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672 lines
14 KiB
C++
672 lines
14 KiB
C++
/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / A nd | Copyright (C) 2011-2016 OpenFOAM Foundation
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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This file is part of OpenFOAM.
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OpenFOAM is free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received a copy of the GNU General Public License
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along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
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\*---------------------------------------------------------------------------*/
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// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
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template<class Cmpt>
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inline Foam::Tensor2D<Cmpt>::Tensor2D()
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{}
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template<class Cmpt>
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inline Foam::Tensor2D<Cmpt>::Tensor2D(const Foam::zero)
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:
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Tensor2D::msType(Zero)
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{}
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template<class Cmpt>
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inline Foam::Tensor2D<Cmpt>::Tensor2D
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(
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const VectorSpace<Tensor2D<Cmpt>, Cmpt, 4>& vs
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)
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:
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Tensor2D::msType(vs)
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{}
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template<class Cmpt>
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inline Foam::Tensor2D<Cmpt>::Tensor2D(const SymmTensor2D<Cmpt>& st)
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{
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this->v_[XX] = st.xx(); this->v_[XY] = st.xy();
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this->v_[YX] = st.xy(); this->v_[YY] = st.yy();
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}
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template<class Cmpt>
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inline Foam::Tensor2D<Cmpt>::Tensor2D(const SphericalTensor2D<Cmpt>& st)
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{
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this->v_[XX] = st.ii(); this->v_[XY] = 0;
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this->v_[YX] = 0; this->v_[YY] = st.ii();
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}
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template<class Cmpt>
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inline Foam::Tensor2D<Cmpt>::Tensor2D
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(
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const Vector2D<Cmpt>& x,
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const Vector2D<Cmpt>& y
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)
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{
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this->v_[XX] = x.x(); this->v_[XY] = x.y();
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this->v_[YX] = y.x(); this->v_[YY] = y.y();
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}
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template<class Cmpt>
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inline Foam::Tensor2D<Cmpt>::Tensor2D
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(
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const Cmpt txx, const Cmpt txy,
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const Cmpt tyx, const Cmpt tyy
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)
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{
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this->v_[XX] = txx; this->v_[XY] = txy;
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this->v_[YX] = tyx; this->v_[YY] = tyy;
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}
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template<class Cmpt>
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inline Foam::Tensor2D<Cmpt>::Tensor2D(Istream& is)
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:
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Tensor2D::msType(is)
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{}
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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template<class Cmpt>
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inline Foam::Vector2D<Cmpt> Foam::Tensor2D<Cmpt>::x() const
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{
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return Vector2D<Cmpt>(this->v_[XX], this->v_[XY]);
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}
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template<class Cmpt>
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inline Foam::Vector2D<Cmpt> Foam::Tensor2D<Cmpt>::y() const
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{
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return Vector2D<Cmpt>(this->v_[YX], this->v_[YY]);
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}
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template<class Cmpt>
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inline const Cmpt& Foam::Tensor2D<Cmpt>::xx() const
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{
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return this->v_[XX];
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}
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template<class Cmpt>
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inline const Cmpt& Foam::Tensor2D<Cmpt>::xy() const
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{
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return this->v_[XY];
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}
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template<class Cmpt>
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inline const Cmpt& Foam::Tensor2D<Cmpt>::yx() const
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{
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return this->v_[YX];
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}
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template<class Cmpt>
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inline const Cmpt& Foam::Tensor2D<Cmpt>::yy() const
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{
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return this->v_[YY];
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}
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template<class Cmpt>
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inline Cmpt& Foam::Tensor2D<Cmpt>::xx()
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{
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return this->v_[XX];
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}
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template<class Cmpt>
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inline Cmpt& Foam::Tensor2D<Cmpt>::xy()
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{
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return this->v_[XY];
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}
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template<class Cmpt>
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inline Cmpt& Foam::Tensor2D<Cmpt>::yx()
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{
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return this->v_[YX];
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}
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template<class Cmpt>
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inline Cmpt& Foam::Tensor2D<Cmpt>::yy()
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{
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return this->v_[YY];
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}
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template<class Cmpt>
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inline Foam::Tensor2D<Cmpt> Foam::Tensor2D<Cmpt>::T() const
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{
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return Tensor2D<Cmpt>
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(
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xx(), yx(),
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xy(), yy()
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);
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}
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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template<class Cmpt>
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inline void Foam::Tensor2D<Cmpt>::operator=(const SymmTensor2D<Cmpt>& st)
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{
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this->v_[XX] = st.xx(); this->v_[XY] = st.xy();
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this->v_[YX] = st.xy(); this->v_[YY] = st.yy();
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}
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template<class Cmpt>
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inline void Foam::Tensor2D<Cmpt>::operator=(const SphericalTensor2D<Cmpt>& st)
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{
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this->v_[XX] = st.ii(); this->v_[XY] = 0;
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this->v_[YX] = 0; this->v_[YY] = st.ii();
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}
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// * * * * * * * * * * * * * * * Member Operators * * * * * * * * * * * * * //
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template<class Cmpt>
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inline void Foam::Tensor2D<Cmpt>::operator=(const Foam::zero)
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{
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Tensor2D::msType::operator=(Zero);
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}
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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namespace Foam
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{
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// * * * * * * * * * * * * * * * Global Operators * * * * * * * * * * * * * //
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//- Inner-product between two tensors
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template<class Cmpt>
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inline typename innerProduct<Tensor2D<Cmpt>, Tensor2D<Cmpt>>::type
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operator&(const Tensor2D<Cmpt>& t1, const Tensor2D<Cmpt>& t2)
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{
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return Tensor2D<Cmpt>
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(
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t1.xx()*t2.xx() + t1.xy()*t2.yx(),
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t1.xx()*t2.xy() + t1.xy()*t2.yy(),
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t1.yx()*t2.xx() + t1.yy()*t2.yx(),
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t1.yx()*t2.xy() + t1.yy()*t2.yy()
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);
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}
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//- Inner-product between a tensor and a vector
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template<class Cmpt>
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inline typename innerProduct<Tensor2D<Cmpt>, Vector2D<Cmpt>>::type
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operator&(const Tensor2D<Cmpt>& t, const Vector2D<Cmpt>& v)
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{
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return Vector2D<Cmpt>
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(
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t.xx()*v.x() + t.xy()*v.y(),
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t.yx()*v.x() + t.yy()*v.y()
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);
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}
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//- Inner-product between a vector and a tensor
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template<class Cmpt>
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inline typename innerProduct<Vector2D<Cmpt>, Tensor2D<Cmpt>>::type
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operator&(const Vector2D<Cmpt>& v, const Tensor2D<Cmpt>& t)
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{
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return Vector2D<Cmpt>
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(
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v.x()*t.xx() + v.y()*t.yx(),
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v.x()*t.xy() + v.y()*t.yy()
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);
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}
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//- Outer-product between two vectors
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template<class Cmpt>
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inline typename outerProduct<Vector2D<Cmpt>, Vector2D<Cmpt>>::type
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operator*(const Vector2D<Cmpt>& v1, const Vector2D<Cmpt>& v2)
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{
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return Tensor2D<Cmpt>
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(
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v1.x()*v2.x(), v1.x()*v2.y(),
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v1.y()*v2.x(), v1.y()*v2.y()
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);
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}
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//- Return the trace of a tensor
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template<class Cmpt>
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inline Cmpt tr(const Tensor2D<Cmpt>& t)
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{
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return t.xx() + t.yy();
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}
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//- Return the spherical part of a tensor
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template<class Cmpt>
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inline SphericalTensor2D<Cmpt> sph(const Tensor2D<Cmpt>& t)
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{
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return 0.5*tr(t);
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}
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//- Return the symmetric part of a tensor
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template<class Cmpt>
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inline SymmTensor2D<Cmpt> symm(const Tensor2D<Cmpt>& t)
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{
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return SymmTensor2D<Cmpt>
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(
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t.xx(), 0.5*(t.xy() + t.yx()),
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t.yy()
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);
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}
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//- Return the twice the symmetric part of a tensor
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template<class Cmpt>
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inline SymmTensor2D<Cmpt> twoSymm(const Tensor2D<Cmpt>& t)
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{
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return SymmTensor2D<Cmpt>
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(
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t.xx() + t.xx(), t.xy() + t.yx(),
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t.yy() + t.yy()
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);
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}
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//- Return the skew-symmetric part of a tensor
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template<class Cmpt>
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inline Tensor2D<Cmpt> skew(const Tensor2D<Cmpt>& t)
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{
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return Tensor2D<Cmpt>
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(
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0.0, 0.5*(t.xy() - t.yx()),
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0.5*(t.yx() - t.xy()), 0.0
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);
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}
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//- Return the deviatoric part of a tensor
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template<class Cmpt>
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inline Tensor2D<Cmpt> dev(const Tensor2D<Cmpt>& t)
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{
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return t - SphericalTensor2D<Cmpt>::oneThirdI*tr(t);
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}
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//- Return the deviatoric part of a tensor
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template<class Cmpt>
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inline Tensor2D<Cmpt> dev2(const Tensor2D<Cmpt>& t)
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{
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return t - SphericalTensor2D<Cmpt>::twoThirdsI*tr(t);
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}
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//- Return the determinant of a tensor
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template<class Cmpt>
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inline Cmpt det(const Tensor2D<Cmpt>& t)
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{
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return(t.xx()*t.yy() - t.xy()*t.yx());
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}
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//- Return the cofactor tensor of a tensor
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template<class Cmpt>
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inline Tensor2D<Cmpt> cof(const Tensor2D<Cmpt>& t)
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{
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return Tensor2D<Cmpt>
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(
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t.yy(), -t.xy(),
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-t.yx(), t.xx()
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);
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}
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//- Return the inverse of a tensor given the determinant
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template<class Cmpt>
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inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t, const Cmpt dett)
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{
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return cof(t)/dett;
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}
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//- Return the inverse of a tensor
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template<class Cmpt>
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inline Tensor2D<Cmpt> inv(const Tensor2D<Cmpt>& t)
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{
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return inv(t, det(t));
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}
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//- Return the 1st invariant of a tensor
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template<class Cmpt>
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inline Cmpt invariantI(const Tensor2D<Cmpt>& t)
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{
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return tr(t);
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}
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//- Return the 2nd invariant of a tensor
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template<class Cmpt>
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inline Cmpt invariantII(const Tensor2D<Cmpt>& t)
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{
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return
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(
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0.5*sqr(tr(t))
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- 0.5*
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(
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t.xx()*t.xx() + t.xy()*t.xy()
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+ t.yx()*t.yx() + t.yy()*t.yy()
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)
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);
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}
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//- Return the 3rd invariant of a tensor
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template<class Cmpt>
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inline Cmpt invariantIII(const Tensor2D<Cmpt>& t)
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{
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return det(t);
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}
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// * * * * * * * * * Mixed Tensor SphericalTensor Operators * * * * * * * * //
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template<class Cmpt>
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inline Tensor2D<Cmpt>
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operator+(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
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{
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return Tensor2D<Cmpt>
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(
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st1.ii() + t2.xx(), t2.xy(),
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t2.yx(), st1.ii() + t2.yy()
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);
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}
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template<class Cmpt>
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inline Tensor2D<Cmpt>
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operator+(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
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{
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return Tensor2D<Cmpt>
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(
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t1.xx() + st2.ii(), t1.xy(),
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t1.yx(), t1.yy() + st2.ii()
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);
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}
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template<class Cmpt>
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inline Tensor2D<Cmpt>
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operator-(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
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{
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return Tensor2D<Cmpt>
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(
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st1.ii() - t2.xx(), -t2.xy(),
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-t2.yx(), st1.ii() - t2.yy()
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);
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}
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template<class Cmpt>
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inline Tensor2D<Cmpt>
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operator-(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
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{
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return Tensor2D<Cmpt>
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(
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t1.xx() - st2.ii(), t1.xy(),
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t1.yx(), t1.yy() - st2.ii()
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);
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}
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//- Inner-product between a spherical tensor and a tensor
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template<class Cmpt>
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inline Tensor2D<Cmpt>
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operator&(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
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{
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return Tensor2D<Cmpt>
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(
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st1.ii()*t2.xx(),
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st1.ii()*t2.xy(),
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st1.ii()*t2.yx(),
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st1.ii()*t2.yy()
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);
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}
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//- Inner-product between a tensor and a spherical tensor
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template<class Cmpt>
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inline Tensor2D<Cmpt>
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operator&(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
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{
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return Tensor2D<Cmpt>
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(
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t1.xx()*st2.ii(),
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t1.xy()*st2.ii(),
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t1.yx()*st2.ii(),
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t1.yy()*st2.ii()
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);
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}
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//- Double-dot-product between a spherical tensor and a tensor
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template<class Cmpt>
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inline Cmpt
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operator&&(const SphericalTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
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{
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return(st1.ii()*t2.xx() + st1.ii()*t2.yy());
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}
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//- Double-dot-product between a tensor and a spherical tensor
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template<class Cmpt>
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inline Cmpt
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operator&&(const Tensor2D<Cmpt>& t1, const SphericalTensor2D<Cmpt>& st2)
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|
{
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return(t1.xx()*st2.ii() + t1.yy()*st2.ii());
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}
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|
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// * * * * * * * * * * Mixed Tensor SymmTensor Operators * * * * * * * * * * //
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template<class Cmpt>
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inline Tensor2D<Cmpt>
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operator+(const SymmTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
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{
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return Tensor2D<Cmpt>
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(
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st1.xx() + t2.xx(), st1.xy() + t2.xy(),
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st1.xy() + t2.yx(), st1.yy() + t2.yy()
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);
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}
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template<class Cmpt>
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inline Tensor2D<Cmpt>
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operator+(const Tensor2D<Cmpt>& t1, const SymmTensor2D<Cmpt>& st2)
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{
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return Tensor2D<Cmpt>
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(
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t1.xx() + st2.xx(), t1.xy() + st2.xy(),
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t1.yx() + st2.xy(), t1.yy() + st2.yy()
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);
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}
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template<class Cmpt>
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inline Tensor2D<Cmpt>
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operator-(const SymmTensor2D<Cmpt>& st1, const Tensor2D<Cmpt>& t2)
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{
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return Tensor2D<Cmpt>
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|
(
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st1.xx() - t2.xx(), st1.xy() - t2.xy(),
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st1.xy() - t2.yx(), st1.yy() - t2.yy()
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);
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}
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|
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template<class Cmpt>
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inline Tensor2D<Cmpt>
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operator-(const Tensor2D<Cmpt>& t1, const SymmTensor2D<Cmpt>& st2)
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{
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return Tensor2D<Cmpt>
|
|
(
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t1.xx() - st2.xx(), t1.xy() - st2.xy(),
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t1.yx() - st2.xy(), t1.yy() - st2.yy()
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);
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}
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|
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//- Inner-product between a spherical tensor and a tensor
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template<class Cmpt>
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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
|
|
|
|
// ************************************************************************* //
|