symmTransform.H

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/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
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    \\  /    A nd           | www.openfoam.com
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-------------------------------------------------------------------------------
    Copyright (C) 2011 OpenFOAM Foundation
    Copyright (C) 2023-2025 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.
 
    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
    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
    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
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 std::enable_if_t<std::is_arithmetic_v<T>, T>
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
 
// ************************************************************************* //