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

Masashi Ohnawa, Yukihito Suzuki

研究成果: Conference contribution

2 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルMathematical Fluid Dynamics, Present and Future
出版社Springer New York LLC
ページ159-180
ページ数22
183
ISBN(印刷版)9784431564553
DOI
出版ステータスPublished - 2016
イベント8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014 - Tokyo, Japan
継続期間: 2014 11 112014 11 14

Other

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

ASJC Scopus subject areas

  • Mathematics(all)

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