Solving a coupled field problem by eigenmode expansion and finite element method

Bernd Baumann, Marcus Wolff, Bernd Kost, Hinrich Groninga

Abstract


The propagation of sound in fluids is governed by a set of coupled partial differential equations supplemented by an appropriate equation of state. In many cases of practical importance one restricts attention to the case of ideal fluids with vanishing transport coefficients. Then, the differential equations decouple and sound propagation can be described by the wave equation. However, when loss mechanisms are important, this is in general not possible and the full set of equations has to be considered. For photoacoustic cells, an alternative procedure has been used for the calculation of the photoacoustic signal of cylinder shaped cells. The method is based on an expansion of the sound pressure in terms of eigenmodes and the incorporation of loss through quality factors of various physical origins. In this paper, we demonstrate that the method can successfully be applied to photoacoustic cells of unconventional geometry using finite element analysis.

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DOI: http://dx.doi.org/10.1260/175095407782219238

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