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Does N.S. represent reality ?

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Old   September 28, 2011, 14:15
Default Does N.S. represent reality ?
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robert michel
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Hi fluid world ,
I am a mechanical engineer (solid side ), and i am wondering about the Navier-Stocks eqts description of the fluid phenomena; my questions are:

- Does N.S. include the turbulence phenomena , at all levels?

- Or, if the humanity, in the next century , build a very very performant computer , can N.S. , alone, predict the fluid physics?

Thanks
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Old   September 28, 2011, 14:20
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Sijal Ahmed Memon (turboenginner@gmail.com)
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yes 1000%, if you can solve the NS
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Old   September 28, 2011, 14:28
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yes 1000%, if you can solve the NS
thanks for the mach 1000 answer , but can you give us some explanations or illustrations. are there any experiences in this field (comuting reality)
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Old   September 28, 2011, 20:11
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Does NS include turbulence - yes, the study of this is called DNS (Direct numerical simulation). But most engineers use the Reynolds Averaged NS eqns and a turbulence model as it is mush easier to apply and does not require super computers.

can N.S. , alone, predict the fluid physics? - The NS equations describe fluid flow with pressure, shear stresses (and others) in a continuous fluid. As long as those assumptions are valid then the NS eqns are valid.

Examples - Does a A380 or a 787 fly? Why? Because lots of engineers did careful CFD simulations.
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Old   September 29, 2011, 04:00
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Yes, NS formulates momentum conservation for fluids. In terms of solid mechanics it is the equivalent of Newtons second law.

Turbulence is a little tricky, and I wouldnt say that we will be able to solve this given a large enough computer (this is a fundamental debate about predicting the future ).

Simply put, under certain parametric circumstances (captured in eg Reynolds number) the set of differential equations becomes ill-posed (in the definition of Hadamard):

- the solution still exists
- the solution is still unique

but

- a small perturbation in boundary conditions causes a very different solution

This instability means the solution of the set of equations at a given time t=t+dt will not fully be defined by the solution at t=t, as is the case in classical dynamics. This phenomenon is called deterministic chaos, and remains a very challenging subject in my humble opinion.

So, yes we can solve turbulent flow fields to the smallest eddy length scale through DNS but from what I understand of it, that will be one possible realisation and not the future.
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