Mathematical and numerical analysis of the rayleigh-plesset and the keller equations

Masashi Ohnawa, Yukihito Suzuki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In the present paper, we conduct mathematical analysis on the Rayleigh- Plesset and the Keller equations, ordinary differential equations of the second order widely used for describing motions of a spherically symmetric single bubble. We show that these equations admit structures of the Hamiltonian system with respect to a physically reasonable energy function perturbed by dissipation and obtain the asymptotic behavior of the solutions. Making use of this structure, we rewrite the equations into gradient systems and develop numerical codes which properly inherit conservation or dissipation of the energy from the original differential equations following the discrete gradient method.

Original languageEnglish
Title of host publicationMathematical Fluid Dynamics, Present and Future
PublisherSpringer New York LLC
Pages159-180
Number of pages22
Volume183
ISBN (Print)9784431564553
DOIs
Publication statusPublished - 2016
Event8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014 - Tokyo, Japan
Duration: 2014 Nov 112014 Nov 14

Other

Other8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014
CountryJapan
CityTokyo
Period14/11/1114/11/14

Fingerprint

Mathematical Analysis
Rayleigh
Numerical Analysis
Dissipation
Gradient System
Gradient Method
Energy Function
Bubble
Hamiltonian Systems
Conservation
Ordinary differential equation
Asymptotic Behavior
Differential equation
Motion
Energy

Keywords

  • Bubble dynamics
  • Discrete gradient method
  • Hamiltonian system
  • Keller equation
  • Rayleigh-Plesset equation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Ohnawa, M., & Suzuki, Y. (2016). Mathematical and numerical analysis of the rayleigh-plesset and the keller equations. In Mathematical Fluid Dynamics, Present and Future (Vol. 183, pp. 159-180). Springer New York LLC. https://doi.org/10.1007/978-4-431-56457-7_7

Mathematical and numerical analysis of the rayleigh-plesset and the keller equations. / Ohnawa, Masashi; Suzuki, Yukihito.

Mathematical Fluid Dynamics, Present and Future. Vol. 183 Springer New York LLC, 2016. p. 159-180.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ohnawa, M & Suzuki, Y 2016, Mathematical and numerical analysis of the rayleigh-plesset and the keller equations. in Mathematical Fluid Dynamics, Present and Future. vol. 183, Springer New York LLC, pp. 159-180, 8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014, Tokyo, Japan, 14/11/11. https://doi.org/10.1007/978-4-431-56457-7_7
Ohnawa M, Suzuki Y. Mathematical and numerical analysis of the rayleigh-plesset and the keller equations. In Mathematical Fluid Dynamics, Present and Future. Vol. 183. Springer New York LLC. 2016. p. 159-180 https://doi.org/10.1007/978-4-431-56457-7_7
Ohnawa, Masashi ; Suzuki, Yukihito. / Mathematical and numerical analysis of the rayleigh-plesset and the keller equations. Mathematical Fluid Dynamics, Present and Future. Vol. 183 Springer New York LLC, 2016. pp. 159-180
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