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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.

MSC:

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

Software:

ECOGEN; HARM
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References:

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