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 jaswi September 8, 2010 13:52

Eigenvector for the largest positive eigenvalue of the symm( fvc::grad ( U ) )

Dear Forum users

Good Evening

For some post processing , I need to find out the eigenvector, which corresponds to the
largest positive eigenvalue of symmetric part of the velocity gradient tensor .

Here is what I am doing :

volVectorField eigenVLarge
(
IOobject
(
"eigenVLarge",
runTime.timeName(),
mesh,
IOobject::NO_WRITE
),
mesh,
dimensionedVector("", dimless, vector(0, 0, 0))
);

forAll(UDef, cellI)
{

// Grab the tensor in the current cell
const tensor& tCurrent = D[cellI];

// Evaluate the eignevalues
vector eVal = eigenValues(tCurrent);

// The routine which returns the eigenvalues, sorts them in increasing order
// of their magnitude. So if i need to find the largest eigenvalue then I have to
// search for the maximum of three numbers. I did a workaround which is
// not very OpenFOAMy style. Here is what I did

label minIndex = -1;
label maxIndex = -1;

if( (eVal.x() <= eVal.y()) && (eVal.x() <= eVal.z()) )
{
minIndex = 0;
if ( eVal.y() < eVal.z())
{
maxIndex = 2;
}
else
{
maxIndex = 1;
}
}

if( (eVal.y() <= eVal.x()) && (eVal.y() <= eVal.z()) )
{
minIndex = 1;
if ( eVal.x() < eVal.z())
{
maxIndex = 2;
}
else
{
maxIndex = 0;
}
}

if( (eVal.z() <= eVal.x()) && (eVal.z() <= eVal.y()) )
{
minIndex = 2;
if ( eVal.x() < eVal.y())
{
maxIndex = 1;
}
else
{
maxIndex = 0;
}
}

// Once I have the maxIndex and minIndex I can get the eigenvectors
// corresponding to the maximum eigenvalues like this

tensor eVector = eigenVectors(tCurrent);

if (maxIndex == 0)
{
eigenVLarge[cellI] = eVector.x();
}
else if (maxIndex == 1)
{
eigenVLarge[cellI] = eVector.y();
}
else if (maxIndex == 2)
{
eigenVLarge[cellI] = eVector.z();
}

eigenVLarge.write();

This is very much not OpenFOAM style and I am sure there is some better way
to get the eigenVector which corresponds to the maximum eigenvalue of the strain rate tensor D

It would be nice if somebody aware of this could please share their experience.

Thanks alot

Best Regards
jaswi

 jaswi September 13, 2010 08:43

Dear Forum Users

Some body with the experience on how to deal with this , please comment.