SymmTensorI.H

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  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
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    This file is part of OpenFOAM.
 
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#include "Vector.H"
#include "Tensor.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
template<class Cmpt>
inline SymmTensor<Cmpt>::SymmTensor()
{}
 
 
template<class Cmpt>
template<class Cmpt2>
inline SymmTensor<Cmpt>::SymmTensor
(
    const VectorSpace<SymmTensor<Cmpt2>, Cmpt2, 6>& vs
)
:
    VectorSpace<SymmTensor<Cmpt>, Cmpt, 6>(vs)
{}
 
 
template<class Cmpt>
inline SymmTensor<Cmpt>::SymmTensor(const SphericalTensor<Cmpt>& st)
{
    this->v_[XX] = st.ii(); this->v_[XY] = 0;       this->v_[XZ] = 0;
                            this->v_[YY] = st.ii(); this->v_[YZ] = 0;
                                                    this->v_[ZZ] = st.ii();
}
 
 
template<class Cmpt>
inline SymmTensor<Cmpt>::SymmTensor
(
    const Cmpt txx, const Cmpt txy, const Cmpt txz,
                    const Cmpt tyy, const Cmpt tyz,
                                    const Cmpt tzz
)
{
    this->v_[XX] = txx; this->v_[XY] = txy; this->v_[XZ] = txz;
                        this->v_[YY] = tyy; this->v_[YZ] = tyz;
                                            this->v_[ZZ] = tzz;
}
 
 
template<class Cmpt>
inline SymmTensor<Cmpt>::SymmTensor(Istream& is)
:
    VectorSpace<SymmTensor<Cmpt>, Cmpt, 6>(is)
{}
 
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::xx() const
{
    return this->v_[XX];
}
 
template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::xy() const
{
    return this->v_[XY];
}
 
template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::xz() const
{
    return this->v_[XZ];
}
 
template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::yy() const
{
    return this->v_[YY];
}
 
template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::yz() const
{
    return this->v_[YZ];
}
 
template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::zz() const
{
    return this->v_[ZZ];
}
 
 
template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::xx()
{
    return this->v_[XX];
}
 
template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::xy()
{
    return this->v_[XY];
}
 
template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::xz()
{
    return this->v_[XZ];
}
 
template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::yy()
{
    return this->v_[YY];
}
 
template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::yz()
{
    return this->v_[YZ];
}
 
template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::zz()
{
    return this->v_[ZZ];
}
 
 
template<class Cmpt>
inline const SymmTensor<Cmpt>& SymmTensor<Cmpt>::T() const
{
    return *this;
}
 
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
template<class Cmpt>
inline void SymmTensor<Cmpt>::operator=(const SphericalTensor<Cmpt>& st)
{
    this->v_[XX] = st.ii(); this->v_[XY] = 0;       this->v_[XZ] = 0;
                            this->v_[YY] = st.ii(); this->v_[YZ] = 0;
                                                    this->v_[ZZ] = st.ii();
}
 
 
 
// * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
 
//- Hodge Dual operator (tensor -> vector)
template<class Cmpt>
inline Vector<Cmpt> operator*(const SymmTensor<Cmpt>& st)
{
    return Vector<Cmpt>(st.yz(), -st.xz(), st.xy());
}
 
 
//- Inner-product between two symmetric tensors
template<class Cmpt>
inline Tensor<Cmpt>
operator&(const SymmTensor<Cmpt>& st1, const SymmTensor<Cmpt>& st2)
{
    return Tensor<Cmpt>
    (
        st1.xx()*st2.xx() + st1.xy()*st2.xy() + st1.xz()*st2.xz(),
        st1.xx()*st2.xy() + st1.xy()*st2.yy() + st1.xz()*st2.yz(),
        st1.xx()*st2.xz() + st1.xy()*st2.yz() + st1.xz()*st2.zz(),
 
        st1.xy()*st2.xx() + st1.yy()*st2.xy() + st1.yz()*st2.xz(),
        st1.xy()*st2.xy() + st1.yy()*st2.yy() + st1.yz()*st2.yz(),
        st1.xy()*st2.xz() + st1.yy()*st2.yz() + st1.yz()*st2.zz(),
 
        st1.xz()*st2.xx() + st1.yz()*st2.xy() + st1.zz()*st2.xz(),
        st1.xz()*st2.xy() + st1.yz()*st2.yy() + st1.zz()*st2.yz(),
        st1.xz()*st2.xz() + st1.yz()*st2.yz() + st1.zz()*st2.zz()
    );
}
 
 
//- Double-dot-product between a symmetric tensor and a symmetric tensor
template<class Cmpt>
inline Cmpt
operator&&(const SymmTensor<Cmpt>& st1, const SymmTensor<Cmpt>& st2)
{
    return
    (
        st1.xx()*st2.xx() + 2*st1.xy()*st2.xy() + 2*st1.xz()*st2.xz()
                          +   st1.yy()*st2.yy() + 2*st1.yz()*st2.yz()
                                                +   st1.zz()*st2.zz()
    );
}
 
 
//- Inner-product between a symmetric tensor and a vector
template<class Cmpt>
inline Vector<Cmpt>
operator&(const SymmTensor<Cmpt>& st, const Vector<Cmpt>& v)
{
    return Vector<Cmpt>
    (
        st.xx()*v.x() + st.xy()*v.y() + st.xz()*v.z(),
        st.xy()*v.x() + st.yy()*v.y() + st.yz()*v.z(),
        st.xz()*v.x() + st.yz()*v.y() + st.zz()*v.z()
    );
}
 
 
//- Inner-product between a vector and a symmetric tensor
template<class Cmpt>
inline Vector<Cmpt>
operator&(const Vector<Cmpt>& v, const SymmTensor<Cmpt>& st)
{
    return Vector<Cmpt>
    (
        v.x()*st.xx() + v.y()*st.xy() + v.z()*st.xz(),
        v.x()*st.xy() + v.y()*st.yy() + v.z()*st.yz(),
        v.x()*st.xz() + v.y()*st.yz() + v.z()*st.zz()
    );
}
 
 
//- Inner-sqr of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt>
innerSqr(const SymmTensor<Cmpt>& st)
{
    return SymmTensor<Cmpt>
    (
        st.xx()*st.xx() + st.xy()*st.xy() + st.xz()*st.xz(),
        st.xx()*st.xy() + st.xy()*st.yy() + st.xz()*st.yz(),
        st.xx()*st.xz() + st.xy()*st.yz() + st.xz()*st.zz(),
 
        st.xy()*st.xy() + st.yy()*st.yy() + st.yz()*st.yz(),
        st.xy()*st.xz() + st.yy()*st.yz() + st.yz()*st.zz(),
 
        st.xz()*st.xz() + st.yz()*st.yz() + st.zz()*st.zz()
    );
}
 
 
template<class Cmpt>
inline Cmpt magSqr(const SymmTensor<Cmpt>& st)
{
    return
    (
        magSqr(st.xx()) + 2*magSqr(st.xy()) + 2*magSqr(st.xz())
                        +   magSqr(st.yy()) + 2*magSqr(st.yz())
                                            +   magSqr(st.zz())
    );
}
 
 
//- Return the trace of a symmetric tensor
template<class Cmpt>
inline Cmpt tr(const SymmTensor<Cmpt>& st)
{
    return st.xx() + st.yy() + st.zz();
}
 
 
//- Return the spherical part of a symmetric tensor
template<class Cmpt>
inline SphericalTensor<Cmpt> sph(const SymmTensor<Cmpt>& st)
{
    return (1.0/3.0)*tr(st);
}
 
 
//- Return the symmetric part of a symmetric tensor, i.e. itself
template<class Cmpt>
inline const SymmTensor<Cmpt>& symm(const SymmTensor<Cmpt>& st)
{
    return st;
}
 
 
//- Return twice the symmetric part of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt> twoSymm(const SymmTensor<Cmpt>& st)
{
    return 2*st;
}
 
 
//- Return the deviatoric part of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt> dev(const SymmTensor<Cmpt>& st)
{
    return st - SphericalTensor<Cmpt>::oneThirdI*tr(st);
}
 
 
//- Return the deviatoric part of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt> dev2(const SymmTensor<Cmpt>& st)
{
    return st - SphericalTensor<Cmpt>::twoThirdsI*tr(st);
}
 
 
//- Return the determinant of a symmetric tensor
template<class Cmpt>
inline Cmpt det(const SymmTensor<Cmpt>& st)
{
    return
    (
        st.xx()*st.yy()*st.zz() + st.xy()*st.yz()*st.xz()
      + st.xz()*st.xy()*st.yz() - st.xx()*st.yz()*st.yz()
      - st.xy()*st.xy()*st.zz() - st.xz()*st.yy()*st.xz()
    );
}
 
 
//- Return the cofactor symmetric tensor of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt> cof(const SymmTensor<Cmpt>& st)
{
    return SymmTensor<Cmpt>
    (
        st.yy()*st.zz() - st.yz()*st.yz(),
        st.xz()*st.yz() - st.xy()*st.zz(),
        st.xy()*st.yz() - st.xz()*st.yy(),
 
        st.xx()*st.zz() - st.xz()*st.xz(),
        st.xy()*st.xz() - st.xx()*st.yz(),
 
        st.xx()*st.yy() - st.xy()*st.xy()
    );
}
 
 
//- Return the inverse of a symmetric tensor give the determinant
template<class Cmpt>
inline SymmTensor<Cmpt> inv(const SymmTensor<Cmpt>& st, const Cmpt detst)
{
    return SymmTensor<Cmpt>
    (
        st.yy()*st.zz() - st.yz()*st.yz(),
        st.xz()*st.yz() - st.xy()*st.zz(),
        st.xy()*st.yz() - st.xz()*st.yy(),
 
        st.xx()*st.zz() - st.xz()*st.xz(),
        st.xy()*st.xz() - st.xx()*st.yz(),
 
        st.xx()*st.yy() - st.xy()*st.xy()
    )/detst;
}
 
 
//- Return the inverse of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt> inv(const SymmTensor<Cmpt>& st)
{
    return inv(st, det(st));
}
 
 
//- Return the 1st invariant of a symmetric tensor
template<class Cmpt>
inline Cmpt invariantI(const SymmTensor<Cmpt>& st)
{
    return tr(st);
}
 
 
//- Return the 2nd invariant of a symmetric tensor
template<class Cmpt>
inline Cmpt invariantII(const SymmTensor<Cmpt>& st)
{
    return
    (
        0.5*sqr(tr(st))
      - 0.5*
        (
           st.xx()*st.xx() + st.xy()*st.xy() + st.xz()*st.xz()
         + st.xy()*st.xy() + st.yy()*st.yy() + st.yz()*st.yz()
         + st.xz()*st.xz() + st.yz()*st.yz() + st.zz()*st.zz()
        )
    );
}
 
 
//- Return the 3rd invariant of a symmetric tensor
template<class Cmpt>
inline Cmpt invariantIII(const SymmTensor<Cmpt>& st)
{
    return det(st);
}
 
 
template<class Cmpt>
inline SymmTensor<Cmpt>
operator+(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
{
    return SymmTensor<Cmpt>
    (
        spt1.ii() + st2.xx(), st2.xy(),             st2.xz(),
                              spt1.ii() + st2.yy(), st2.yz(),
                                                    spt1.ii() + st2.zz()
    );
}
 
 
template<class Cmpt>
inline SymmTensor<Cmpt>
operator+(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
{
    return SymmTensor<Cmpt>
    (
        st1.xx() + spt2.ii(), st1.xy(),             st1.xz(),
                              st1.yy() + spt2.ii(), st1.yz(),
                                                    st1.zz() + spt2.ii()
    );
}
 
 
template<class Cmpt>
inline SymmTensor<Cmpt>
operator-(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
{
    return SymmTensor<Cmpt>
    (
        spt1.ii() - st2.xx(), -st2.xy(),             -st2.xz(),
                               spt1.ii() - st2.yy(), -st2.yz(),
                                                      spt1.ii() - st2.zz()
    );
}
 
 
template<class Cmpt>
inline SymmTensor<Cmpt>
operator-(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
{
    return SymmTensor<Cmpt>
    (
        st1.xx() - spt2.ii(), st1.xy(),             st1.xz(),
                              st1.yy() - spt2.ii(), st1.yz(),
                                                    st1.zz() - spt2.ii()
    );
}
 
 
//- Inner-product between a spherical symmetric tensor and a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt>
operator&(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
{
    return SymmTensor<Cmpt>
    (
        spt1.ii()*st2.xx(), spt1.ii()*st2.xy(), spt1.ii()*st2.xz(),
                            spt1.ii()*st2.yy(), spt1.ii()*st2.yz(),
                                                spt1.ii()*st2.zz()
    );
}
 
 
//- Inner-product between a tensor and a spherical tensor
template<class Cmpt>
inline SymmTensor<Cmpt>
operator&(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
{
    return SymmTensor<Cmpt>
    (
        st1.xx()*spt2.ii(), st1.xy()*spt2.ii(), st1.xz()*spt2.ii(),
                            st1.yy()*spt2.ii(), st1.yz()*spt2.ii(),
                                                st1.zz()*spt2.ii()
    );
}
 
 
//- Double-dot-product between a spherical tensor and a symmetric tensor
template<class Cmpt>
inline Cmpt
operator&&(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
{
    return(spt1.ii()*st2.xx() + spt1.ii()*st2.yy() + spt1.ii()*st2.zz());
}
 
 
//- Double-dot-product between a tensor and a spherical tensor
template<class Cmpt>
inline Cmpt
operator&&(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
{
    return(st1.xx()*spt2.ii() + st1.yy()*spt2.ii() + st1.zz()*spt2.ii());
}
 
 
template<class Cmpt>
inline SymmTensor<Cmpt> sqr(const Vector<Cmpt>& v)
{
    return SymmTensor<Cmpt>
    (
        v.x()*v.x(), v.x()*v.y(), v.x()*v.z(),
                     v.y()*v.y(), v.y()*v.z(),
                                  v.z()*v.z()
    );
}
 
 
template<class Cmpt>
class outerProduct<SymmTensor<Cmpt>, Cmpt>
{
public:
 
    typedef SymmTensor<Cmpt> type;
};
 
template<class Cmpt>
class outerProduct<Cmpt, SymmTensor<Cmpt> >
{
public:
 
    typedef SymmTensor<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<SymmTensor<Cmpt>, SymmTensor<Cmpt> >
{
public:
 
    typedef Tensor<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<SymmTensor<Cmpt>, Vector<Cmpt> >
{
public:
 
    typedef Vector<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<Vector<Cmpt>, SymmTensor<Cmpt> >
{
public:
 
    typedef Vector<Cmpt> type;
};
 
 
template<class Cmpt>
class typeOfSum<SphericalTensor<Cmpt>, SymmTensor<Cmpt> >
{
public:
 
    typedef SymmTensor<Cmpt> type;
};
 
template<class Cmpt>
class typeOfSum<SymmTensor<Cmpt>, SphericalTensor<Cmpt> >
{
public:
 
    typedef SymmTensor<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<SphericalTensor<Cmpt>, SymmTensor<Cmpt> >
{
public:
 
    typedef SymmTensor<Cmpt> type;
};
 
template<class Cmpt>
class innerProduct<SymmTensor<Cmpt>, SphericalTensor<Cmpt> >
{
public:
 
    typedef SymmTensor<Cmpt> type;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// ************************************************************************* //