A two step viscothermal acoustic FE method

W.R. Kampinga, Ysbrand H. Wijnant, Andries de Boer

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Previously, the authors presented a finite element for viscothermal acoustics. This element has the velocity vector, the temperature and the pressure as degrees of freedom. It can be used, for example, to model sound propagation in miniature acoustical transducers. Unfortunately, the large number of coupled degrees of freedom can make the models big and time consuming to solve. A method with reduced calculation time has been developed. It is possible to partially decouple the temperature degree of freedom, as result of the differences in the characteristic length scales of acoustics and heat conduction. This leads to a method that uses two sequential steps. In the first step, a scalar field containing information about the thermal effects is calculated (not the temperature). This is a relatively small FE calculation. In the second step, the actual viscothermal acoustical equations are solved. This calculation uses the field calculated in the first step and has the velocity vector and the pressure as the degrees of freedom. The temperature is not a degree of freedom anymore, but it can be easily calculated in a post processing step. The required computational effort is reduced significantly, while the difference in the results, compared to the fully coupled method, is negligible. Along with the theoretical basis for the method, a specific FE calculation is presented to illustrate its accuracy and improvement in calculation time.
Original languageUndefined
Title of host publicationInternational Congress on Sound and Vibration (cd-rom)
EditorsM Pawełczyk
Place of PublicationKraków
PublisherInternational Institute of Acoustics and Vibration
Number of pages8
Publication statusPublished - 2009
Event16th International Congress on Sound and Vibration, ICSV 2009 - Kraków, Poland
Duration: 5 Jul 20099 Jul 2009
Conference number: 16


Conference16th International Congress on Sound and Vibration, ICSV 2009
Abbreviated titleICSV
Internet address


  • METIS-262716
  • IR-69343

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