An assessment of multicomponent flow models and interface capturing schemes for spherical bubble dynamics. (English) Zbl 1453.76108

Summary: 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 G. Allaire et al. [J. Comput. Phys. 181, No. 2, 577–616 (2002; Zbl 1169.76407)] and J. Massoni et al. [Int. J. Heat Mass Transfer 45, No. 6, 1287–1307 (2002; Zbl 1121.76378)], the 5-equation model of A. K. Kapila et al. [Phys. Fluids 13, No. 10, Paper No. 3002, 23 p. (2001; Zbl 1184.76268)], and the 6-equation model of R. Saurel et al. [J. Comput. Phys. 228, No. 5, 1678–1712 (2009; Zbl 1409.76105)] 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 for spherical bubble collapse problems and explain the corresponding advantages of the augmented model of Kapila et al. [loc. cit.] 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 the pressure-disequilibrium model. Lastly, the performance of the 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.


76M12 Finite volume methods applied to problems in fluid mechanics
76T10 Liquid-gas two-phase flows, bubbly flows


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