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 Sibel January 31, 2005 19:47

curvilinear coordinates

Hi, my thesis statement requires 2D cartesian koordinates turn 2D curvilinear coordinates. So velocity u,v how to change?? Firstly I have get velocity u and v scaler value, but after?? In curvilinear coordinates how to change velocity??

 Runge_Kutta January 31, 2005 23:01

Re: curvilinear coordinates

Welcome to tensor analysis. Brace yourself. There are 3 essential components to vectors and tensors here:

1) Covariant components 2) Contravariant components 3) Physical components

If you use 1) or 2), your velocity components may not have the dimensions of L/T. Ultimately, your final output will need to make dimensional sense. If you are sticking to orthogonal coordinates, you might fare better by simply coding physical components.

Try looking at

http://www.amazon.com/exec/obidos/tg...glance&s=books

or

http://www.amazon.com/exec/obidos/tg...glance&s=books

Also, for a tour de force in this kind of stuff,

http://www.amazon.de/exec/obidos/ASIN/3528080787/qid%3D1107226722/028-8855481-7414120

Shear Flow in Surface-Oriented Coordinates

Ernst-Heinrich Hirschel, Wilhelm Kordulla

ISBN: 3528080787

Format: Paperback, 266pp

Pub. Date: January 1981

Publisher: Ballen Bkslr

 sibel February 1, 2005 03:41

Re: curvilinear coordinates

contravariant or covariant, which can I use contravariant , covariant? is this important for my problem? I cant understant this, so I cannot developed my code? Please explain me this. can you see a numerical examples? I cannot animated on my mind. if I understant this, I will start developed CFD code, but I cannot understant. Please give me some example..I will wait your answer. Every day I am studying until morning, but I am at the same pleace. I cannot develop even one step. please help me. You cannot think how much I want this and how much I need

 zxaar February 1, 2005 03:52

Re: curvilinear coordinates

read the book by peric , that will be better , an dtry to follow the codes he has on his site .. some of them are for curvilinear also .. (but might confuse you since most of them he uses multigrid acceleration ..so u might have to clear multigrids idea too )

 Runge_Kutta February 1, 2005 04:03

Re: curvilinear coordinates

There is no way anyone can just give you a wonderfully simple answer in the context of this forum. Rather than panicking, go to the library and grab several of the books that have been mentioned. Try to figure out what is going on. As you get smarter, come back to this forum and ask specific questions. The book by Warsi is very useful but you may need to get some help from some of your collegues.

My rule of thumb in asking for help is whether I have made a serious attempt to solve the problem myself. Once I have done that, I try to get a helping hand.

 sibel February 1, 2005 04:53

Re: curvilinear coordinates

Yes I understant you, but there is no people to my help. I must do something myself. My problem is very difficult. I get lesson Mr. Z.U.A Warsi from Missisipi State University, when he came to turkey. but he go back Newyork.

 sibel February 1, 2005 05:33

Re: curvilinear coordinates

Mr. Warsi is excellent, but he went. Do yuo know some links about basic code ( include curvilinerar coordinates) Thanks for your suggestions.

 BradAeroHead February 1, 2005 23:11

Re: curvilinear coordinates

Sibel,

My dissertation (on DNS of complex curved channel flows) contains a chapter in which the incompressible 3-D Navier-Stokes equations are expanded into general curvlinear coordinates, using covariant and contravariant components as described above. It includes several examples like a cylindrical channel and a channel with bumps, expressed in these coordinates. I'd be happy to send it to you by email if you like.

My suggestion mirrors those above--you will need to spend some time doing the derivations yourself to get comfortable with this. One key to understanding the concept is the "repeating index" notation, meaning that when you have repeating indices in a product, you must expand the product, like u_i u_i = u_1 u_1 + u_2 u_2 + u_3 u_3, etc.

 sibel February 2, 2005 03:38

Re: curvilinear coordinates

Hi brad thanks your suggestion, you can sent your document to skarabulut@be.itu.edu.tr. My derivative is finished on paper, but I must apply to my source code.

I dont understant repeating indices completly. What do you want to say?

 windwave August 21, 2014 22:47

Hi Brad,
i'd be happy to take a look at your dissertation, if you are willing to email to me as well. I'm trying to write NS equations in orthogonal curvilinear coordinates, above waves.
thanks!
Marc

Quote:
 Originally Posted by BradAeroHead ;32646 Sibel, My dissertation (on DNS of complex curved channel flows) contains a chapter in which the incompressible 3-D Navier-Stokes equations are expanded into general curvlinear coordinates, using covariant and contravariant components as described above. It includes several examples like a cylindrical channel and a channel with bumps, expressed in these coordinates. I'd be happy to send it to you by email if you like. My suggestion mirrors those above--you will need to spend some time doing the derivations yourself to get comfortable with this. One key to understanding the concept is the "repeating index" notation, meaning that when you have repeating indices in a product, you must expand the product, like u_i u_i = u_1 u_1 + u_2 u_2 + u_3 u_3, etc.

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