Linear Iterative Procedure to Solve a Rayleigh–Plesset Equation

A nonlinear Rayleigh–Plesset equation for describing the behavior of a gas bubble in an acoustic field written in terms of bubble-volume variation is solved through a linear iterative procedure. The model is validated, and its accuracy and fast convergence are shown through the analysis of several e...

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Bibliographic Details
Published in:Acoustics (Basel, Switzerland) Switzerland), 2021-03, Vol.3 (1), p.212-220
Main Author: Vanhille, Christian
Format: Article
Language:English
Subjects:
Acoustics
Algorithms
Approximation
Integrals
Iterative algorithms
Iterative methods
linear iterative procedure
Linear systems
Model accuracy
nonlinear acoustics
nonlinear Rayleigh–Plesset equation
Nonlinear systems
Ordinary differential equations
Problem solving
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Summary:A nonlinear Rayleigh–Plesset equation for describing the behavior of a gas bubble in an acoustic field written in terms of bubble-volume variation is solved through a linear iterative procedure. The model is validated, and its accuracy and fast convergence are shown through the analysis of several examples of different physical meanings. The simplicity and usefulness of the presented method here in relation to the direct resolution of the whole nonlinear system, which is also discussed, make the method very attractive to solving a problem. This iterative method allows us to solve only linear systems instead of the nonlinear differential problem. Moreover, the implementation of the iterative algorithm includes a tolerance-dependent stopping criterion that is also tested.
ISSN:2624-599X
2624-599X
DOI:10.3390/acoustics3010015