A numerical comparison of 5-, 6-, and 7-equation Baer-Nunziato-based diffuse interface methods

The Baer-Nunziato equations are often used to represent multiphase flows and solve them via the diffuse interface method. These equations solve for phasic volume, mass, momentum, and energy in the most general form (the 7-equation model). Since a pressure and velocity equality is maintained at a multiphase interface, reduced forms such as 5- (one pressure, one velocity) and 6-equation (two pressures, one velocity) models can be appropriate approximations for the full model. These are widely used for resolved multiphase modeling due to their simplicity. However, the 7-equation model offers advantages in handling independent and arbitrary equations of state and its validity in regions with unresolved multiphase entities. We recently developed a numerical method for solving the 7-equation model. Here, we compare this approach to existing ones for the 6- and 5-equation models. Numerical results for a shock-droplet interaction problem (Mach 1.4 and 2.5) are assessed. Simulation results are validated against established experimental data, and theory is used to help describe the observed differences.