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Navier-Stokes-Equations in curvilinear coordinates

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Old   February 25, 2013, 12:22
Default Navier-Stokes-Equations in curvilinear coordinates
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I am trying to set up a CFD code for the analysis of the boundary layer around a blunt body. I want to couple an external flow from potential theory with a finite difference grid representing the boundary layer. The idea was to use curvilinear coordinates as it might be the most accurate solution for my type of flow. I don't want to go into detail concerning turbulence model etc.
But in the boundary layer bible "Boundary Layer Theory" from Schlichting, Hermann (1979) you can find representations of the Navier-Stokes-equations already including the metrics of coordinate transformations. I have attached a picture of the equations in there.

Now here is my question: How can I derive these equations from the NSEs in cartesian coordinates. I tried to figure it out myself, but without any success. I was wondering if there are assumptions or simplifications that enable the attached version of the NSE. This could be crucial for my project! Does anybody have any idea what's the trick behind or where I can find a clarifying derivation? Schlichtings book has a reference on Tollmien, W.: Grenzsschichttheorie. Handbuch der Experimentalphysik, Vol. IV, Part 1, 241-287 (1931). I couldn't find this document.

Can anybody help me out?
Thanks in advance!
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File Type: jpg Navier-Stokes-Curvilinear.jpg (67.3 KB, 26 views)
File Type: jpg CurvLinCoord.jpg (8.5 KB, 14 views)
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boundary layer, curvilinear coordinate, navier stokes equations

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