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590 lines
14 KiB
C++
590 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) 2011-2013 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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#include "Vector.H"
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#include "Tensor.H"
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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namespace Foam
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{
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// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
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template<class Cmpt>
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inline SymmTensor<Cmpt>::SymmTensor()
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{}
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template<class Cmpt>
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template<class Cmpt2>
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inline SymmTensor<Cmpt>::SymmTensor
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(
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const VectorSpace<SymmTensor<Cmpt2>, Cmpt2, 6>& vs
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)
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:
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VectorSpace<SymmTensor<Cmpt>, Cmpt, 6>(vs)
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{}
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template<class Cmpt>
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inline SymmTensor<Cmpt>::SymmTensor(const SphericalTensor<Cmpt>& st)
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{
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this->v_[XX] = st.ii(); this->v_[XY] = 0; this->v_[XZ] = 0;
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this->v_[YY] = st.ii(); this->v_[YZ] = 0;
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this->v_[ZZ] = st.ii();
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}
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template<class Cmpt>
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inline SymmTensor<Cmpt>::SymmTensor
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(
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const Cmpt txx, const Cmpt txy, const Cmpt txz,
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const Cmpt tyy, const Cmpt tyz,
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const Cmpt tzz
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)
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{
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this->v_[XX] = txx; this->v_[XY] = txy; this->v_[XZ] = txz;
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this->v_[YY] = tyy; this->v_[YZ] = tyz;
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this->v_[ZZ] = tzz;
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}
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template<class Cmpt>
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inline SymmTensor<Cmpt>::SymmTensor(Istream& is)
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:
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VectorSpace<SymmTensor<Cmpt>, Cmpt, 6>(is)
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{}
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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template<class Cmpt>
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inline const Cmpt& SymmTensor<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& SymmTensor<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& SymmTensor<Cmpt>::xz() const
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{
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return this->v_[XZ];
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}
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template<class Cmpt>
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inline const Cmpt& SymmTensor<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 const Cmpt& SymmTensor<Cmpt>::yz() const
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{
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return this->v_[YZ];
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}
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template<class Cmpt>
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inline const Cmpt& SymmTensor<Cmpt>::zz() const
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{
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return this->v_[ZZ];
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}
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template<class Cmpt>
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inline Cmpt& SymmTensor<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& SymmTensor<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& SymmTensor<Cmpt>::xz()
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{
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return this->v_[XZ];
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}
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template<class Cmpt>
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inline Cmpt& SymmTensor<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 Cmpt& SymmTensor<Cmpt>::yz()
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{
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return this->v_[YZ];
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}
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template<class Cmpt>
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inline Cmpt& SymmTensor<Cmpt>::zz()
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{
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return this->v_[ZZ];
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}
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template<class Cmpt>
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inline const SymmTensor<Cmpt>& SymmTensor<Cmpt>::T() const
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{
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return *this;
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}
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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template<class Cmpt>
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inline void SymmTensor<Cmpt>::operator=(const SphericalTensor<Cmpt>& st)
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{
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this->v_[XX] = st.ii(); this->v_[XY] = 0; this->v_[XZ] = 0;
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this->v_[YY] = st.ii(); this->v_[YZ] = 0;
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this->v_[ZZ] = st.ii();
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}
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// * * * * * * * * * * * * * * * Global Operators * * * * * * * * * * * * * //
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//- Hodge Dual operator (tensor -> vector)
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template<class Cmpt>
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inline Vector<Cmpt> operator*(const SymmTensor<Cmpt>& st)
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{
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return Vector<Cmpt>(st.yz(), -st.xz(), st.xy());
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}
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//- Inner-product between two symmetric tensors
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template<class Cmpt>
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inline Tensor<Cmpt>
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operator&(const SymmTensor<Cmpt>& st1, const SymmTensor<Cmpt>& st2)
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{
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return Tensor<Cmpt>
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(
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st1.xx()*st2.xx() + st1.xy()*st2.xy() + st1.xz()*st2.xz(),
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st1.xx()*st2.xy() + st1.xy()*st2.yy() + st1.xz()*st2.yz(),
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st1.xx()*st2.xz() + st1.xy()*st2.yz() + st1.xz()*st2.zz(),
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st1.xy()*st2.xx() + st1.yy()*st2.xy() + st1.yz()*st2.xz(),
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st1.xy()*st2.xy() + st1.yy()*st2.yy() + st1.yz()*st2.yz(),
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st1.xy()*st2.xz() + st1.yy()*st2.yz() + st1.yz()*st2.zz(),
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st1.xz()*st2.xx() + st1.yz()*st2.xy() + st1.zz()*st2.xz(),
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st1.xz()*st2.xy() + st1.yz()*st2.yy() + st1.zz()*st2.yz(),
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st1.xz()*st2.xz() + st1.yz()*st2.yz() + st1.zz()*st2.zz()
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);
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}
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//- Double-dot-product between a symmetric tensor and a symmetric tensor
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template<class Cmpt>
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inline Cmpt
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operator&&(const SymmTensor<Cmpt>& st1, const SymmTensor<Cmpt>& st2)
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{
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return
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(
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st1.xx()*st2.xx() + 2*st1.xy()*st2.xy() + 2*st1.xz()*st2.xz()
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+ st1.yy()*st2.yy() + 2*st1.yz()*st2.yz()
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+ st1.zz()*st2.zz()
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);
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}
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//- Inner-product between a symmetric tensor and a vector
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template<class Cmpt>
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inline Vector<Cmpt>
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operator&(const SymmTensor<Cmpt>& st, const Vector<Cmpt>& v)
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{
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return Vector<Cmpt>
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(
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st.xx()*v.x() + st.xy()*v.y() + st.xz()*v.z(),
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st.xy()*v.x() + st.yy()*v.y() + st.yz()*v.z(),
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st.xz()*v.x() + st.yz()*v.y() + st.zz()*v.z()
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);
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}
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//- Inner-product between a vector and a symmetric tensor
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template<class Cmpt>
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inline Vector<Cmpt>
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operator&(const Vector<Cmpt>& v, const SymmTensor<Cmpt>& st)
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{
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return Vector<Cmpt>
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(
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v.x()*st.xx() + v.y()*st.xy() + v.z()*st.xz(),
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v.x()*st.xy() + v.y()*st.yy() + v.z()*st.yz(),
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v.x()*st.xz() + v.y()*st.yz() + v.z()*st.zz()
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);
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}
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template<class Cmpt>
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inline Cmpt magSqr(const SymmTensor<Cmpt>& st)
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{
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return
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(
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magSqr(st.xx()) + 2*magSqr(st.xy()) + 2*magSqr(st.xz())
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+ magSqr(st.yy()) + 2*magSqr(st.yz())
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+ magSqr(st.zz())
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);
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}
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//- Return the trace of a symmetric tensor
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template<class Cmpt>
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inline Cmpt tr(const SymmTensor<Cmpt>& st)
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{
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return st.xx() + st.yy() + st.zz();
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}
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//- Return the spherical part of a symmetric tensor
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template<class Cmpt>
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inline SphericalTensor<Cmpt> sph(const SymmTensor<Cmpt>& st)
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{
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return (1.0/3.0)*tr(st);
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}
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//- Return the symmetric part of a symmetric tensor, i.e. itself
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template<class Cmpt>
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inline const SymmTensor<Cmpt>& symm(const SymmTensor<Cmpt>& st)
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{
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return st;
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}
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//- Return twice the symmetric part of a symmetric tensor
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template<class Cmpt>
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inline SymmTensor<Cmpt> twoSymm(const SymmTensor<Cmpt>& st)
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{
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return 2*st;
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}
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//- Return the deviatoric part of a symmetric tensor
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template<class Cmpt>
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inline SymmTensor<Cmpt> dev(const SymmTensor<Cmpt>& st)
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{
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return st - SphericalTensor<Cmpt>::oneThirdI*tr(st);
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}
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//- Return the deviatoric part of a symmetric tensor
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template<class Cmpt>
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inline SymmTensor<Cmpt> dev2(const SymmTensor<Cmpt>& st)
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{
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return st - SphericalTensor<Cmpt>::twoThirdsI*tr(st);
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}
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//- Return the determinant of a symmetric tensor
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template<class Cmpt>
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inline Cmpt det(const SymmTensor<Cmpt>& st)
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{
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return
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(
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st.xx()*st.yy()*st.zz() + st.xy()*st.yz()*st.xz()
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+ st.xz()*st.xy()*st.yz() - st.xx()*st.yz()*st.yz()
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- st.xy()*st.xy()*st.zz() - st.xz()*st.yy()*st.xz()
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);
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}
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//- Return the cofactor symmetric tensor of a symmetric tensor
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template<class Cmpt>
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inline SymmTensor<Cmpt> cof(const SymmTensor<Cmpt>& st)
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{
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return SymmTensor<Cmpt>
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(
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st.yy()*st.zz() - st.yz()*st.yz(),
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st.xz()*st.yz() - st.xy()*st.zz(),
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st.xy()*st.yz() - st.xz()*st.yy(),
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st.xx()*st.zz() - st.xz()*st.xz(),
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st.xy()*st.xz() - st.xx()*st.yz(),
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st.xx()*st.yy() - st.xy()*st.xy()
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);
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}
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//- Return the inverse of a symmetric tensor give the determinant
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template<class Cmpt>
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inline SymmTensor<Cmpt> inv(const SymmTensor<Cmpt>& st, const Cmpt detst)
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{
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return SymmTensor<Cmpt>
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(
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st.yy()*st.zz() - st.yz()*st.yz(),
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st.xz()*st.yz() - st.xy()*st.zz(),
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st.xy()*st.yz() - st.xz()*st.yy(),
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st.xx()*st.zz() - st.xz()*st.xz(),
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st.xy()*st.xz() - st.xx()*st.yz(),
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st.xx()*st.yy() - st.xy()*st.xy()
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)/detst;
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}
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//- Return the inverse of a symmetric tensor
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template<class Cmpt>
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inline SymmTensor<Cmpt> inv(const SymmTensor<Cmpt>& st)
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{
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return inv(st, det(st));
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}
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//- Return the 1st invariant of a symmetric tensor
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template<class Cmpt>
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inline Cmpt invariantI(const SymmTensor<Cmpt>& st)
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{
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return tr(st);
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}
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//- Return the 2nd invariant of a symmetric tensor
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template<class Cmpt>
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inline Cmpt invariantII(const SymmTensor<Cmpt>& st)
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{
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return
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(
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0.5*sqr(tr(st))
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- 0.5*
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(
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st.xx()*st.xx() + st.xy()*st.xy() + st.xz()*st.xz()
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+ st.xy()*st.xy() + st.yy()*st.yy() + st.yz()*st.yz()
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+ st.xz()*st.xz() + st.yz()*st.yz() + st.zz()*st.zz()
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)
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);
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}
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//- Return the 3rd invariant of a symmetric tensor
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template<class Cmpt>
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inline Cmpt invariantIII(const SymmTensor<Cmpt>& st)
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{
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return det(st);
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}
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template<class Cmpt>
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inline SymmTensor<Cmpt>
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operator+(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
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{
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return SymmTensor<Cmpt>
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(
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spt1.ii() + st2.xx(), st2.xy(), st2.xz(),
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spt1.ii() + st2.yy(), st2.yz(),
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spt1.ii() + st2.zz()
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);
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}
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template<class Cmpt>
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inline SymmTensor<Cmpt>
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operator+(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
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{
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return SymmTensor<Cmpt>
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(
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st1.xx() + spt2.ii(), st1.xy(), st1.xz(),
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st1.yy() + spt2.ii(), st1.yz(),
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st1.zz() + spt2.ii()
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);
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}
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template<class Cmpt>
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inline SymmTensor<Cmpt>
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operator-(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
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{
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return SymmTensor<Cmpt>
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(
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spt1.ii() - st2.xx(), -st2.xy(), -st2.xz(),
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spt1.ii() - st2.yy(), -st2.yz(),
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spt1.ii() - st2.zz()
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);
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}
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template<class Cmpt>
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inline SymmTensor<Cmpt>
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operator-(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
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{
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return SymmTensor<Cmpt>
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(
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st1.xx() - spt2.ii(), st1.xy(), st1.xz(),
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st1.yy() - spt2.ii(), st1.yz(),
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st1.zz() - spt2.ii()
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);
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}
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//- Inner-product between a spherical symmetric tensor and a symmetric tensor
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template<class Cmpt>
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inline SymmTensor<Cmpt>
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operator&(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
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{
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return SymmTensor<Cmpt>
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(
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spt1.ii()*st2.xx(), spt1.ii()*st2.xy(), spt1.ii()*st2.xz(),
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spt1.ii()*st2.yy(), spt1.ii()*st2.yz(),
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spt1.ii()*st2.zz()
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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 SymmTensor<Cmpt>
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operator&(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
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{
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return SymmTensor<Cmpt>
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(
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st1.xx()*spt2.ii(), st1.xy()*spt2.ii(), st1.xz()*spt2.ii(),
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st1.yy()*spt2.ii(), st1.yz()*spt2.ii(),
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st1.zz()*spt2.ii()
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);
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}
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//- Double-dot-product between a spherical tensor and a symmetric tensor
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template<class Cmpt>
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inline Cmpt
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operator&&(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
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{
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return(spt1.ii()*st2.xx() + spt1.ii()*st2.yy() + spt1.ii()*st2.zz());
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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 SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
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{
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return(st1.xx()*spt2.ii() + st1.yy()*spt2.ii() + st1.zz()*spt2.ii());
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}
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template<class Cmpt>
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inline SymmTensor<Cmpt> sqr(const Vector<Cmpt>& v)
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{
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return SymmTensor<Cmpt>
|
|
(
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v.x()*v.x(), v.x()*v.y(), v.x()*v.z(),
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v.y()*v.y(), v.y()*v.z(),
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v.z()*v.z()
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);
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}
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template<class Cmpt>
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class outerProduct<SymmTensor<Cmpt>, Cmpt>
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{
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public:
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|
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typedef SymmTensor<Cmpt> type;
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};
|
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template<class Cmpt>
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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
|
|
|
|
// ************************************************************************* //
|