Semi-Numerical, Semi-Analytical Approximations of the Rayleigh Equation for Gas-Filled Hyper-Spherical Bubble

Yupeng Qin; Zhen Wang; Li Zou; Mingfeng He

doi:10.1142/S0219876218500949

Semi-Numerical, Semi-Analytical Approximations of the Rayleigh Equation for Gas-Filled Hyper-Spherical Bubble

Yupeng Qin
, Zhen Wang^*
, Li Zou
, Mingfeng He

^*Corresponding author for this work

Dalian University of Technology
Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

A new semi-numerical, semi-analytical approach based on the differential transform method is proposed to solve the problems of a gas-filled hyper-spherical bubble governed by the Rayleigh equation. Semi-numerical, semi-analytical approximations are constructed for the Rayleigh equation in the form of piecewise functions. The proposed approach is compared with the standard fourth-order Runge-Kutta method and the standard differential transform method, respectively. The results reveal two main benefits of the new approach, one is that it possesses result with higher precision than the standard fourth-order Runge-Kutta method, the other is that it remains valid and accurate for longer time compared to the standard differential transform method. In addition, we also consider the Rayleigh equation in N dimensions when the surface tension is not zero.

Original language	English
Article number	1850094
Journal	International Journal of Computational Methods
Volume	16
Issue number	1
DOIs	https://doi.org/10.1142/S0219876218500949
State	Published - 1 Feb 2019
Externally published	Yes

Keywords

Rayleigh equation
differential transform method
gas-filled hyper-spherical bubble
semi-numerical, semi-analytical approximations

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10.1142/S0219876218500949

Cite this

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title = "Semi-Numerical, Semi-Analytical Approximations of the Rayleigh Equation for Gas-Filled Hyper-Spherical Bubble",

abstract = "A new semi-numerical, semi-analytical approach based on the differential transform method is proposed to solve the problems of a gas-filled hyper-spherical bubble governed by the Rayleigh equation. Semi-numerical, semi-analytical approximations are constructed for the Rayleigh equation in the form of piecewise functions. The proposed approach is compared with the standard fourth-order Runge-Kutta method and the standard differential transform method, respectively. The results reveal two main benefits of the new approach, one is that it possesses result with higher precision than the standard fourth-order Runge-Kutta method, the other is that it remains valid and accurate for longer time compared to the standard differential transform method. In addition, we also consider the Rayleigh equation in N dimensions when the surface tension is not zero.",

keywords = "Rayleigh equation, differential transform method, gas-filled hyper-spherical bubble, semi-numerical, semi-analytical approximations",

author = "Yupeng Qin and Zhen Wang and Li Zou and Mingfeng He",

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doi = "10.1142/S0219876218500949",

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T1 - Semi-Numerical, Semi-Analytical Approximations of the Rayleigh Equation for Gas-Filled Hyper-Spherical Bubble

AU - Qin, Yupeng

AU - Wang, Zhen

AU - Zou, Li

AU - He, Mingfeng

PY - 2019/2/1

Y1 - 2019/2/1

N2 - A new semi-numerical, semi-analytical approach based on the differential transform method is proposed to solve the problems of a gas-filled hyper-spherical bubble governed by the Rayleigh equation. Semi-numerical, semi-analytical approximations are constructed for the Rayleigh equation in the form of piecewise functions. The proposed approach is compared with the standard fourth-order Runge-Kutta method and the standard differential transform method, respectively. The results reveal two main benefits of the new approach, one is that it possesses result with higher precision than the standard fourth-order Runge-Kutta method, the other is that it remains valid and accurate for longer time compared to the standard differential transform method. In addition, we also consider the Rayleigh equation in N dimensions when the surface tension is not zero.

AB - A new semi-numerical, semi-analytical approach based on the differential transform method is proposed to solve the problems of a gas-filled hyper-spherical bubble governed by the Rayleigh equation. Semi-numerical, semi-analytical approximations are constructed for the Rayleigh equation in the form of piecewise functions. The proposed approach is compared with the standard fourth-order Runge-Kutta method and the standard differential transform method, respectively. The results reveal two main benefits of the new approach, one is that it possesses result with higher precision than the standard fourth-order Runge-Kutta method, the other is that it remains valid and accurate for longer time compared to the standard differential transform method. In addition, we also consider the Rayleigh equation in N dimensions when the surface tension is not zero.

KW - Rayleigh equation

KW - differential transform method

KW - gas-filled hyper-spherical bubble

KW - semi-numerical, semi-analytical approximations

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DO - 10.1142/S0219876218500949

M3 - 文章

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VL - 16

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Semi-Numerical, Semi-Analytical Approximations of the Rayleigh Equation for Gas-Filled Hyper-Spherical Bubble

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Keywords

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