Numerical simulation of bubble dynamics and cavitation is challenging; even
the seemingly simple problem of a collapsing spherical bubble is difficult to
compute accurately with a general, three-dimensional, compressible,
multicomponent flow solver. Difficulties arise due to both the physical model
and the numerical method chosen for its solution. We consider the 5-equation
model of Allaire et al. [1], the 5-equation model of Kapila et al. [2], and the
6-equation model of Saurel et al. [3] as candidate approaches for spherical
bubble dynamics, and both MUSCL and WENO interface-capturing methods are
implemented and compared. We demonstrate the inadequacy of the traditional
5-equation model of Allaire et al. [1] for spherical bubble collapse problems
and explain the corresponding advantages of the augmented model of Kapila et
al. [2] for representing this phenomenon. Quantitative comparisons between the
augmented 5-equation and 6-equation models for three-dimensional bubble
collapse problems demonstrate the versatility of pressure-disequilibrium
models. Lastly, the performance of pressure disequilibrium model for
representing a three-dimensional spherical bubble collapse for different bubble
interior/exterior pressure ratios is evaluated for different numerical methods.
Pathologies associated with each factor and their origins are identified and
discussed
