Modeling approaches for bubbly, cavitating flows

We compare two approaches for modeling bubbly, cavitating flows. The first approach is a deterministic model, for which bubbles are represented in a Lagrangian framework as advected particles, each sampled from a distribution of equilibrium bubble sizes. The dynamic coupling to the liquid phase is modeled through local volume averaging. The second approach is stochastic; ensemble-phase averaging is used to derive mixture-averaged equations and the field equations are evolved in an Eulerian reference frame for the associated bubble properties, each representing bins of an underlying equilibrium distribution. In both cases the equations are closed by solving Rayleigh-Plesset-like equations for the bubble dynamics as forced by the local or mixture-averaged pressure, respectively. Computationally, there are complex tradeoffs between these two approaches, especially for modern, parallel architectures. As a step towards negotiating this landscape, we simulate an acoustically excited dilute bubble screen and compare the computationally efficiency of the two approaches, testing the sensitivity of each to resolution and under-sampling.