The continuum surface force model proposed by Brackbill et al. (1992) is used for surface tension effects. The pressure-based, segregated solution procedure is employed, the advection terms are explicitly integrated to suppress the numerical diffusion, and the other terms are implicitly solved by an iterative method. For the stability of the iterative calculation, the mixture sound speed included in the pressure equation is linearized by using the solution of the previous iteration, and the density is directly calculated from the equation of state. The proposed method is validated by conducting a shock tube problem, a one-dimensional oscillating bubble problem, and a two-dimensional static bubble problem governed by the Laplace law. In these problems, the numerical results are in good agreement with exact solutions. Finally, a two-dimensional collapsing bubble problem is presented to demonstrate the applicability of the proposed method.