Example #1
0
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 << "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, 
    vector zP