Tensor2DI.H

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/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     |
    \\  /    A nd           | Copyright (C) 2011-2013 OpenFOAM Foundation
     \\/     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
    (at your option) any later version.
 
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    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    for more details.
 
    You should have received a copy of the GNU General Public License
    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
template<class Cmpt>
inline Tensor2D<Cmpt>::Tensor2D()
{}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>::Tensor2D(const VectorSpace<Tensor2D<Cmpt>, Cmpt, 4>& vs)
:
    VectorSpace<Tensor2D<Cmpt>, Cmpt, 4>(vs)
{}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>::Tensor2D(const SymmTensor2D<Cmpt>& st)
{
    this->v_[XX] = st.xx(); this->v_[XY] = st.xy();
    this->v_[YX] = st.xy(); this->v_[YY] = st.yy();
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>::Tensor2D(const SphericalTensor2D<Cmpt>& st)
{
    this->v_[XX] = st.ii(); this->v_[XY] = 0;
    this->v_[YX] = 0; this->v_[YY] = st.ii();
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>::Tensor2D
(
    const Vector2D<Cmpt>& x,
    const Vector2D<Cmpt>& y
)
{
    this->v_[XX] = x.x(); this->v_[XY] = x.y();
    this->v_[YX] = y.x(); this->v_[YY] = y.y();
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>::Tensor2D
(
    const Cmpt txx, const Cmpt txy,
    const Cmpt tyx, const Cmpt tyy
)
{
    this->v_[XX] = txx; this->v_[XY] = txy;
    this->v_[YX] = tyx; this->v_[YY] = tyy;
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>::Tensor2D(Istream& is)
:
    VectorSpace<Tensor2D<Cmpt>, Cmpt, 4>(is)
{}
 
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
template<class Cmpt>
inline Vector2D<Cmpt> Tensor2D<Cmpt>::x() const
{
    return Vector2D<Cmpt>(this->v_[XX], this->v_[XY]);
}
 
template<class Cmpt>
inline Vector2D<Cmpt> Tensor2D<Cmpt>::y() const
{
    return Vector2D<Cmpt>(this->v_[YX], this->v_[YY]);
}
 
 
template<class Cmpt>
inline const Cmpt& Tensor2D<Cmpt>::xx() const
{
    return this->v_[XX];
}
 
template<class Cmpt>
inline const Cmpt& Tensor2D<Cmpt>::xy() const
{
    return this->v_[XY];
}
 
template<class Cmpt>
inline const Cmpt& Tensor2D<Cmpt>::yx() const
{
    return this->v_[YX];
}
 
template<class Cmpt>
inline const Cmpt& Tensor2D<Cmpt>::yy() const
{
    return this->v_[YY];
}
 
 
template<class Cmpt>
inline Cmpt& Tensor2D<Cmpt>::xx()
{
    return this->v_[XX];
}
 
template<class Cmpt>
inline Cmpt& Tensor2D<Cmpt>::xy()
{
    return this->v_[XY];
}
 
template<class Cmpt>
inline Cmpt& Tensor2D<Cmpt>::yx()
{
    return this->v_[YX];
}
 
template<class Cmpt>
inline Cmpt& Tensor2D<Cmpt>::yy()
{
    return this->v_[YY];
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt> Tensor2D<Cmpt>::T() const
{
    return Tensor2D<Cmpt>
    (
        xx(), yx(),
        xy(), yy()
    );
}
 
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
template<class Cmpt>
inline void Tensor2D<Cmpt>::operator=(const SymmTensor2D<Cmpt>& st)
{
    this->v_[XX] = st.xx(); this->v_[XY] = st.xy();
    this->v_[YX] = st.xy(); this->v_[YY] = st.yy();
}
 
 
template<class Cmpt>
inline void Tensor2D<Cmpt>::operator=(const SphericalTensor2D<Cmpt>& st)
{
    this->v_[XX] = st.ii(); this->v_[XY] = 0;
    this->v_[YX] = 0; this->v_[YY] = st.ii();
}
 
 
 
// * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
 
//- Inner-product between two tensors
template<class Cmpt>
inline typename innerProduct<Tensor2D<Cmpt>, Tensor2D<Cmpt> >::type
operator&(const Tensor2D<Cmpt>& t1, const Tensor2D<Cmpt>& t2)
{
    return Tensor2D<Cmpt>
    (
        t1.xx()*t2.xx() + t1.xy()*t2.yx(),
        t1.xx()*t2.xy() + t1.xy()*t2.yy(),
 
        t1.yx()*t2.xx() + t1.yy()*t2.yx(),
        t1.yx()*t2.xy() + t1.yy()*t2.yy()
    );
}
 
//- Inner-product between a tensor and a vector
template<class Cmpt>
inline typename innerProduct<Tensor2D<Cmpt>, Vector2D<Cmpt> >::type
operator&(const Tensor2D<Cmpt>& t, const Vector2D<Cmpt>& v)
{
    return Vector2D<Cmpt>
    (
        t.xx()*v.x() + t.xy()*v.y(),
        t.yx()*v.x() + t.yy()*v.y()
    );
}
 
//- Inner-product between a vector and a tensor
template<class Cmpt>
inline typename innerProduct<Vector2D<Cmpt>, Tensor2D<Cmpt> >::type
operator&(const Vector2D<Cmpt>& v, const Tensor2D<Cmpt>& t)
{
    return Vector2D<Cmpt>
    (
        v.x()*t.xx() + v.y()*t.yx(),
        v.x()*t.xy() + v.y()*t.yy()
    );
}
 
//- Outer-product between two vectors
template<class Cmpt>
inline typename outerProduct<Vector2D<Cmpt>, Vector2D<Cmpt> >::type
operator*(const Vector2D<Cmpt>& v1, const Vector2D<Cmpt>& v2)
{
    return Tensor2D<Cmpt>
    (
        v1.x()*v2.x(), v1.x()*v2.y(),
        v1.y()*v2.x(), v1.y()*v2.y()
    );
}
 
 
//- Return the trace of a tensor
template<class Cmpt>
inline Cmpt tr(const Tensor2D<Cmpt>& t)
{
    return t.xx() + t.yy();
}
 
 
//- Return the spherical part of a tensor
template<class Cmpt>
inline SphericalTensor2D<Cmpt> sph(const Tensor2D<Cmpt>& t)
{
    return 0.5*tr(t);
}
 
 
//- Return the symmetric part of a tensor
template<class Cmpt>
inline SymmTensor2D<Cmpt> symm(const Tensor2D<Cmpt>& t)
{
    return SymmTensor2D<Cmpt>
    (
        t.xx(), 0.5*(t.xy() + t.yx()),
                t.yy()
    );
}
 
//- Return the twice the symmetric part of a tensor
template<class Cmpt>
inline SymmTensor2D<Cmpt> twoSymm(const Tensor2D<Cmpt>& t)
{
    return SymmTensor2D<Cmpt>
    (
        t.xx() + t.xx(), t.xy() + t.yx(),
                         t.yy() + t.yy()
    );
}
 
//- Return the skew-symmetric part of a tensor
template<class Cmpt>
inline Tensor2D<Cmpt> skew(const Tensor2D<Cmpt>& t)
{
    return Tensor2D<Cmpt>
    (
        0.0, 0.5*(t.xy() - t.yx()),
        0.5*(t.yx() - t.xy()), 0.0
    );
}
 
 
//- Return the deviatoric part of a tensor
template<class Cmpt>
inline Tensor2D<Cmpt> dev(const Tensor2D<Cmpt>& t)
{
    return t - SphericalTensor2D<Cmpt>::oneThirdI*tr(t);
}
 
 
//- Return the deviatoric part of a tensor
template<class Cmpt>
inline Tensor2D<Cmpt> dev2(const Tensor2D<Cmpt>& t)
{
    return t - SphericalTensor2D<Cmpt>::twoThirdsI*tr(t);
}
 
 
//- Return the determinant of a tensor
template<class Cmpt>
inline Cmpt det(const Tensor2D<Cmpt>& t)
{
    return(t.xx()*t.yy() - t.xy()*t.yx());
}
 
 
//- Return the cofactor tensor of a tensor
template<class Cmpt>
inline Tensor2D<Cmpt> cof(const Tensor2D<Cmpt>& t)
{
    return Tensor2D<Cmpt>
    (
        t.yy(), -t.xy(),
       -t.yx(),  t.xx()
    );
}
 
 
//- Return the inverse of a tensor given the determinant
template<class Cmpt>
inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t, const Cmpt dett)
{
    return cof(t)/dett;
}
 
 
//- Return the inverse of a tensor
template<class Cmpt>
inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t)
{
    return inv(t, det(t));
}
 
 
//- Return the 1st invariant of a tensor
template<class Cmpt>
inline Cmpt invariantI(const Tensor2D<Cmpt>& t)
{
    return tr(t);
}
 
 
//- Return the 2nd invariant of a tensor
template<class Cmpt>
inline Cmpt invariantII(const Tensor2D<Cmpt>& t)
{
    return
    (
        0.5*sqr(tr(t))
      - 0.5*
        (
           t.xx()*t.xx() + t.xy()*t.xy()
         + t.yx()*t.yx() + t.yy()*t.yy()
        )
    );
}
 
 
//- Return the 3rd invariant of a tensor
template<class Cmpt>
inline Cmpt invariantIII(const Tensor2D<Cmpt>& t)
{
    return det(t);
}
 
 
// * * * * * * * * * Mixed Tensor SphericalTensor Operators  * * * * * * * * //
 
template<class Cmpt>
inline Tensor2D<Cmpt>
operator+(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
{
    return Tensor2D<Cmpt>
    (
        st1.ii() + t2.xx(), t2.xy(),
        t2.yx(),            st1.ii() + t2.yy()
    );
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>
operator+(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
{
    return Tensor2D<Cmpt>
    (
        t1.xx() + st2.ii(), t1.xy(),
        t1.yx(),            t1.yy() + st2.ii()
    );
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>
operator-(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
{
    return Tensor2D<Cmpt>
    (
        st1.ii() - t2.xx(), -t2.xy(),
       -t2.yx(),             st1.ii() - t2.yy()
    );
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>
operator-(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
{
    return Tensor2D<Cmpt>
    (
        t1.xx() - st2.ii(), t1.xy(),
        t1.yx(),            t1.yy() - st2.ii()
    );
}
 
 
//- Inner-product between a spherical tensor and a tensor
template<class Cmpt>
inline Tensor2D<Cmpt>
operator&(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
{
    return Tensor2D<Cmpt>
    (
        st1.ii()*t2.xx(),
        st1.ii()*t2.xy(),
                          st1.ii()*t2.yx(),
                          st1.ii()*t2.yy()
    );
}
 
 
//- Inner-product between a tensor and a spherical tensor
template<class Cmpt>
inline Tensor2D<Cmpt>
operator&(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
{
    return Tensor2D<Cmpt>
    (
        t1.xx()*st2.ii(),
                          t1.xy()*st2.ii(),
 
        t1.yx()*st2.ii(),
                          t1.yy()*st2.ii()
    );
}
 
 
//- Double-dot-product between a spherical tensor and a tensor
template<class Cmpt>
inline Cmpt
operator&&(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
{
    return(st1.ii()*t2.xx() + st1.ii()*t2.yy());
}
 
 
//- Double-dot-product between a tensor and a spherical tensor
template<class Cmpt>
inline Cmpt
operator&&(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
{
    return(t1.xx()*st2.ii() + t1.yy()*st2.ii());
}
 
 
// * * * * * * * * * * Mixed Tensor SymmTensor Operators * * * * * * * * * * //
 
template<class Cmpt>
inline Tensor2D<Cmpt>
operator+(const SymmTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
{
    return Tensor2D<Cmpt>
    (
        st1.xx() + t2.xx(), st1.xy() + t2.xy(),
        st1.xy() + t2.yx(), st1.yy() + t2.yy()
    );
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>
operator+(const Tensor2D<Cmpt>& t1, const SymmTensor2D<Cmpt>& st2)
{
    return Tensor2D<Cmpt>
    (
        t1.xx() + st2.xx(), t1.xy() + st2.xy(),
        t1.yx() + st2.xy(), t1.yy() + st2.yy()
    );
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>
operator-(const SymmTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
{
    return Tensor2D<Cmpt>
    (
        st1.xx() - t2.xx(), st1.xy() - t2.xy(),
        st1.xy() - t2.yx(), st1.yy() - t2.yy()
    );
}
 
 
template<class Cmpt>
inline Tensor2D<Cmpt>
operator-(const Tensor2D<Cmpt>& t1, const SymmTensor2D<Cmpt>& st2)
{
    return Tensor2D<Cmpt>
    (
        t1.xx() - st2.xx(), t1.xy() - st2.xy(),
        t1.yx() - st2.xy(), t1.yy() - st2.yy()
    );
}
 
 
//- Inner-product between a spherical tensor and a tensor
template<class Cmpt>
inline Tensor2D<Cmpt>
operator&(const SymmTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
{
    return Tensor2D<Cmpt>
    (
        st1.xx()*t2.xx() + st1.xy()*t2.yx(),
        st1.xx()*t2.xy() + st1.xy()*t2.yy(),
 
        st1.xy()*t2.xx() + st1.yy()*t2.yx(),
        st1.xy()*t2.xy() + st1.yy()*t2.yy()
    );
}
 
 
//- Inner-product between a tensor and a spherical tensor
template<class Cmpt>
inline Tensor2D<Cmpt>
operator&(const Tensor2D<Cmpt>& t1, const SymmTensor2D<Cmpt>& st2)
{
    return Tensor2D<Cmpt>
    (
        t1.xx()*st2.xx() + t1.xy()*st2.xy(),
        t1.xx()*st2.xy() + t1.xy()*st2.yy(),
 
        t1.yx()*st2.xx() + t1.yy()*st2.xy(),
        t1.yx()*st2.xy() + t1.yy()*st2.yy()
    );
}
 
 
//- Double-dot-product between a spherical tensor and a tensor
template<class Cmpt>
inline Cmpt
operator&&(const SymmTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
{
    return
    (
        st1.xx()*t2.xx() + st1.xy()*t2.xy()
      + st1.xy()*t2.yx() + st1.yy()*t2.yy()
    );
}
 
 
//- Double-dot-product between a tensor and a spherical tensor
template<class Cmpt>
inline Cmpt
operator&&(const Tensor2D<Cmpt>& t1, const SymmTensor2D<Cmpt>& st2)
{
    return
    (
        t1.xx()*st2.xx() + t1.xy()*st2.xy()
      + t1.yx()*st2.xy() + t1.yy()*st2.yy()
    );
}
 
 
template<class Cmpt>
class typeOfSum<SphericalTensor2D<Cmpt>, Tensor2D<Cmpt> >
{
public:
 
    typedef Tensor2D<Cmpt> type;
};
 
template<class Cmpt>
class typeOfSum<Tensor2D<Cmpt>, SphericalTensor2D<Cmpt> >
{
public:
 
    typedef Tensor2D<Cmpt> type;
};
 
 
template<class Cmpt>
class innerProduct<Tensor2D<Cmpt>, Tensor2D<Cmpt> >
{
public:
 
    typedef Tensor2D<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<SphericalTensor2D<Cmpt>, Tensor2D<Cmpt> >
{
public:
 
    typedef Tensor2D<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<Tensor2D<Cmpt>, SphericalTensor2D<Cmpt> >
{
public:
 
    typedef Tensor2D<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<Tensor2D<Cmpt>, Vector2D<Cmpt> >
{
public:
 
    typedef Vector2D<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<Vector2D<Cmpt>, Tensor2D<Cmpt> >
{
public:
 
    typedef Vector2D<Cmpt> type;
};
 
 
template<class Cmpt>
class outerProduct<Vector2D<Cmpt>, Vector2D<Cmpt> >
{
public:
 
    typedef Tensor2D<Cmpt> type;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// ************************************************************************* //