SymmTensor2DI.H

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    Copyright (C) 2011-2016 OpenFOAM Foundation
    Copyright (C) 2019-2020 OpenCFD Ltd.
-------------------------------------------------------------------------------
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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    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    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
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#include "Tensor2D.H"
 
// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
template<class Cmpt>
inline Foam::SymmTensor2D<Cmpt>::SymmTensor2D(const Foam::zero)
:
    SymmTensor2D::vsType(Zero)
{}
 
 
template<class Cmpt>
inline Foam::SymmTensor2D<Cmpt>::SymmTensor2D
(
    const VectorSpace<SymmTensor2D<Cmpt>, Cmpt, 3>& vs
)
:
    SymmTensor2D::vsType(vs)
{}
 
 
template<class Cmpt>
inline Foam::SymmTensor2D<Cmpt>::SymmTensor2D(const SphericalTensor2D<Cmpt>& st)
{
    this->v_[XX] = st.ii(); this->v_[XY] = Zero;
    this->v_[YY] = st.ii();
}
 
 
template<class Cmpt>
inline Foam::SymmTensor2D<Cmpt>::SymmTensor2D
(
    const Cmpt txx, const Cmpt txy,
                    const Cmpt tyy
)
{
    this->v_[XX] = txx; this->v_[XY] = txy;
                        this->v_[YY] = tyy;
}
 
 
template<class Cmpt>
inline Foam::SymmTensor2D<Cmpt>::SymmTensor2D(Istream& is)
:
    SymmTensor2D::vsType(is)
{}
 
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
template<class Cmpt>
inline const Cmpt& Foam::SymmTensor2D<Cmpt>::xx() const
{
    return this->v_[XX];
}
 
template<class Cmpt>
inline const Cmpt& Foam::SymmTensor2D<Cmpt>::xy() const
{
    return this->v_[XY];
}
 
template<class Cmpt>
inline const Cmpt& Foam::SymmTensor2D<Cmpt>::yx() const
{
    return this->v_[XY];
}
 
template<class Cmpt>
inline const Cmpt& Foam::SymmTensor2D<Cmpt>::yy() const
{
    return this->v_[YY];
}
 
 
template<class Cmpt>
inline Cmpt& Foam::SymmTensor2D<Cmpt>::xx()
{
    return this->v_[XX];
}
 
template<class Cmpt>
inline Cmpt& Foam::SymmTensor2D<Cmpt>::xy()
{
    return this->v_[XY];
}
 
template<class Cmpt>
inline Cmpt& Foam::SymmTensor2D<Cmpt>::yx()
{
    return this->v_[XY];
}
 
template<class Cmpt>
inline Cmpt& Foam::SymmTensor2D<Cmpt>::yy()
{
    return this->v_[YY];
}
 
 
template<class Cmpt>
inline Foam::Vector2D<Cmpt> Foam::SymmTensor2D<Cmpt>::diag() const
{
    return Vector2D<Cmpt>(this->v_[XX], this->v_[YY]);
}
 
 
template<class Cmpt>
inline void Foam::SymmTensor2D<Cmpt>::diag(const Vector2D<Cmpt>& v)
{
    this->v_[XX] = v.x(); this->v_[YY] = v.y();
}
 
 
template<class Cmpt>
inline const Foam::SymmTensor2D<Cmpt>& Foam::SymmTensor2D<Cmpt>::T() const
{
    return *this;
}
 
 
// * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
 
template<class Cmpt>
inline void Foam::SymmTensor2D<Cmpt>::operator=
(
    const SphericalTensor2D<Cmpt>& st
)
{
    this->v_[XX] = st.ii(); this->v_[XY] = Zero;
                            this->v_[YY] = st.ii();
}
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
// * * * * * * * * * * * * * * * Global Functions  * * * * * * * * * * * * * //
 
//- Return the trace of a SymmTensor2D
template<class Cmpt>
inline Cmpt tr(const SymmTensor2D<Cmpt>& st)
{
    return st.xx() + st.yy();
}
 
 
//- Return the spherical part of a SymmTensor2D
template<class Cmpt>
inline SphericalTensor2D<Cmpt> sph(const SymmTensor2D<Cmpt>& st)
{
    return SphericalTensor2D<Cmpt>
    (
        0.5*tr(st)
    );
}
 
 
//- Return the symmetric part of a SymmTensor2D, i.e. itself
template<class Cmpt>
inline const SymmTensor2D<Cmpt>& symm(const SymmTensor2D<Cmpt>& st)
{
    return st;
}
 
 
//- Return twice the symmetric part of a SymmTensor2D, i.e. twice itself
template<class Cmpt>
inline SymmTensor2D<Cmpt> twoSymm(const SymmTensor2D<Cmpt>& st)
{
    return 2*st;
}
 
 
//- Return the deviatoric part of a SymmTensor2D
template<class Cmpt>
inline SymmTensor2D<Cmpt> dev(const SymmTensor2D<Cmpt>& st)
{
    return st - sph(st);
}
 
 
//- Return the two-third deviatoric part of a SymmTensor2D
template<class Cmpt>
inline SymmTensor2D<Cmpt> dev2(const SymmTensor2D<Cmpt>& st)
{
    return st - 2*sph(st);
}
 
 
//- Return the determinant of a SymmTensor2D
template<class Cmpt>
inline Cmpt det(const SymmTensor2D<Cmpt>& st)
{
    return (st.xx()*st.yy() - st.xy()*st.xy());
}
 
 
//- Return the cofactor SymmTensor2D of a SymmTensor2D
template<class Cmpt>
inline SymmTensor2D<Cmpt> cof(const SymmTensor2D<Cmpt>& st)
{
    return SymmTensor2D<Cmpt>
    (
        st.yy(), -st.yx(),
                  st.xx()
    );
}
 
 
//- Return the inverse of a SymmTensor2D using a given determinant
template<class Cmpt>
inline SymmTensor2D<Cmpt> inv(const SymmTensor2D<Cmpt>& st, const Cmpt detst)
{
    #ifdef FULLDEBUG
    if (mag(detst) < SMALL)
    {
        FatalErrorInFunction
            << "SymmTensor2D is not invertible due to the zero determinant:"
            << "det(SymmTensor2D) = " << mag(detst)
            << abort(FatalError);
    }
    #endif
    // cofactor and adjugate matrices of SymmTensor are the same, hence no .T()
    return cof(st)/detst;
}
 
 
//- Return the inverse of a SymmTensor2D
template<class Cmpt>
inline SymmTensor2D<Cmpt> inv(const SymmTensor2D<Cmpt>& st)
{
    return inv(st, det(st));
}
 
 
//- Return the 1st invariant of a SymmTensor2D
template<class Cmpt>
inline Cmpt invariantI(const SymmTensor2D<Cmpt>& st)
{
    return tr(st);
}
 
 
//- Return the 2nd invariant of a SymmTensor2D
template<class Cmpt>
inline Cmpt invariantII(const SymmTensor2D<Cmpt>& st)
{
    return det(st);
}
 
 
//- Return the inner-product of a SymmTensor2D with itself
template<class Cmpt>
inline SymmTensor2D<Cmpt>
innerSqr(const SymmTensor2D<Cmpt>& st)
{
    return SymmTensor2D<Cmpt>
    (
        st.xx()*st.xx() + st.xy()*st.xy(),
        st.xx()*st.xy() + st.xy()*st.yy(),
        st.xy()*st.xy() + st.yy()*st.yy()
    );
}
 
 
//- Return the square of Frobenius norm of a SymmTensor2D as a Cmpt
template<class Cmpt>
inline Cmpt magSqr(const SymmTensor2D<Cmpt>& st)
{
    return Cmpt
    (
        mag(st.xx()*st.xx()) + 2*mag(st.xy()*st.xy())
                             +   mag(st.yy()*st.yy())
    );
}
 
 
//- Outer-product of a Vector2D with itself
template<class Cmpt>
inline SymmTensor2D<Cmpt> sqr(const Vector2D<Cmpt>& v)
{
    return SymmTensor2D<Cmpt>
    (
        v.x()*v.x(), v.x()*v.y(),
                     v.y()*v.y()
    );
}
 
 
// * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
 
//- Sum of a SphericalTensor2D and a SymmTensor2D
template<class Cmpt>
inline SymmTensor2D<Cmpt>
operator+(const SphericalTensor2D<Cmpt>& spt1, const SymmTensor2D<Cmpt>& st2)
{
    return SymmTensor2D<Cmpt>
    (
        spt1.ii() + st2.xx(), st2.xy(),
                              spt1.ii() + st2.yy()
    );
}
 
 
//- Sum of a SymmTensor2D and a SphericalTensor2D
template<class Cmpt>
inline SymmTensor2D<Cmpt>
operator+(const SymmTensor2D<Cmpt>& st1, const SphericalTensor2D<Cmpt>& spt2)
{
    return SymmTensor2D<Cmpt>
    (
        st1.xx() + spt2.ii(), st1.xy(),
                              st1.yy() + spt2.ii()
    );
}
 
 
//- Subtract a SymmTensor2D from a SphericalTensor2D
template<class Cmpt>
inline SymmTensor2D<Cmpt>
operator-(const SphericalTensor2D<Cmpt>& spt1, const SymmTensor2D<Cmpt>& st2)
{
    return SymmTensor2D<Cmpt>
    (
        spt1.ii() - st2.xx(), -st2.xy(),
                               spt1.ii() - st2.yy()
    );
}
 
 
//- Subtract a SphericalTensor2D from a SymmTensor2D
template<class Cmpt>
inline SymmTensor2D<Cmpt>
operator-(const SymmTensor2D<Cmpt>& st1, const SphericalTensor2D<Cmpt>& spt2)
{
    return SymmTensor2D<Cmpt>
    (
        st1.xx() - spt2.ii(), st1.xy(),
                              st1.yy() - spt2.ii()
    );
}
 
 
//- Division of a SymmTensor2D by a Cmpt
template<class Cmpt>
inline SymmTensor2D<Cmpt>
operator/(const SymmTensor2D<Cmpt>& st, const Cmpt s)
{
    return SymmTensor2D<Cmpt>
    (
        st.xx()/s, st.xy()/s,
                   st.yy()/s
    );
}
 
 
//- Inner-product of a SymmTensor2D and a SymmTensor2D
template<class Cmpt>
inline Tensor2D<Cmpt>
operator&(const SymmTensor2D<Cmpt>& st1, const SymmTensor2D<Cmpt>& st2)
{
    return Tensor2D<Cmpt>
    (
        st1.xx()*st2.xx() + st1.xy()*st2.xy(),
        st1.xx()*st2.xy() + st1.xy()*st2.yy(),
 
        st1.xy()*st2.xx() + st1.yy()*st2.xy(),
        st1.xy()*st2.xy() + st1.yy()*st2.yy()
    );
}
 
 
//- Inner-product of a SphericalTensor2D and a SymmTensor2D
template<class Cmpt>
inline SymmTensor2D<Cmpt>
operator&(const SphericalTensor2D<Cmpt>& spt1, const SymmTensor2D<Cmpt>& st2)
{
    return SymmTensor2D<Cmpt>
    (
        spt1.ii()*st2.xx(), spt1.ii()*st2.xy(),
                            spt1.ii()*st2.yy()
    );
}
 
 
//- Inner-product of a SymmTensor2D and a SphericalTensor2D
template<class Cmpt>
inline SymmTensor2D<Cmpt>
operator&(const SymmTensor2D<Cmpt>& st1, const SphericalTensor2D<Cmpt>& spt2)
{
    return SymmTensor2D<Cmpt>
    (
        st1.xx()*spt2.ii(), st1.xy()*spt2.ii(),
                            st1.yy()*spt2.ii()
    );
}
 
 
//- Inner-product of a SymmTensor2D and a Vector2D
template<class Cmpt>
inline Vector2D<Cmpt>
operator&(const SymmTensor2D<Cmpt>& st, const Vector2D<Cmpt>& v)
{
    return Vector2D<Cmpt>
    (
        st.xx()*v.x() + st.xy()*v.y(),
        st.xy()*v.x() + st.yy()*v.y()
    );
}
 
 
//- Inner-product of a Vector2D and a SymmTensor2D
template<class Cmpt>
inline Vector2D<Cmpt>
operator&(const Vector2D<Cmpt>& v, const SymmTensor2D<Cmpt>& st)
{
    return Vector2D<Cmpt>
    (
        v.x()*st.xx() + v.y()*st.xy(),
        v.x()*st.xy() + v.y()*st.yy()
    );
}
 
 
//- Double-inner-product of a SymmTensor2D and a SymmTensor2D
template<class Cmpt>
inline Cmpt
operator&&(const SymmTensor2D<Cmpt>& st1, const SymmTensor2D<Cmpt>& st2)
{
    return
    (
        st1.xx()*st2.xx() + 2*st1.xy()*st2.xy()
                          +   st1.yy()*st2.yy()
    );
}
 
 
//- Double-inner-product of a SphericalTensor2D and a SymmTensor2D
template<class Cmpt>
inline Cmpt
operator&&(const SphericalTensor2D<Cmpt>& spt1, const SymmTensor2D<Cmpt>& st2)
{
    return (spt1.ii()*st2.xx() + spt1.ii()*st2.yy());
}
 
 
//- Double-inner-product of a SymmTensor2D and a SphericalTensor2D
template<class Cmpt>
inline Cmpt
operator&&(const SymmTensor2D<Cmpt>& st1, const SphericalTensor2D<Cmpt>& spt2)
{
    return (st1.xx()*spt2.ii() + st1.yy()*spt2.ii());
}
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
template<class Cmpt>
class outerProduct<SymmTensor2D<Cmpt>, Cmpt>
{
public:
 
    typedef SymmTensor2D<Cmpt> type;
};
 
template<class Cmpt>
class outerProduct<Cmpt, SymmTensor2D<Cmpt>>
{
public:
 
    typedef SymmTensor2D<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<SymmTensor2D<Cmpt>, SymmTensor2D<Cmpt>>
{
public:
 
    typedef Tensor2D<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<SymmTensor2D<Cmpt>, Vector2D<Cmpt>>
{
public:
 
    typedef Vector2D<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<Vector2D<Cmpt>, SymmTensor2D<Cmpt>>
{
public:
 
    typedef Vector2D<Cmpt> type;
};
 
 
template<class Cmpt>
class typeOfSum<SphericalTensor2D<Cmpt>, SymmTensor2D<Cmpt>>
{
public:
 
    typedef SymmTensor2D<Cmpt> type;
};
 
template<class Cmpt>
class typeOfSum<SymmTensor2D<Cmpt>, SphericalTensor2D<Cmpt>>
{
public:
 
    typedef SymmTensor2D<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<SphericalTensor2D<Cmpt>, SymmTensor2D<Cmpt>>
{
public:
 
    typedef SymmTensor2D<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<SymmTensor2D<Cmpt>, SphericalTensor2D<Cmpt>>
{
public:
 
    typedef SymmTensor2D<Cmpt> type;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// ************************************************************************* //