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Sommerfeld radiation condition in COMSOL

Posted Mar 28, 2018, 10:55 p.m. EDT Acoustics & Vibrations Version 5.3 1 Reply

Minsik Seo
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Hi, I've been trying to compare approximated Sommerfeld radiation condition and perfectly matched layer in COMSOL with "Pressure Acoustics, Frequency Domain" Physics. So I implemented Sommerfeld radiation condition by using "Impedance" node.

I know the Sommerfeld radiation condition has the form of

And it can be approximated as

on

Since the equation for "Impedance" node in Pressure Acoustics physics is like,

Therefore, letting I can implement the "Sommerfeld radiation condition"

In the result, however, the radiation condition is applied when the sign of the impedance is opposite. That is, .

Why this happened? Is the Sommerfeld radiation condition defined differently in COMSOL?

1 Reply Last Post Mar 29, 2018, 4:52 a.m. EDT
Elin Svensson COMSOL Employee

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Posted: 7 years ago Mar 29, 2018, 4:52 a.m. EDT

Hi,

The Sommerfeld radiation condition depends on the definition of the Fourier transform which determines how a time-harmonic wave varies with time. COMSOL uses . Then you need replace with in the first equation. See, for example, Wikipedia, where this is discussed.

Kind regards, Elin

Hi, The Sommerfeld radiation condition depends on the definition of the Fourier transform which determines how a time-harmonic wave varies with time. COMSOL uses p(\mathbf{x}, t) = p(\mathbf{x})e^{i\omega t}. Then you need replace -i with +i in the first equation. See, for example, [Wikipedia](https://en.wikipedia.org/wiki/Sommerfeld_radiation_condition), where this is discussed. Kind regards, Elin

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