# A hybrid, mesoscale method for turbulent bubbly flows

Simulation of flows that include both small bubble nuclei and large, gaseous regions is challenging due to the disperse length scales. Unfortunately, such flows are perverse in application. I formulated a subgrid-bubble homogeneous-mixture hybrid model to address this problem; it recovers the 5-equation model in the fully-resolved-bubble limit and the ensemble phase-averaged flow equations when the bubbles are much smaller than the grid. Otherwise, source terms are implemented to switch between either modeling effort.

*This work is currently under preparation for peer review*

# Ensemble- and volume-averaged stochastic models for cavitating flows

Ensemble- and volume-averaging are phase-averaged methods for disperse, bubbly flows. While built upon similar assumptions, it is challenging to assess their relative merits. Volume-averaging is an intrinsically 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. Ensemble-phase averaging is stochastic, and uses ensemble-averaging 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. We assess their relative complexity and cost via high-resolution simulations.