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Double fictitious background media formulation for the Helmholtz equation in inhomogeneous media

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Abstract

This paper describes a BEM technique for acoustic problems in the frequency domain in inhomogeneous media. Since these problems are modeled by the Helmholtz equation with variable wave number, it is observed that the simple algebraic procedure to add and subtract a term in the original differential equation permits to reformulate the problem considering two terms: a fictitious background homogeneous medium related to an appropriate Green’s function and an additional reactive term that strongly influences the numerical solution. The influence of the reactive term in the numerical solution can be strongly reduced by introducing a new pressure unknown \(\hat{P}\) in the kernel of the domain integral (the reactive term integral). The introduction of the \(\hat{P}\) causes a break of symmetry between the original pressure unknown P and the new unknown pressure \(\hat{P}\). Through weighted residual sentences, it is shown that the error minimization acts in different form between the original unknown pressure P and the new unknown \(\hat{P}\), resulting in a considerable gain of accuracy. Numerical results presented here show that the proposed technique leads to meaningful superior accuracy compared to other alternatives.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Federal Institute of Espírito Santo, Cachoeiro de Itapemirim, Espírito Santo, 29300-970, Brazil

    Markcilei Lima Dan

  2. COPPE/Department of Civil Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Rio de Janeiro, 21945-970, Brazil

    Webe João Mansur

  3. PPGEM/Department of Mechanical Engineering, Federal University of Espírito Santo, Vitória, Espírito Santo, 29075-910, Brazil

    Carlos Friedrich Loeffler

Authors
  1. Markcilei Lima Dan
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  2. Webe João Mansur
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  3. Carlos Friedrich Loeffler
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Correspondence to Markcilei Lima Dan.

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Technical Editor: Samuel da Silva.

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Dan, M.L., Mansur, W.J. & Loeffler, C.F. Double fictitious background media formulation for the Helmholtz equation in inhomogeneous media. J Braz. Soc. Mech. Sci. Eng. 44, 63 (2022). https://doi.org/10.1007/s40430-022-03365-6

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  • DOI: https://doi.org/10.1007/s40430-022-03365-6

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