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

Masashi Ohnawa; Yukihito Suzuki

doi:10.1007/978-4-431-56457-7_7

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

Masashi Ohnawa^*, Yukihito Suzuki

^*Corresponding author for this work

Organization for University Research Initiatives

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Citations (Scopus)

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 language	English
Title of host publication	Mathematical Fluid Dynamics, Present and Future
Publisher	Springer New York LLC
Pages	159-180
Number of pages	22
Volume	183
ISBN (Print)	9784431564553
DOIs	https://doi.org/10.1007/978-4-431-56457-7_7
Publication status	Published - 2016
Event	8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014 - Tokyo, Japan Duration: 2014 Nov 11 → 2014 Nov 14

Other

Other	8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014
Country/Territory	Japan
City	Tokyo
Period	14/11/11 → 14/11/14

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/978-4-431-56457-7_7

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, 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

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title = "Mathematical and numerical analysis of the rayleigh-plesset and the keller equations",

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.",

keywords = "Bubble dynamics, Discrete gradient method, Hamiltonian system, Keller equation, Rayleigh-Plesset equation",

author = "Masashi Ohnawa and Yukihito Suzuki",

year = "2016",

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language = "English",

isbn = "9784431564553",

volume = "183",

pages = "159--180",

booktitle = "Mathematical Fluid Dynamics, Present and Future",

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AU - Ohnawa, Masashi

AU - Suzuki, Yukihito

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Bubble dynamics

KW - Discrete gradient method

KW - Hamiltonian system

KW - Keller equation

KW - Rayleigh-Plesset equation

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DO - 10.1007/978-4-431-56457-7_7

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AN - SCOPUS:85009786070

SN - 9784431564553

VL - 183

SP - 159

EP - 180

BT - Mathematical Fluid Dynamics, Present and Future

PB - Springer New York LLC

T2 - 8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014

Y2 - 11 November 2014 through 14 November 2014

ER -

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

Abstract

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Keywords

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