A mathematical model for the simulation of the dynamics of spherical vapor-air bubbles and its numerical implementation is presented. Heat and mass transfer and phase transition in terms of evaporation and condensation as well as air absorption and desorption are considered. Flow variables are discretized by a mixed finite volume / finite difference scheme and solved either by a Crank-Nicolson or Runge-Kutta scheme. Due to the assumption of homogeneous bubble pressure (homobaricity), the solution of momentum equations is restricted to the Rayleigh-Plesset equation which makes the model computationally efficient. The model is validated by measurement data for bubble growth and applied to bubble collapse and rebound. By a comparison with Navier-Stokes results from literature, the homobaricity assumption is shown to be appropriate even in the last stage of bubble collapse. The relation of the local velocity and temperature field with heat and mass transfer is discussed. Equilibrium bubble interface conditions (liquid and gaseous side have the same temperature and chemical potential) are compared to non-equilibrium conditions and are shown to yield the same local velocity and temperature field for each stage of bubble collapse and rebound.

提出了一种模拟球形蒸汽-气泡动力学的数学模型及其数值实现。考虑了在蒸发和冷凝以及空气吸收和解吸方面的传热和传质以及相变。流量变量通过混合有限体积/有限差分方案离散化，并通过Crank-Nicolson方案或Runge-Kutta方案求解。由于假设了均匀的气泡压力（同质性），所以动量方程的解仅限于Rayleigh-Plesset方程，这使得模型的计算效率很高。该模型通过气泡增长的测量数据进行了验证，并应用于气泡破裂和回弹。通过与来自文学的Navier-Stokes结果进行比较，事实证明，即使在泡沫破裂的最后阶段，均压假设也是合适的。讨论了局部速度和温度场与传热和传质的关系。将平衡气泡界面条件（液体和气体侧具有相同的温度和化学势）与非平衡条件进行比较，结果表明，在气泡破裂和回弹的每个阶段，它们都产生相同的局部速度和温度场。