scholarly journals Numerical simulations of three-dimensional nonlinear acoustic waves in bubbly liquids

2013 ◽  
Vol 20 (3) ◽  
pp. 963-969 ◽  
Author(s):  
Christian Vanhille ◽  
Cleofé Campos-Pozuelo
Keyword(s):  
Numerical Simulations ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Bubbly Liquids ◽  
Nonlinear Acoustic

scholarly journals New Explicit Solutions to the Fractional-Order Burgers’ Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
M. Hafiz Uddin ◽  
Mohammad Asif Arefin ◽  
M. Ali Akbar ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Rational Function ◽  
Acoustic Waves ◽  
Burgers Equation ◽  
Three Dimensional ◽  
Wall Friction ◽  
Weakly Nonlinear ◽  
Bubbly Liquids ◽  
Fractional Differential ◽  
Accuracy Of Results

The closed-form wave solutions to the time-fractional Burgers’ equation have been investigated by the use of the two variables G ′ / G , 1 / G -expansion, the extended tanh function, and the exp-function methods translating the nonlinear fractional differential equations (NLFDEs) into ordinary differential equations. In this article, we ascertain the solutions in terms of tanh , sech , sinh , rational function, hyperbolic rational function, exponential function, and their integration with parameters. Advanced and standard solutions can be found by setting definite values of the parameters in the general solutions. Mathematical analysis of the solutions confirms the existence of different soliton forms, namely, kink, single soliton, periodic soliton, singular kink soliton, and some other types of solitons which are shown in three-dimensional plots. The attained solutions may be functional to examine unidirectional propagation of weakly nonlinear acoustic waves, the memory effect of the wall friction through the boundary layer, bubbly liquids, etc. The methods suggested are direct, compatible, and speedy to simulate using algebraic computation schemes, such as Maple, and can be used to verify the accuracy of results.

Waves of Acoustically Induced Transparency in Bubbly Liquids: Theoretical Prediction and Experimental Validation

2013 ◽  
Author(s):  
Nail A. Gumerov ◽  
Iskander S. Akhatov ◽  
Claus-Dieter Ohl ◽  
Sergei P. Sametov ◽  
Maxim V. Khasimulin ◽  
...  
Keyword(s):  
Acoustic Field ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Self Organization ◽  
Nonlinear Phenomenon ◽  
Three Dimensional Model ◽  
Bubbly Liquids ◽  
Strongly Nonlinear ◽  
Induced Transparency ◽  
Good Agreement

Self-organization of bubbles in acoustic fields, or self-action of the acoustic waves in bubbly liquids is a strongly nonlinear phenomenon due to two-way interaction of the bubbles and the acoustic field. Theoretical model and preliminary computations predict that waves of self-induced acoustic transparency may exist. Such effect is confirmed in the experiments presented in this paper. Formation of a wave of void fraction which rapidly propagates through the bubbly medium leaving a region almost free of bubbles behind its front is observed in the experiments. Measurements of the dynamics of such a wave at different acoustic frequencies and amplitudes are carried out. A three dimensional model of self-organization of a polydisperse bubble continuum in acoustic field is developed and the results of simulations are compared with experiments. A good agreement of the theory and experiment is found.

scholarly journals A research and modeling of wave processes at the scattering of nonlinear acoustic waves on cylindrical bodies

2019 ◽  
Vol 5 (5) ◽  
pp. 32-44
Author(s):  
Iftikhar B. Abbasov
Keyword(s):  
Small Parameter ◽  
Acoustic Waves ◽  
Acoustic Pressure ◽  
Three Dimensional ◽  
Parameter Method ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Wave Processes ◽  
Frequency Wave ◽  
Nonlinear Acoustic

The article is devoted to the study of the scattering of nonlinear acoustic waves on cylindrical bodies. There was made a review of publications on the scattering of acoustic waves by inhomogeneities of the medium in the form of cylindrical bodies and shells. There were noted features of the small parameter method application in nonlinear acoustics. A three-dimensional model of the geometry of the problem in cylindrical coordinates was presented, nonlinear wave processes occurring between the falling plane and scattered cylindrical waves were described. The inhomogeneous wave equation is solved by the method of successive approximations of series expansion in a small parameter. An asymptotic expression for the acoustic pressure of a difference-frequency wave was obtained. A program for calculating scattering diagrams has been developed, and an algorithm for its operation is given. The acoustic pressure scattering diagram of a differential frequency wave on a rigid cylinder and its three-dimensional model are presented. The radius of convergence of the used method of expansion in a small parameter is determined.

scholarly journals $L^{p}-L^{q}$-Maximal regularity of the Van Wijngaarden–Eringen equation in a cylindrical domain

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Carlos Lizama ◽  
Marina Murillo-Arcila
Keyword(s):  
Acoustic Waves ◽  
Maximal Regularity ◽  
Bubble Radius ◽  
Fourier Multipliers ◽  
Cylindrical Domain ◽  
Lebesgue Spaces ◽  
Regularity Problem ◽  
Bubbly Liquids

Abstract We consider the maximal regularity problem for a PDE of linear acoustics, named the Van Wijngaarden–Eringen equation, that models the propagation of linear acoustic waves in isothermal bubbly liquids, wherein the bubbles are of uniform radius. If the dimensionless bubble radius is greater than one, we prove that the inhomogeneous version of the Van Wijngaarden–Eringen equation, in a cylindrical domain, admits maximal regularity in Lebesgue spaces. Our methods are based on the theory of operator-valued Fourier multipliers.

Simulation of multiwavelength conditions in laser picosecond ultrasonics

SIMULATION ◽  
2021 ◽  
pp. 003754972199645
Author(s):  
Philippe Babilotte
Keyword(s):  
Numerical Simulations ◽  
Acoustic Signal ◽  
Acoustic Waves ◽  
Bulk Material ◽  
Deformation Field ◽  
Optical Pump ◽  
Pump And Probe ◽  
Oriented Object ◽  
Numerical Approaches ◽  
Picosecond Ultrasonics

Complete numerical simulations are given under SciLab® and MATLAB® coding environments, concerning propagative acoustic wavefronts, for laser picosecond ultrasonics under multiwavelength conditions. Simulations of the deformation field and its propagation into bulk material are given under different wavelength configurations for optical pump and probe beams, which are used to generate and to detect the acoustic signal. Complete insights concerning the dynamics of the acoustic waves are given, considering the absence of carrier diffusions into the material. Several numerical approaches are proposed concerning both the functions introduced to simulate the wavefront ( Heaviside or error) and the coding approach (linear/vectorized/ Oriented Object Programming), under the pure thermo-elastic approach.

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