Computations of Homogeneous-Equilibrium Two-Phase Flows with Accurate and Efficient Shock-Stable Schemes

For accurate and efficient computations of compressible gas–liquid two-phase mixture flows, the AUSMPW and RoeM schemes (for which the accuracy, efficiency, and robustness have been successfully demonstrated in gas dynamics) are extended to two-phase flows at all speeds. From the mixture equations of state, a new shock-discontinuity-sensing term suitably scaled for two-phase flows is derived and its performance is validated. In addition, several numerical difficulties appearing in the development of the two-phase AUSMPW and RoeM schemes are analyzed and successfully cured. The two-phase AUSMPW and RoeM schemes are then efficiently preconditioned for the simulation of all Mach number flows by employing the existing AUSM or Harten–Lax–van Leer with contact restoration types of preconditioning strategies. Various gas–liquid two-phase flows, from highly compressible to nearly incompressible flow conditions, are tested. The numerical results show the accurate and robust behavior of the proposed schemes for all speeds of two-phase flows. ; The authors appreciate the financial support by the Agency for Defense Development (ADD) and by the Brain Korea-21 Program for Mechanical and Aerospace Engineering Research at Seoul National University.