Linear acoustics

Fabian82 · March 9, 2012, 06:45

Hi,
I'am performing some validation tests of a compressible hydrodynamics code against solutions obtained from linear acoustics. How strong may sound waves be in terms of relative pressure fluctuations in order that the linear acoustic approximation is valid? At the moment, I need relative pressure fluctuations smaller than 1e-3 in order to have deviations from the analytical solution which are smaller than 1% (the simulations are converged in terms of grid resolution and the size of the time step). Can anyone confirm such a behaviour?

Thank you very much for your help.
Fabian

FMDenaro · March 9, 2012, 11:47

The classic theory states that the linearization is valid for |p'|/p0| <<1, |rho'|/|rho0|<<1 for omo-entropic flows with constant speed of sound a0.
In my opinion, practical applications require less than 1% ...

March 9, 2012, 06:45	Linear acoustics	#1
Fabian82 New Member Join Date: Mar 2012 Posts: 8 Rep Power: 14	Hi, I'am performing some validation tests of a compressible hydrodynamics code against solutions obtained from linear acoustics. How strong may sound waves be in terms of relative pressure fluctuations in order that the linear acoustic approximation is valid? At the moment, I need relative pressure fluctuations smaller than 1e-3 in order to have deviations from the analytical solution which are smaller than 1% (the simulations are converged in terms of grid resolution and the size of the time step). Can anyone confirm such a behaviour? Thank you very much for your help. Fabian

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March 9, 2012, 11:47		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	The classic theory states that the linearization is valid for \|p'\|/p0\| <<1, \|rho'\|/\|rho0\|<<1 for omo-entropic flows with constant speed of sound a0. In my opinion, practical applications require less than 1% ...