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student_58 May 22, 2009 16:59

Elliptic Grid Generation
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I need your help to solve my problem. My problem is grid generation.I have a geometry.İt isn`t rectangular. I attach image. Attachment 336

İn the geometry, There is a radius. I have to use elliptical grid generation method to solve problem.Firstly, I convert physical domain to computational domain. How can ı make this? I wait your help......

jchawner May 23, 2009 11:12

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Hello student_58.

It's not clear exactly what kind of help you're seeking (but not knowing the question never stopped me from offering an answer).

Since you're interested in elliptic grid generation, I'll assume your grid is structured quads (also known as a mapped mesh). So the first issue is one of topology; how will you map the region in the image to a rectangle.

I propose that the easiest way to do this is to locate the 4 corners of the computational domain as follows.
1. upper left corner
2. upper right corner
3. lower right corner
4. top of the quarter circle on the left
See the topology in the attached picture.

Assuming you can create the geometry of the bounding edges, the next step is to distribute grid points along the edges. In the attached picture the points are simply equally spaced. Of course, you have to use the same number of points on the top and bottom edges and the left and right edges.

Before applying the elliptic PDE technique you have to first initialize the points on the interior of the domain. While I suppose you could just initialize them all to (0,0) a better approach would be to apply a transfinite interpolation (TFI) method. TFI methods are well documented in most every CFD text that discusses grid generation.

With the interior mesh points initialized, you then iteratively apply the elliptic PDE method to move the points to improve smoothness, clustering, orthogonality, or any other geometric property of the grid. I assume that your professor has described how the elliptic PDE method works so I won't go into that here.

Hope this helps.

student_58 May 23, 2009 12:36

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Thanks for your interest,Jchawner.
I read your answer and ı see your grid.But it isn`t right answer.Because ı want to convert phsyical domain to computational domain.For this, ı use numerical methods and elliptic grid generator method.You probably make this grid at a packet program(gambit,gridgen or otherwise).But ı have to make a program for this, using MATLAB. My computational domain has to be rectangular.I attach domain image which ı want to make.Attachment 339

jchawner May 23, 2009 13:14

I guess that I really don't understand your question. I don't know anything about MATLAB so I can't help you with that.

You write that your computational domain "has to be rectangular". The computational domain for the grid in the picture I attached is rectangular. Generating a computational domain is trivial. You could create the computational domain in Microsoft Word by simply typing in the coordinates.

What exactly is the problem?

harishg May 24, 2009 03:17

You are confusing two things. The way you do it is generate the grid using elliptic grid generator and then solve the Navier-Stokes equations in curvilinear coordinates. So even though you have a curvy grid, your solution is performed in a rectangular coordinate. Check the grid generation book of Thompson available online to understand how it should be done.

When you post on a forum, ensure that you had already searched using google and do not just post a question and expect someone else to solve it fuly for you.

student_58 May 24, 2009 06:53

Sure that, ı search a lot for this,harishg.
My question is about radius area.My physical cordinate are x,y.Comptutational cordinate ksi,eta.Radius area prevent me to solve the problem.
I haven`t any transforming equation, like ksi=x or eta=x/y^2.
How do ı convert x,y cordinate to ksi and eta?
Your grid cell are rectangular.But ı want to move my geometry to a rectangular domain.Radius area will be a rectangular.Then ı will solve the problem with mapped mesh.

harishg May 24, 2009 12:25

You generate an elliptic grid using some elliptic grid generation method. You can assume deta, dpsi = 1 respectively. With the values of x and y known, you calculate

dphi/dx = - J dx/dsi ... , you have four such formulae. Check some grid generation or CFD book.

Then say your equation is

df/dt + df/dx =0

You transform it to

df/dt + df/dphi*dphi/dx + df/dsi*dsi/dx =0 , and since u know the grid changes, you calculate df/dphi in the rectangular grid and proceed with your computation. Take a look at any CFD book and you would have the whole procedure explained clearly.

jchawner May 24, 2009 14:57

Hello Again student_58.

Perhaps the best help I can offer is a link to Thompson's classic book on grid generration.

makinay June 9, 2010 02:31

hi student_58 my problem is same,

if you solve your problem could you help me

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