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A finite volume approach for the simulation of nonlinear dissipative acoustic wave propagation

Roberto Velasco-Segura, Pablo L. Rendon
Grupo de Acustica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnologico, Universidad Nacional Autonoma de Mexico, Ciudad Universitaria-Mexico, D.F. 04510 Mexico
arXiv:1311.3004 [physics.flu-dyn], (13 Nov 2013)

@article{2013arXiv1311.3004V,

   author={Velasco-Segura}, R. and {Rend{‘o}n}, P.~L.},

   title={"{A finite volume approach for the simulation of nonlinear dissipative acoustic wave propagation}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1311.3004},

   primaryClass={"physics.flu-dyn"},

   keywords={Physics – Fluid Dynamics},

   year={2013},

   month={nov},

   adsurl={http://adsabs.harvard.edu/abs/2013arXiv1311.3004V},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A CLAWPACK based, 2D finite volume method using the Roe linearization was implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a HIFU system, both with satisfactory results. The code is based on CLAWPACK and is written for parallel execution on a GPU, thus improving performance by a factor of over 60 when compared to the standard CLAWPACK code.
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