A numerical method of solving the problem of acoustic wave radiation in the presence of a rigid scatterer is described. It combines the finite element method and the boundary algebraic equation one. In the proposed method, the exterior domain around the scatterer is discretized, so that there appear an infinite domain with regular discretization and a relatively small layer with irregular mesh. For the infinite regular mesh, the boundary algebraic equation method is used with spurious resonance suppression according to Burton and Miller. In the thin layer with irregular mesh, the finite element method is used. The proposed method is characterized by simple implementation, fair accuracy, and absence of spurious resonances.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
B. A. Voinov, Akust. Zh. 40, 935 (1994).
I. P. Getman and N. V. Kurbatova, Akust. Zh. 40, 581 (1994).
C. Saltzer, Discrete Potential Theory for Two-Dimensional Laplace and Poisson Difference Equations, Technical Report No. 4086 (National Advisory Committee on Aeronautics, 1958).
V. S. Ryaben’kii, Math. Nachr. 177, 251 (1996).
P.-G. Martinsson and G. J. Rodin, Proc. R. Soc. A 465, 2489 (2009).
S. V. Tsynkov, J. Sci. Comput. 18, 155 (2003).
J. Poblet-Puig and A. V. Shanin, J. Integr. Equations Appl. 27, 233 (2016).
A. J. Burton and G. F. Miller, Proc. R. Soc. London, Ser. A 323, 201 (1971).
S. Katsura and S. Inawashi, J. Math. Phys. 12, 1622 (1971).
P. A. Martin, Wave Motion 43, 619 (2006).
O. C. Zienkiewicz, The Finite Element Method in Engineering Science, 2nd ed. (McGraw-Hill, London, New York, 1971).
Original Russian Text © J. Poblet-Puig, A.V. Shanin, 2018, published in Akusticheskii Zhurnal, 2018, Vol. 64, No. 2, pp. 257–265.
The paper is based on the talk given at the Fourth International Symposium and the Sixth All-Russia Conference “Computational Experiment in Aeroacoustics” held on September 19–24, 2016, in Svetlogorsk, Kaliningrad region, http://ceaa-w.imamod.ru.
About this article
Cite this article
Poblet-Puig, J., Shanin, A.V. A New Numerical Method for Solving the Acoustic Radiation Problem. Acoust. Phys. 64, 252–259 (2018). https://doi.org/10.1134/S1063771018020148
- finite element method
- boundary element method
- boundary algebraic equations
- discrete Green’s function