[AndreaCFD]

Dear group members,

I would like to retrieve the matrix of coefficients of the linearized Navier-Stokes equations and possibly compute its eigenvectors and eigenvalues directly in OpenFOAM-v1912. Is it possible? Which are the input files/commands?

My application is a 2D-flow past a circular cylinder @ Re=100.

Thanks in advance.

AndreaCFD

[Bloerb]

If I unterstand your question correctly you want to do DMD.


You might want to take a look at the dynamic mode decomposition function object in OF-v2006:

https://www.openfoam.com/releases/op...processing.php

[AndreaCFD]

Thanks for answering Bloerb,

Actually I only want to calculate the eigenvalues/eigenvectors of the matrix of coefficients of the discretized Navier-Stokes. So I need a function that gets the matrix UEqn and computes the eigendecomposition. I will use them to reduce the dimensionality of the system similarly to DMD but with a different technique.

Best,

Andrea

[HPE]

there is also a new dense-matrix eigen decomposition solver in v2006: EigenMatrix.

[AndreaCFD]

Thanks for answering HPE,

Could you give me some further info on how to use it? Do I have to download the .C and .H files and recompile my OpenFoam? Which is the right folder to save them?

In case I have a matrix A, its eigenvecors are computed with the commands:
eigenvectors(A.EVecs()) and complexEigenvectors(A.complexEVecs())

Sorry for the stupid questions but I am a bit lost.

Best,

Andrea

[HPE]

No question is stupid!

Please search Test-EigenMatrix.C or EigenMatrix.H files for usage examples. They are extensive.

You dont need to download anything unless you compile/install OFv2006.

Im writing on my phone, if you cant find those files, let us know.

[AndreaCFD]

Originally Posted by HPE

No question is stupid!

Please search Test-EigenMatrix.C or EigenMatrix.H files for usage examples. They are extensive.

You dont need to download anything unless you compile/install OFv2006.

Im writing on my phone, if you cant find those files, let us know.

Dear HPE,

I installed the new version of OFv2006 and checked the references.

What I have understood is that EigenMatrix.C performs the eigendecomposition of a matrix of type SquareMatrix. The matrix of coefficients UEqn (the one I need to decompose) is of type fvmVectorMatrix, hence the compiler produces an error.

Is there a way to convert one type to the other? Namely reconstruct the sparse matrix from the dense one? Are there functions that directly perform the eigendecomposition on the dense matrix?

Thanks for answering,

Andrea

[HPE]

Hi,

The type of UEqn is not any sort of matrix, but a system of algebraic system. Therefore, there is no eigen decomposition for it.

EigenMatrix works on only SquareMatrix type, which can be sparse or dense.

[dlahaye]

Possibly this helps:

1/ Use ofgdb to print matrix to file. See https://openfoamwiki.net/images/1/18/GdbOF-Manual.pdf

2/ Read file into Matlab, Python, Julia, Octave, Scilab or what have you;

3/ Convert matrix from sparse to dense and use eigenvalue computations provided for dense matrices;

Above might work small meshes. For large meshes instead, you might want to revert to the interface to PETSc and use the SLEPc components of PETSc to compute eigenvalues.

OpenFoam-PETSc interface: https://develop.openfoam.com/modules/external-solver

[mufeng]

Originally Posted by AndreaCFD

Dear group members,

I would like to retrieve the matrix of coefficients of the linearized Navier-Stokes equations and possibly compute its eigenvectors and eigenvalues directly in OpenFOAM-v1912. Is it possible? Which are the input files/commands?

My application is a 2D-flow past a circular cylinder @ Re=100.

Thanks in advance.

AndreaCFD

Hi AndreaCFD. I have the similar question which is about to retrieve the matrix of coefficients of the linearized Navier-Stokes equations and possibly compute its eigenvectors and eigenvalues directly in OpenFOAM. Have you ever solved your question?
Would you like to share some experience on this issue?