Tensor Eigensystem

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Tensor Eigensystem

Postby Aeronautics » Thu Mar 08, 2012 2:44 pm

In the Tensor tools I am supposed to enter the Symmetric Matrix Components. There are places for entry but I could not find any information on which component goes where. I would appreciate it if someone has an answer to this. Please keep in mind that the eigenvalues produced will be different for different entries. I speculated that the entries are as follows:
Left: A33
Center top: A22
Center bottom: A23
Left top: A11
Left middle: A12
Left bottom:A13
Is this right?

Thanks

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salter
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Re: Tensor Eigensystem

Postby salter » Fri Mar 09, 2012 6:12 am

It seems you are attempting to show the following:

Code: Select all

--           --
| A11 A12 A13 |
| A21 A22 A23 |
| A31 A32 A33 |
--           --


The question is what do you want to do with this? You can set this up to be a zone of 3x3 in X and Y, but I'm unsure of what you are attempting to do with this or apply this in Tecplot.
Steve...

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Aerothermodynamics Branch
NASA Langley Research Center

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Re: Tensor Eigensystem

Postby Aeronautics » Fri Mar 09, 2012 7:26 am

Thank you for replying.
I am trying to show eigenvalues where I use them to identify vortices. If you view the "Tensor Tool", you will see the components entries I am talking about.

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salter
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Re: Tensor Eigensystem

Postby salter » Mon Mar 12, 2012 4:44 am

Again, a tensor is a 3x3 matrix. In this case, the matrix has to be symmetric so that A12=A21, A23=A32, and A13=A31. In the addon, you need to be performing Tensor analysis. The example in the manual shows how to do this for vortex core visualization. It is not a simple analysis, so the addon helps perform the variety of computations for you. Another example would be to find the eigenvalues of a successive over relaxation (SOR) method to determine the stiffness of the solution matrix. However, if you are using upwinding to solve a non-linear, non-homogenous partial differential equation (PDE), the matrix is not symmetric. Omitting the upwinding would give you a symmetric matrix you could solve for the eigenvalues. Then using the ratio of the maximum to minimum eigenvalue for a system of equations, you could determine the stiffness of the system. But you'll have to do the derivation of the system you are using and place the components by variable names into the addon to do the computation. For a standard second order accurate computation of discretized PDEs, you will get a 3x3 matrix of components for 2D planes in the solution; i+1, i-1, j+1, j-1, and i,j. For 3D there are 3 matricies IxJ, JxK, and KxI. Filling out the matrix for each 2D plane of data will give you the information you need for a tensor.

Have fun.
Steve...



Aerospace Research Engineer

Aerothermodynamics Branch

NASA Langley Research Center


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