|February 19, 2011, 17:56||
Transform N-S equations.
Join Date: Feb 2011
Posts: 14Rep Power: 6
Is there anyone know how to transform the N-S equation, which is steady in (x,y) coordinates to time dependent in (Epsliong, Etta) coordinates.
Maybe that is a transform from Euler to Lagrange. But I do not know how.
Any idea will be greatly appreciated. I thought about it for quite a long time.
|February 21, 2011, 10:50||
Join Date: Jan 2011
Location: London, U.K.
Posts: 63Rep Power: 7
The basic idea is simply coordinate transformation (or, should I say, chain rule). If you have never done it before, it's very tricky to get every term right.
Most textbooks give you results on orthogonal curvilinear coordinates, which should be enough if your coordinate system is orthogonal. Otherwise, you'll need a more general result, you may need to derive them by hand, a good starting point is the wikipedia link on curvilinear coordinates.
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