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Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/CE246EDE-494C-4EEC-AACD-F2C861FC874C | ||
| Year | 2013 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | N. A. Kampanis, A. I. Delis, D. C. Antonopoulou and G. Kozyrakis, "A finite element discretization of the standard parabolic equation in generalized boundary fitting coordinates," Appl. Num. Math., vol. 67, pp. 152-166, May 2013. doi:10.1016/j.apnum.2011.05.005 https://doi.org/10.1016/j.apnum.2011.05.005 | ||
| Appears in Collections |
A simplified, but quantitatively reliable approximation of atmospheric sound propagation is given by the standard parabolic equation. The waveguide is a cylindrically symmetric, unbounded, domain with an irregular lower boundary. The associated initial-boundary value problem uses a mixed-type boundary condition along the lower boundary and a nonlocal, absorbing boundary condition of the DtN (or NtD) type, applied on an artificial upper boundary. Exterior wave fields of a constant index of refraction and a linear, when squared (as function of height) one, are considered. The physical, complex waveguide reduces to an orthogonal computational domain by the means of a numerical transformation to generalized coordinates, fitting the lower, irregular boundary. The technique presented is of practical interest for its proper handling of complex ground topographies; it is interfaced with a mesh generator and processes the topographic data retrieved from a geographic information system, hence the transformation of coordinates is computed numerically. The transformed initial-boundary value problem (on the orthogonal computational domain) is discretized by the Crank–Nicolson in time and a continuous, piecewise linear finite element method in space. The propagation of cylindrically symmetric sound waves over a complex terrain, emitted to the atmosphere by a harmonic source, has been studied. The effectiveness of the numerical method introduced, is exploited on several test cases.
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