Geodesic
Calculation of sound fields in turbofan engine intakes based on azimuthal fourier decomposition
Matematičeskoe modelirovanie, Tome 19 (2007) no. 8, pp. 113-122.

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In paper the approach applicable for calculation of acoustic fields in axisymmetrical channels of the complex form based on the numerical solution of linearized Euler's equations is considered. The initial 3D system of the equations with use of Fourier-transformation of sound perturbation in azimuthal direction is reduced to sequence of 2D systems for a set of the most significant azimuthal acoustic modes. Such approach is especially actual at research of tonal noise of the turbofan when the amount of researched modes is not many. For solution of the obtained 2D systems the explicit numerical method based on DRP-approximation of 4-th order on space and optimized Runge–Kutta schema of 4-th order for approximation on time is used. The numerical method uses the structured curvilinear grids adapted to geometry of the channel. The technics of buffer zones (Sponge Layers) is applied to input/output of waves in/from calculation area. Verification of a code carried out on problems on distribution of sound modes in cylindrical and annular channels having the analytical solution. 
@article{MM_2007_19_8_a13,
     author = {M. V. Usanin},
     title = {Calculation of sound fields in turbofan engine intakes based on azimuthal fourier decomposition},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {113--122},
     publisher = {mathdoc},
     volume = {19},
     number = {8},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_8_a13/}
}
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M. V. Usanin. Calculation of sound fields in turbofan engine intakes based on azimuthal fourier decomposition. Matematičeskoe modelirovanie, Tome 19 (2007) no. 8, pp. 113-122. http://geodesic.mathdoc.fr/item/MM_2007_19_8_a13/

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