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