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Euler equations vs NS equations

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Old   June 10, 2018, 04:57
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Originally Posted by FMDenaro View Post
Euler approximation is a mathematical model...the solutions you get can or cannot be an acceptable approximation of the physics, depending on what you want to describe.
The singularity is mathematic, shock Waves are not a discontinuiy in a small scale
hm, Now I get it. I guess it would be ridiculous to use Euler to simulate turbulence.
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Old   June 10, 2018, 06:04
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hm, Now I get it. I guess it would be ridiculous to use Euler to simulate turbulence.



This is an example of turbulence problem studied assuming no physical viscosity
https://www.researchgate.net/profile...kman-layer.pdf
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Old   June 10, 2018, 06:07
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Correct me if I am wrong: so you mean, with high-speed flow, the physical drag force will be small, and so lacking of viscous terms (not artificial viscosity) will not cause too much of problem for Euler equations; instead, pressure drag is important, and Euler can compute it well. Am I right?
Viscous drag can be split in friction drag, directly due to \mu \frac{\partial u}{\partial n} at the wall, and pressure drag, due to the fact that the viscous losses will eventually subtract energy from the flow (not only at walls). As a consequence, pressure cannot recover at the rear stagnation point and you get a drag due to the pressure difference.

Viscous drag needs a form of viscosity to be present, either real or numerical.

In a direct Euler computation it is typically present in the form of numerical viscosity due to the numerical convective scheme. Thus, by nature, it cannot be actually accurate.

But, imagine an aircraft at high speed with attached flow (low angle of attack). The numerical viscosity, in this case, will help you get lift and its induced drag, which is a form of pressure drag. If you know the lift-drag plot, you should know that the lift induced drag can be much higher than the base friction drag.

The same, of course, won't work on a sphere or a cube.

But, the idea of using Euler equations, is not much in getting an estimate of the drag, but in computing flows that, due to such feature, can return reliable evaluation of other quantities, like the lift, knowing that the neglected and/or miscomputed drag is not playing a dominant role in your computation.

In a word... engineering.
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Old   June 10, 2018, 06:11
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Originally Posted by TurbJet View Post
hm. So you are talking about extremely high-speed flow. I was thinking about in the regime of regular supersonic flight.
In the base Euler/NS equations with an ideal gas law (remember that we are talking about the equations, not the real flow), there is no such distinction between supersonic or hypersonic. So, what I wrote just applies to any supersonic flow with such model equations.
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