symmTransform.H

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    Copyright (C) 2011 OpenFOAM Foundation
    Copyright (C) 2023 OpenCFD Ltd.
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License
    This file is part of OpenFOAM.

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InNamespace
    Foam

Description
    3D symmetric tensor transformation operations.

\*---------------------------------------------------------------------------*/

#ifndef Foam_symmTransform_H
#define Foam_symmTransform_H

#include "transform.H"

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

namespace Foam
{

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

//- No-op rotational transform for base types
template<class T>
constexpr typename std::enable_if<std::is_arithmetic<T>::value, T>::type
transform(const symmTensor&, const T val)
{
    return val;
}


//- No-op rotational transform for spherical tensor
template<class Cmpt>
inline SphericalTensor<Cmpt> transform
(
    const symmTensor&,
    const SphericalTensor<Cmpt>& val
)
{
    return val;
}


//- Use rotational tensor to transform a vector
//  Same as (rot & v)
template<class Cmpt>
inline Vector<Cmpt> transform(const symmTensor& tt, const Vector<Cmpt>& v)
{
    return tt & v;
}


//- Use rotational tensor to transform a tensor.
//  Same as (rot & input & rot.T())
template<class Cmpt>
inline Tensor<Cmpt> transform(const symmTensor& stt, const Tensor<Cmpt>& t)
{
    return Tensor<Cmpt>
    (
        // xx:
        (stt.xx()*t.xx() + stt.xy()*t.yx() + stt.xz()*t.zx())*stt.xx()
      + (stt.xx()*t.xy() + stt.xy()*t.yy() + stt.xz()*t.zy())*stt.xy()
      + (stt.xx()*t.xz() + stt.xy()*t.yz() + stt.xz()*t.zz())*stt.xz(),

        // xy:
        (stt.xx()*t.xx() + stt.xy()*t.yx() + stt.xz()*t.zx())*stt.xy()
      + (stt.xx()*t.xy() + stt.xy()*t.yy() + stt.xz()*t.zy())*stt.yy()
      + (stt.xx()*t.xz() + stt.xy()*t.yz() + stt.xz()*t.zz())*stt.yz(),

        // xz:
        (stt.xx()*t.xx() + stt.xy()*t.yx() + stt.xz()*t.zx())*stt.xz()
      + (stt.xx()*t.xy() + stt.xy()*t.yy() + stt.xz()*t.zy())*stt.yz()
      + (stt.xx()*t.xz() + stt.xy()*t.yz() + stt.xz()*t.zz())*stt.zz(),

        // yx:
        (stt.xy()*t.xx() + stt.yy()*t.yx() + stt.yz()*t.zx())*stt.xx()
      + (stt.xy()*t.xy() + stt.yy()*t.yy() + stt.yz()*t.zy())*stt.xy()
      + (stt.xy()*t.xz() + stt.yy()*t.yz() + stt.yz()*t.zz())*stt.xz(),

        // yy:
        (stt.xy()*t.xx() + stt.yy()*t.yx() + stt.yz()*t.zx())*stt.xy()
      + (stt.xy()*t.xy() + stt.yy()*t.yy() + stt.yz()*t.zy())*stt.yy()
      + (stt.xy()*t.xz() + stt.yy()*t.yz() + stt.yz()*t.zz())*stt.yz(),

        // yz:
        (stt.xy()*t.xx() + stt.yy()*t.yx() + stt.yz()*t.zx())*stt.xz()
      + (stt.xy()*t.xy() + stt.yy()*t.yy() + stt.yz()*t.zy())*stt.yz()
      + (stt.xy()*t.xz() + stt.yy()*t.yz() + stt.yz()*t.zz())*stt.zz(),

        // zx:
        (stt.xz()*t.xx() + stt.yz()*t.yx() + stt.zz()*t.zx())*stt.xx()
      + (stt.xz()*t.xy() + stt.yz()*t.yy() + stt.zz()*t.zy())*stt.xy()
      + (stt.xz()*t.xz() + stt.yz()*t.yz() + stt.zz()*t.zz())*stt.xz(),

        // zy:
        (stt.xz()*t.xx() + stt.yz()*t.yx() + stt.zz()*t.zx())*stt.xy()
      + (stt.xz()*t.xy() + stt.yz()*t.yy() + stt.zz()*t.zy())*stt.yy()
      + (stt.xz()*t.xz() + stt.yz()*t.yz() + stt.zz()*t.zz())*stt.yz(),

        // zz:
        (stt.xz()*t.xx() + stt.yz()*t.yx() + stt.zz()*t.zx())*stt.xz()
      + (stt.xz()*t.xy() + stt.yz()*t.yy() + stt.zz()*t.zy())*stt.yz()
      + (stt.xz()*t.xz() + stt.yz()*t.yz() + stt.zz()*t.zz())*stt.zz()
    );
}


//- Use rotational tensor to transform a symmTensor
//  Same as (rot & input & rot.T())
template<class Cmpt>
inline SymmTensor<Cmpt> transform
(
    const symmTensor& stt,
    const SymmTensor<Cmpt>& st
)
{
    return SymmTensor<Cmpt>
    (
        // xx:
        (stt.xx()*st.xx() + stt.xy()*st.xy() + stt.xz()*st.xz())*stt.xx()
      + (stt.xx()*st.xy() + stt.xy()*st.yy() + stt.xz()*st.yz())*stt.xy()
      + (stt.xx()*st.xz() + stt.xy()*st.yz() + stt.xz()*st.zz())*stt.xz(),

        // xy:
        (stt.xx()*st.xx() + stt.xy()*st.xy() + stt.xz()*st.xz())*stt.xy()
      + (stt.xx()*st.xy() + stt.xy()*st.yy() + stt.xz()*st.yz())*stt.yy()
      + (stt.xx()*st.xz() + stt.xy()*st.yz() + stt.xz()*st.zz())*stt.yz(),

        // xz:
        (stt.xx()*st.xx() + stt.xy()*st.xy() + stt.xz()*st.xz())*stt.xz()
      + (stt.xx()*st.xy() + stt.xy()*st.yy() + stt.xz()*st.yz())*stt.yz()
      + (stt.xx()*st.xz() + stt.xy()*st.yz() + stt.xz()*st.zz())*stt.zz(),

        // yy:
        (stt.xy()*st.xx() + stt.yy()*st.xy() + stt.yz()*st.xz())*stt.xy()
      + (stt.xy()*st.xy() + stt.yy()*st.yy() + stt.yz()*st.yz())*stt.yy()
      + (stt.xy()*st.xz() + stt.yy()*st.yz() + stt.yz()*st.zz())*stt.yz(),

        // yz:
        (stt.xy()*st.xx() + stt.yy()*st.xy() + stt.yz()*st.xz())*stt.xz()
      + (stt.xy()*st.xy() + stt.yy()*st.yy() + stt.yz()*st.yz())*stt.yz()
      + (stt.xy()*st.xz() + stt.yy()*st.yz() + stt.yz()*st.zz())*stt.zz(),

        // zz:
        (stt.xz()*st.xx() + stt.yz()*st.xy() + stt.zz()*st.xz())*stt.xz()
      + (stt.xz()*st.xy() + stt.yz()*st.yy() + stt.zz()*st.yz())*stt.yz()
      + (stt.xz()*st.xz() + stt.yz()*st.yz() + stt.zz()*st.zz())*stt.zz()
    );
}


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

template<>
inline sphericalTensor transformMask<sphericalTensor>(const symmTensor& st)
{
    return sph(st);
}


template<>
inline symmTensor transformMask<symmTensor>(const symmTensor& st)
{
    return st;
}


template<>
inline tensor transformMask<tensor>(const symmTensor& st)
{
    return st;
}


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

} // End namespace Foam

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

#endif

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