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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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Online
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1569-3953
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Volume 20, Issue 3-4 (Dec 2012)

Issues

Fictitious domain method to model a movable rigid body in a sound wave

D. Imbert
  • Institut de Physique de Rennes (IPR), UMR Universit´e de Rennes 1 - CNRS 6251, Campus de Beaulieu - bˆat. 11A, 263 avenue du G´en´eral Leclerc, CS 74205, 35042 RENNES CEDEX
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  • Institut de Physique de Rennes (IPR), UMR Universit´e de Rennes 1 - CNRS 6251, Campus de Beaulieu - bˆat. 11A, 263 avenue du G´en´eral Leclerc, CS 74205, 35042 RENNES CEDEX
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Published Online: 2013-03-30 | DOI: https://doi.org/10.1515/jnum-2012-0014

Abstract

Motivated by experiments on the acoustics of submerged granular media, we have developed a new fictitious domain method that combines the acoustic wave equation with the equations of motion of a rigid body. The coupling is realized through the natural boundary conditions of the wave equation on the surface of the body and enforced with boundary Lagrange multipliers. The method is validated using analytic solutions for a movable rigid sphere in a sound wave. Results show that the method is promising because numerical results and analytic solutions are close for long wavelengths, although some deviations occur when the wavelength is smaller to the sphere radius. This method permits us to use a discrete element method for particle motion and interaction, and finite elements for wave propagation in the fluid.

Keywords : fictitious domainmethod; acoustic wave; combined equation ofmotion,mixed finite element; granular media; discrete element method; freefem++

About the article

Published Online: 2013-03-30

Published in Print: 2012-12-01


Citation Information: Journal of Numerical Mathematics, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnum-2012-0014.

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