Use of modern simulation for industrial applications of high power ultrasonics

Landes, H.; Hoffelner, J.; Simkovics, R.

doi:10.1109/ultsym.2002.1193491

Cited by 12 publications

(17 citation statements)

References 3 publications

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“…High-power ultrasound sources have found their way into a wide variety of applications, ranging from medical ultrasound, like lithotripsy or HIFU-therapy (High-Intensity Focused Ultrasound) to ultrasonic cleaning or welding and sonochemistry [16]. In contrast to ultrasonic applications with low amplitude pressure waves non-linear effects like sawtooth and shock formation occur within high-power ultrasound.…”

Section: High-intensity Focused Ultrasoundmentioning

confidence: 99%

Computational Acoustics in Multi-Field Problems

KALTENBACHER

2011

J. Comp. Acous.

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We present physical/mathematical models base on partial differential equations (PDEs) and efficient numerical simulation schemes based on the Finite Element (FE) method for multi-field problems, where the acoustic field is the field of main interest. Acoustics, the theory of sound, is an emerging scientific field including disciplines from physics over engineering to medical science. We concentrate on the following three topics: vibro-acoustics, aero-acoustics and high intensity focused ultrasound. For each topic, we discuss the physical/mathematical modeling, efficient numerical schemes and provide practical applications.

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Section: High-intensity Focused Ultrasoundmentioning

confidence: 99%

Computational Acoustics in Multi-Field Problems

KALTENBACHER

2011

J. Comp. Acous.

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“…We here especially mention high-intensity ultrasound used in medical imaging and therapy, but also for industrial purposes, such as ultrasound cleaning or welding; see, e.g., Refs. 1,8,23, and the given references therein. For the physical fundamentals of nonlinear acoustics, we refer to, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

The Jordan–Moore–Gibson–Thompson Equation: Well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time

Kaltenbacher

Nikolić

2019

Math. Models Methods Appl. Sci.

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In this paper, we consider the Jordan-Moore-Gibson-Thompson equation, a third order in time wave equation describing the nonlinear propagation of sound that avoids the infinite signal speed paradox of classical second order in time strongly damped models of nonlinear acoustics, such as the Westervelt and the Kuznetsov equation. We show well-posedness in an acoustic velocity potential formulation with and without gradient nonlinearity, corresponding to the Kuznetsov and the Westervelt nonlinearities, respectively. Moreover, we consider the limit as the parameter of the third order time derivative that plays the role of a relaxation time tends to zero, which again leads to the classical Kuznetsov and Westervelt models. To this end, we establish appropriate energy estimates for the linearized equations and employ fixed-point arguments for well-posedness of the nonlinear equations. The theoretical results are illustrated by numerical experiments. ,(1.5) respectively. As has been observed in, e.g., Ref. 16, the use of classical Fourier's lawwhere ϑ, q, and K denote the absolute temperature, heat flux vector, and thermal conductivity, respectively, leads to an infinite signal speed paradox, which appears to be unnatural in wave propagation. Therefore in Ref. 16, several other constitutive relations for the heat flux are considered within the derivation of nonlinear acoustic wave equations. Among these is the Maxwell-Cattaneo law τ q t + q = −K∇ϑ,

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“…Time integration methods for the equations of nonlinear acoustics have been investigated in DREYER ET AL. (2000); KALTENBACHER ET AL. (2002); however, the use of transient simulations within the mathematical optimisation of high intensity ultrasound devices still seems to be beyond the scope of these approaches.…”

Section: Introductionmentioning

confidence: 99%

Efficient time integration methods based on operator splitting and application to the Westervelt equation

Kaltenbacher¹,

Nikolić²,

Thalhammer³

2014

IMA J Numer Anal

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Efficient time integration methods based on operator splitting are introduced for the Westervelt equation, a nonlinear damped wave equation that arises in nonlinear acoustics as mathematical model for the propagation of sound waves in high intensity ultrasound applications. For the first-order Lie-Trotter splitting method a global error estimate is deduced, confirming that the splitting method remains stable and that the nonstiff convergence order is retained in situations where the problem data are sufficiently regular. Fundamental ingredients in the stability and error analysis are regularity results for the Westervelt equation and related linear evolution equations of hyperbolic and parabolic type. Numerical examples illustrate and complement the theoretical investigations.

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Use of modern simulation for industrial applications of high power ultrasonics

Cited by 12 publications

References 3 publications

Computational Acoustics in Multi-Field Problems

Computational Acoustics in Multi-Field Problems

The Jordan–Moore–Gibson–Thompson Equation: Well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time

Efficient time integration methods based on operator splitting and application to the Westervelt equation

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