Does N.S. represent reality ?
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 :rolleyes: ;)
yes 1000%, if you can solve the NS
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.
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
- 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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