Using compressible CFD methods such as the lattice Boltzmann method, it is easy to set up initial conditions that result in sound waves.
One example is a Gaussian density distribution in an otherwise quiescent fluid, which results in an outgoing sound pulse. Another example is Poiseuille flow initialisation of the flow field in a simple 2D channel with an obstacle; sound waves will propagate until the flow is stabilised.
My intuition suggests that if Ma
It is indeed possible and often assumed to decompose the flow field into an incompressible field and an acoustic one. The necessary condition is Ma
I give some references here:
Article Hybrid aeroacoustic computation of a low Mach number non-iso...
Thanks for the reply. I'm familiar with hybrid aeroacoustics methods where incompressible flow simulations are coupled to acoustics simulations. That's not quite what I mean, though. Rather, what I'm thinking of is this issue: Given a flow field ρ(x,t), u(x,t), p(x,t), can we directly separate this field into an incompressible flow part ρi, ui, pi and an acoustic part ρa, ua, pa? Are there any references to this particular issue in your article?
What you are looking for is the holy graal of all aeroacoustics! One simple way could be to remove the temporal average for steady DNS simulations and there will remain "mostly" only acoustics. Problem is that it is not only acoustics! Maybe then remove the Favre average could be useful. I hope this answers your question.
One trick could be to use the result of a compressible simulation as initial condition for an incompressible solver on some iterations. Then deduce from the difference the acoustic part.
Have a look at Silva, Nicoud, Moreau AIAA "Extracting the Acoustic Pressure Field from Large Eddy Simulation of Confined reactive flows"
Also De Roeck etal ISMA 2006, "On the Use of Filtering Techniques For Hybrid Methods in Computational Aeroacoustics"
(be careful of the BC)
Last very fundamental article: Chu & Kovasznay JFM 1958, "Non-linear interactions in a viscous heat-conducting compressible gas"
There is no single answer to this question for various reasons. One of them is that if you make the pertaining equations (Euler, say) dimensionless, you will find three relevant dimensionless numbers: Mach M, Helmholtz H and Strouhal S. Since M = H/S, the results for M -> 0 depend on the way H and S are kept relative to each other.
You may use an orthogonal decomposition of your pressure field into its mean value plus its fluctuation around the mean value, and the orthogonal Helmholtz decomposition of your velocity field into a divergence free component and a curl free component. Then the incompressible component will be the mean value (and thus constant) pressure and the divergence free velocity. And the acoustic part will be the fluctuation of the pressure and the curl free component of the velocity. This is a 'continuous' (non discretized) point of view. The discretized equivalent of this point of view depends on your numerical scheme. I don't know enough about lbm to help you on that, but we have looked at that topic in the context of finite volumes. If you are interested take a look at the publication I co-authored with S. Dellacherie and F. Rieper in the JCP in 2010. Best regards. Pascal
The defining characteristic of incompressible flows is div V = 0. In general incompressible flows will have ∇2p ≠ 0, but no sound waves. The value of ∇2p is determined by the requirement that the velocity remain solenoidal.
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