# why some solvers use non-dimentionalized form of navier-stokes equations?

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 May 20, 2022, 06:37 why some solvers use non-dimentionalized form of navier-stokes equations? #1 Senior Member   Sayan Bhattacharjee Join Date: Mar 2020 Posts: 385 Rep Power: 5 NASA's CFL3D and FUN3D solvers seems to non-dimensionalize the governing equations. I could not find or understand the reason behind such a decision. Can anyone please explain why they did it, and was there any benefit or side-effect from doing it?

 May 20, 2022, 08:12 #2 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 4,850 Rep Power: 57 1) Governing equations are never truly non-dimensionalized at the linear solver level. You have a coefficient matrix that needs solving and that's it. What's different is the user-interface: the user must provide a mesh (dimensional or non-dimensional) and then make sure that all the boundary conditions and settings (all user inputs) are in units consistent with the mesh provided. 2) NASA and many other US/English-companies engineer using English units. We're talking about inches-feet-miles, pounds, slugs, Farenheit, inches of water, psi, and so on. It is deeply ingrained in these work cultures to have conversion factors everywhere in all their equations and for them, it's really no big deal whether a particular software is dimensional or non-dimensional because they always go through the same process of converting units in and out of English units anyway. It's not any better one way or another. sbaffini and aerosayan like this.

 May 20, 2022, 11:24 #3 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,062 Rep Power: 64 There is a fundamental theoretical reason to work in non-dimensional form. If you choose correctly the characteristic scales of the problem you have that the variables will be O(1). This way is quite practical to check for correct results. aerosayan likes this.

May 20, 2022, 11:30
#4
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Sayan Bhattacharjee
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Quote:
 Originally Posted by FMDenaro If you choose correctly the characteristic scales of the problem you have that the variables will be O(1). This way is quite practical to check for correct results.

Thanks for your answer. English isn't my first language so I couldn't understand this part. Do you mean that the solution values come out in range [0.0, 1.0] , (like Cl and Cd for lift and drag), so it becomes easy for us to check if our results are correct without too much hassle?

May 20, 2022, 14:41
#5
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Filippo Maria Denaro
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Quote:
 Originally Posted by aerosayan Thanks for your answer. English isn't my first language so I couldn't understand this part. Do you mean that the solution values come out in range [0.0, 1.0] , (like Cl and Cd for lift and drag), so it becomes easy for us to check if our results are correct without too much hassle?

Well, it could be also 3, 5.1, 6 ... the term O(1) means that. The key is to have the correct knowledge of the problem and to choice the proper reference values.

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