Multiscale Cavitation Sub-Grid Modeling via Population Balances as Linear Stochastic Process

A multiscale sub-grid cavitation model is developed in which the bubble size distribution evolves as a linear stochastic process in radius space. Starting from the integrated Rayleigh--Plesset equation, the population balance is recast as a hyperbolic transport equation for the number density per radius, whose method-of-characteristics solution, projected onto a discrete histogram basis, yields a column-stochastic Markov chain governing the bubble counts per size bin. The transition matrix factors into a precomputable, mesh-only geometric part and a local, pressure-dependent shift, isolating the coupling to the surrounding flow into a single dimensionless vector per cell. The framework recovers classical homogeneous-mixture cavitation closures in the limit of a single representative scale.