how many BC's should be assigned physically in navier stokes runs?
how many BC's on inlet and outlet have to be assigned in navier stokes equations?and what are they?
There is a table for euler and navier stokes but isn't clear enough for inlet and outlet. 
It can be as few as none with the pressurefree modifiedHermite finite element method.

I'm not familiar with this method dear Jonas.I want to know about ordinary cases with navierstokes equations.
I know we need p,T and direction of U for inlet and only p for outlet.is it true? then whats the difference between navierstokes and Euler equations? 
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see http://adsabs.harvard.edu/abs/1992JCoPh.101..104P 
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In principle, one could form exactly divfree functions from non divfree functions by subtracting off the gradient of an irrotational function. The problem is that one cannot do this with a FE and still preserve the element BCs. So it is common to satisfy the divfree condition only weakly. Here it gets complicated with infsup conditions and such. This function to be subtracted out satisfies an equation just like the pressure equation, but with different boundary conditions. But here it gets confusing because people use the symbol p to represent this projection function, and worse yet, they call it the pressure. And, they apply physical arguments about the pressure to this function. So you are really asking about conditions on this projection function. I don't know if a firm mathematical answer exists. The practical answers are based on lore and are part of the mystique of CFD. Including a coupled energy equation does not change the argument above, nor does inclusion of magnetic effects with conducting fluids. And there are some interesting possibilities using a fully FE method with moving domains. While this applies to the Euler equation, that subject is treated differently because of an additional simplification. 
thanks Jonas for this fundamental argument you did.when you speak about FE do you use it in contradiction of finite volume method(FV)?

My interest is in FEM for incompressible flow by the method described using modified Hermite finite elements. I have also applied the method to magnetohydrodynamics and am presently extending the work to moving fluid domains. I have placed a couple of educational codes using the method on the CFD Wiki.

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These features are very important especially for outlet boundaries treatment where non reflective BC is repquired especially for Euler equations. 
I have some problem with my boundary condition that how i utilize the neumann condition(∂φ/∂x = 0) at outlet. Can i select pressure outlet at outlet?
my inlet condition is : flat velocity profile =40m/s Re=1.916*10^5 turbulent intensity=4.5% And Inlet height of duct=5mm I select velocity inlet at inlet because my flow is incompresible. And axis boundary condition applied along the centerline. and no slip condition at wall. pls help me. 
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I have to say one thing,NavierStokes in steadystate mode is elliptic but in unsteady form,is parabolic.and why you say its necessarily 2nd order in space?we can descritize space in 1st order methods like upwind. and in related to Euler,I think it depends on Mach number,if Mach<.7 its elliptic,if M>1.4 its hyperbolic and in .7<M<1.4 its a combination of elliptic and hyperbolic. 
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Note also that the timedependent Euler equations are always hyperbolics, whatever the Mach numeber is, since the characteristic lines (or surface) are always real. 
Hi immortality!
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Hi Immortality
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NS equation is second order derivative for the diffusive term: div(mu (grad(u) + grad(u) T) ) term with d²u/dx², d²u/dy² etc... Quote:
I agree with Filippo 
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