tensor2D.C

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/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     |
    \\  /    A nd           | Copyright (C) 1991-2010 OpenCFD Ltd.
     \\/     M anipulation  |
-------------------------------------------------------------------------------
License
    This file is part of OpenFOAM.

    OpenFOAM is free software: you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
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    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
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\*---------------------------------------------------------------------------*/

#include "tensor2D.H"
#include <OpenFOAM/mathematicalConstants.H>

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

namespace Foam
{

// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //

template<>
const char* const tensor2D::typeName = "tensor2D";

template<>
const char* tensor2D::componentNames[] =
{
    "xx", "xy",
    "yx", "yy"
};

template<>
const tensor2D tensor2D::zero
(
    0, 0,
    0, 0
);

template<>
const tensor2D tensor2D::one
(
    1, 1,
    1, 1
);

template<>
const tensor2D tensor2D::max
(
    VGREAT, VGREAT,
    VGREAT, VGREAT
);

template<>
const tensor2D tensor2D::min
(
    -VGREAT, -VGREAT,
    -VGREAT, -VGREAT
);


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

// Return eigenvalues in ascending order of absolute values
vector2D eigenValues(const tensor2D& t)
{
    scalar i = 0;
    scalar ii = 0;

    if (mag(t.xy()) < SMALL && mag(t.yx()) < SMALL)
    {
        i = t.xx();
        ii = t.yy();
    }
    else
    {
        scalar mb = t.xx() + t.yy();
        scalar c = t.xx()*t.yy() - t.xy()*t.yx();

        // If there is a zero root
        if (mag(c) < SMALL)
        {
            i = 0;
            ii = mb;
        }
        else
        {
            scalar disc = sqr(mb) - 4*c;

            if (disc > 0)
            {
                scalar q = sqrt(disc);

                i = 0.5*(mb - q);
                ii = 0.5*(mb + q);
            }
            else
            {
                FatalErrorIn("eigenValues(const tensor2D&)")
                    << "zero and complex eigenvalues in tensor2D: " << t
                    << abort(FatalError);
            }
        }
    }

    // Sort the eigenvalues into ascending order
    if (mag(i) > mag(ii))
    {
        Swap(i, ii);
    }

    return vector2D(i, ii);
}


vector2D eigenVector(const tensor2D& t, const scalar lambda)
{
    if (lambda < SMALL)
    {
        return vector2D::zero;
    }

    if (mag(t.xy()) < SMALL && mag(t.yx()) < SMALL)
    {
        if (lambda > min(t.xx(), t.yy()))
        {
            return vector2D(1, 0);
        }
        else
        {
            return vector2D(0, 1);
        }
    }
    else if (mag(t.xy()) < SMALL)
    {
        return vector2D(lambda - t.yy(), t.yx());
    }
    else
    {
        return vector2D(t.xy(), lambda - t.yy());
    }
}


tensor2D eigenVectors(const tensor2D& t)
{
    vector2D evals(eigenValues(t));

    tensor2D evs
    (
        eigenVector(t, evals.x()),
        eigenVector(t, evals.y())
    );

    return evs;
}


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

} // End namespace Foam

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