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Journal of the Acoustical Society of America

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May 2012

Volume 131, Issue 5, pp. EL355-4232

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A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation

Olivier Bou Matar, Pierre-Yves Guerder, YiFeng Li, Bart Vandewoestyne, and Koen Van Den Abeele

J. Acoust. Soc. Am. Volume 131, Issue 5, pp. 3650-3663 (2012); (14 pages)

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A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb’s problem and plane wave nonlinear propagation.
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43.25.Dc Nonlinear acoustics of solids
43.20.Bi Mathematical theory of wave propagation
43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves

Acoustic radiation force analysis using finite difference time domain method

A. Grinenko, P. D. Wilcox, C. R. P. Courtney, and B. W. Drinkwater

J. Acoust. Soc. Am. Volume 131, Issue 5, pp. 3664-3670 (2012); (7 pages)

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Acoustic radiation force exerted by standing waves on particles is analyzed using a finite difference time domain Lagrangian method. This method allows the acoustic radiation force to be obtained directly from the solution of nonlinear fluid equations, without any assumptions on size or geometry of the particles, boundary conditions, or acoustic field amplitude. The model converges to analytical results in the limit of small particle radii and low field amplitudes, where assumptions within the analytical models apply. Good agreement with analytical and numerical models based on solutions of linear scattering problems is observed for compressible particles, whereas some disagreement is detected when the compressibility of the particles decreases.
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43.25.Qp Radiation pressure
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