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On the use of Gegenbauer reconstructions for shock wave propagation modeling
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10.1121/1.3621485
/content/asa/journal/jasa/130/3/10.1121/1.3621485
http://aip.metastore.ingenta.com/content/asa/journal/jasa/130/3/10.1121/1.3621485
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Profiles of shock waves produced from an initial sinusoidal wave at a distance σ 1 = 5.2. (a) Numerical simulations before and after the Gegenbauer reconstructions, as well as the first order derivative. (b) Numerical simulations before and after the Gegenbauer reconstructions, as well as the analytic solution. (c) Frequency spectrums before and after the amplification. (d) Numerical simulations before and after the Gegenbauer reconstructions. The frequency spectrums after the amplification were used.

Image of FIG. 2.
FIG. 2.

(a) Profiles of shock waves produced from an N wave. Two results are presented at a distance of z = 20 mm, one before the Gegenbauer reconstructions, one after. The first order gradient is shown to indicate approximately where the edge is. (b) Simulation results after the Gegenbauer reconstructions are compared with the analytic solution at various distances 20, 40, 60, and 80 mm, where the longer the distance, the lower the peak pressure.

Image of FIG. 3.
FIG. 3.

(a) Portions of the profile of a shock wave produced from a Gaussian-modulated sinusoidal wave. Two results are presented at a distance of 7.9σ, one before the Gegenbauer reconstructions, one after. The first order gradient is also shown. Simulation results after the Gegenbauer reconstructions are compared with the benchmark solution at distances of (b) 7.9σ, (c) 6.5σ, and (d) 5.2σ.

Image of FIG. 4.
FIG. 4.

(Color online) Frequency spectrums for the Fay solution to the one-dimensional continuous problem discussed in Sec. III A 2. Three results are shown, one with 16 harmonics, one with 32 harmonics, and one with 160 harmonics. Only the results up to the 32th harmonics are presented.

Image of FIG. 5.
FIG. 5.

Profile of a shock wave produced from a focused circular transducer. Simulation results before and after Gegenbauer reconstructions with 50 harmonics are compared with the result before the Gegenbauer reconstructions with 250 harmonics at a distance of 15 mm on the axis. The 50 harmonics results after Gegenbauer reconstructions are resampled to include in total 250 harmonics. (a) Depicts a full cycle. (b) Depicts the shock fronts. Corresponding spectral results. (c) Spectrums for the first 250 harmonics. (d) Spectrums for the first 60 harmonics.

Image of FIG. 6.
FIG. 6.

Profile of two shock waves produced from an unfocused circular transducer. Simulation results before and after Gegenbauer reconstructions with 100 harmonics are compared with result before the Gegenbauer reconstructions with 450 harmonics at a distance of 255 mm on the axis. The 100 harmonics results after Gegenbauer reconstructions are resampled to include in total 500 harmonics. (a) Depicts a full cycle. (b) Depicts the shock fronts. Corresponding spectral results. (c) Spectrums for the first 500 harmonics. (d) Spectrums for the first 120 harmonics.

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/content/asa/journal/jasa/130/3/10.1121/1.3621485
2011-09-02
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the use of Gegenbauer reconstructions for shock wave propagation modeling
http://aip.metastore.ingenta.com/content/asa/journal/jasa/130/3/10.1121/1.3621485
10.1121/1.3621485
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