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September 28, 2011, 14:15 |
Does N.S. represent reality ?
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#1 |
New Member
robert michel
Join Date: Sep 2011
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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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September 28, 2011, 14:28 |
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#3 |
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robert michel
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September 28, 2011, 20:11 |
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#4 |
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Glenn Horrocks
Join Date: Mar 2009
Location: Sydney, Australia
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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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September 29, 2011, 04:00 |
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#5 |
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Join Date: Dec 2009
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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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