Comparison of Dynamics of Gas Bubbles in a Spherical Cluster Simulated by Continuous and Discrete Models

Numerical simulation of the dynamics of gas bubbles in a spherical cluster by a continuous medium model and a particle model has been compared. To this end, a problem of bubble dynamics in a spherical cluster under a single cosinusoidal liquid pressure oscillation has been considered. The cluster consists of 203 initially equal spherical bubbles that are located at the nodes of a uniform cubic mesh, one of which is positioned at the cluster center. This arrangement approximately corresponds to a cluster with uniform bubble distribution and gas volume fraction close to 0.02 . The amplitude of the liquid pressure oscillation is varied up to the value of the static liquid pressure. It is shown that at small liquid pressure oscillation amplitude the dynamics of the cluster bubbles derived by the two models under consideration is nearly the same. With increasing the amplitude, the deviation of the bubble dynamics grows. The most difference arises in the dynamics of bubbles in the central region of the cluster in the stage of their rebounds, which follows after their first expansion and subsequent collapse.