Foam::vector Foam::eigenValues(const symmTensor& t)
{
scalar i = 0;
scalar ii = 0;
scalar iii = 0;
if
(
(
mag(t.xy()) + mag(t.xz()) + mag(t.xy())
+ mag(t.yz()) + mag(t.xz()) + mag(t.yz())
)
< SMALL
)
{
// diagonal matrix
i = t.xx();
ii = t.yy();
iii = t.zz();
}
else
{
scalar a = -t.xx() - t.yy() - t.zz();
scalar b = t.xx()*t.yy() + t.xx()*t.zz() + t.yy()*t.zz()
- t.xy()*t.xy() - t.xz()*t.xz() - t.yz()*t.yz();
scalar c = - t.xx()*t.yy()*t.zz() - t.xy()*t.yz()*t.xz()
- t.xz()*t.xy()*t.yz() + t.xz()*t.yy()*t.xz()
+ t.xy()*t.xy()*t.zz() + t.xx()*t.yz()*t.yz();
// If there is a zero root
if (mag(c) < ROOTVSMALL)
{
scalar disc = sqr(a) - 4*b;
if (disc >= -SMALL)
{
scalar q = -0.5*sqrt(max(0.0, disc));
i = 0;
ii = -0.5*a + q;
iii = -0.5*a - q;
}
else
{
FatalErrorIn("eigenValues(const tensor&)")
<< "zero and complex eigenvalues in tensor: " << t
<< abort(FatalError);
}
}
else
{
scalar Q = (a*a - 3*b)/9;
scalar R = (2*a*a*a - 9*a*b + 27*c)/54;
scalar R2 = sqr(R);
scalar Q3 = pow3(Q);
// Three different real roots
if (R2 < Q3)
{
scalar sqrtQ = sqrt(Q);
scalar theta = acos(R/(Q*sqrtQ));
scalar m2SqrtQ = -2*sqrtQ;
scalar aBy3 = a/3;
i = m2SqrtQ*cos(theta/3) - aBy3;
ii = m2SqrtQ*cos((theta + twoPi)/3) - aBy3;
iii = m2SqrtQ*cos((theta - twoPi)/3) - aBy3;
}
else
{
scalar A = cbrt(R + sqrt(R2 - Q3));
// Three equal real roots
if (A < SMALL)
{
scalar root = -a/3;
return vector(root, root, root);
}
else
{
// Complex roots
WarningIn("eigenValues(const symmTensor&)")
<< "complex eigenvalues detected for symmTensor: " << t
<< endl;
return vector::zero;
}
}
}
}
// Sort the eigenvalues into ascending order
if (i > ii)
{
Swap(i, ii);
}
if (ii > iii)
{
Swap(ii, iii);
}
if (i > ii)
{
Swap(i, ii);
}
return vector(i, ii, iii);
}
// Info << "Sp = " << Sp << endl;
// Info << "S = " << S << endl;
//}
//if ((loc[facei].x() < 1501 && loc[facei].x() > 1499) &&
// (loc[facei].y() < 1501 && loc[facei].y() > 1499))
//{
// Pout << "loc = " << loc[facei] << endl;
// Pout << "UParallel " << UParallel[facei] << endl;
// Pout << "UParallelP " << UParallelP[facei] << endl;
// Pout << "xP, yP, zP " << xP << tab << yP << tab << zP << endl;
// Pout << "RwP " << RwP << endl;
// Pout << "Rw " << Rw[facei] << endl;
//}
}
symmTensor RwMean = gSum(Rw * area) / areaTotal;
scalar RwMeanMag = Foam::sqrt(Foam::sqr(RwMean.xz()) + Foam::sqr(RwMean.yz()));
scalar RwMagMean = gSum(RwMag * area) / areaTotal;
Info << "RwMagMean = " << RwMagMean << tab
<< "RwMeanMag = " << RwMeanMag << tab
<< "sqrt(RwMagMean) = " << Foam::sqrt(RwMagMean) << tab
<< "sqrt(RwMeanMag) = " << Foam::sqrt(RwMeanMag) << tab
<< "uStarMean = " << uStarMean << endl;
}
vector SchumannGrotzbachFvPatchField::transformVectorCartToLocal
(
vector v,
vector xP,
vector yP,
