A conservative diffuse-interface method for simulation of two-phase compressible flows with acoustics *

Bubble acoustics and liquid fuel injection are example applications in which important dynamical processes involve coupling between flow compressibility and two-phase flow effects. The numerical study of acoustics and turbulent flows require stable, non-dissipative and conservative numerical methods. We have developed a diffuse-interface five-equation model that (a) can be solved using non-dissipative numerical methods (low and high-order central-difference schemes), (b) discretely conserves mass of each phase, total momentum and total energy in the system, (c) maintains mechanical equilibrium (uniform velocity) and thermodynamic equilibrium (uniform pressure) across the interface (d) maintains a steady interface thickness. Results from test cases such as (a) acoustic wave incident on an interface  - showing the accuracy in capturing the theoretically predicted transmitted and reflected wave amplitudes (b) oscillating bubble under a driven pressure pulse – showing the capturing of predicted decay of oscillation for very long time integration, will be discussed.