132 lines
4.9 KiB
TeX
132 lines
4.9 KiB
TeX
%-----------------------------------------------------------------------------
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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 | www.openfoam.com
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% \\/ M anipulation |
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%------------------------------------------------------------------------------
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% Copyright (C) 2011 OpenFOAM Foundation
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%------------------------------------------------------------------------------
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% License
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% This file is part of OpenFOAM.
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%
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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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%
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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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%
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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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% LaTeX Style file
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% tensorOperator.sty
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%
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% Description
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% Standard OpenFOAM LaTeX macros for typesetting tensor algebra.
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%
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%------------------------------------------------------------------------------
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% tensor style
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% ~~~~~~~~~~~~
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\renewcommand{\vec}[1] {\ensuremath{\mathbf #1}}
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\newcommand{\gvec}[1] {\ensuremath{\mbox{\boldmath$\bf#1$}}}
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% products
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% ~~~~~~~~
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\newcommand{\anyprod}{\star}
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\newcommand{\cprod} {\times}
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\newcommand{\dprod} {\,{\scriptscriptstyle \stackrel{\bullet}{{}}}\,}
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\newcommand{\ddprod} {\,{\scriptscriptstyle \stackrel{\bullet}{\bullet}}\,}
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\newcommand{\tdprod} {\,{\scriptscriptstyle \stackrel{3}{\bullet}}\,}
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\newcommand{\tprod} {\,{\scriptscriptstyle \stackrel{\otimes}{{}}}\,}
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% operations
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% ~~~~~~~~~~
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\newcommand{\adj} {\ensuremath{\operatorname{adj}}}
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\newcommand{\cof} {\ensuremath{\operatorname{cof}}}
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\newcommand{\diag} {\ensuremath{\operatorname{diag}}}
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\newcommand{\dev} {\ensuremath{\operatorname{dev}}}
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\newcommand{\Hodge} {\ensuremath{\operatorname{\stackrel{\displaystyle \ast}{}}}}
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\newcommand{\hyd} {\ensuremath{\operatorname{hyd}}}
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%\renewcommand{\max} {\ensuremath{\operatorname{max}}}
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%\renewcommand{\min} {\ensuremath{\operatorname{min}}}
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\newcommand{\inv} {\ensuremath{\operatorname{inv}}}
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\newcommand{\sym} {\ensuremath{\operatorname{symm}}} % symm ?
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\newcommand{\skw} {\ensuremath{\operatorname{skew}}} % skew already defined
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\newcommand{\tr} {\ensuremath{\operatorname{tr}}}
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\newcommand{\trans}[1] {\ensuremath{#1^{\operatorname{T}}}}
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\newcommand{\symm}[1] {\ensuremath{frac{1}{2}\left(#1 + {#1}^T\right)}}
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% alternative tensor operators for hypersonics etc.
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% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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\newcommand{\devs}[1] {\overset{\scriptscriptstyle\circ}{#1}}
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%\newcommand{\trans}[1] {\ensuremath{#1^{\operatorname{T}}}}
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\newcommand{\symms}[1] {\overleftrightarrow{#1}}
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\newlength{\skewslength}
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\newlength{\skewsheight}
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\newcommand{\skews}[1]{
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\settowidth{\skewslength}{#1}%
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\settoheight{\skewsheight}{#1}%
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\addtolength{\skewsheight}{0.4mm}%
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{\overleftrightarrow{#1}\hspace{-.5\skewslength}%
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\rule[\skewsheight]{.4pt}{1.4mm}
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\hspace{.5\skewslength}%
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}}
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%\newcommand{\skew}[1] {\ensuremath{#1^{\operatorname{A}}}}
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% spatial derivatives
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% ~~~~~~~~~~~~~~~~~~~
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\newcommand{\curl}{\ensuremath{\nabla\cprod}}
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\renewcommand{\div} {\ensuremath{\nabla\dprod}}
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\newcommand{\grad}{\ensuremath{\nabla}}
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\newcommand{\laplacian}{\ensuremath{\nabla^{2}}}
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% temporal derivatives
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% ~~~~~~~~~~~~~~~~~~~~
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\newcommand{\ddt}[1] {\ensuremath{\frac{\partial #1}{\partial t }}}
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\newcommand{\DDt}[1] {\ensuremath{\frac{D #1}{D t}}}
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\newcommand{\DpDt}[2] {\ensuremath{\frac{d_{#1} #2}{d t }}}
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\newcommand{\dsdts}[1] {\ensuremath{\frac{\partial ^2 #1}{\partial t^2}}}
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\newcommand{\rate}[1] {\ensuremath{\dot{#1}}}
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\newcommand{\genDer}{\mathcal{L}}
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% time average symbols
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% ~~~~~~~~~~~~~~~~~~~~
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\newcommand{\av}[1] {\ensuremath{\overline{#1}}}
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\newcommand{\corrtwo}[2] {{\dwea{\dprime{#1} \dprime{#2}}}}
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\newcommand{\curly}[1] {{\cal #1}}
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\newcommand{\dprime}[1] {\ensuremath{{#1}^{^{\prime \prime}}}}
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\newcommand{\dwea}[1] {\ensuremath{\widetilde{#1}}}
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\newcommand{\dweafluc}[1] {\ensuremath{\dprime{#1}}}
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\newcommand{\fluc}[1] {\ensuremath{#1^{\prime}}}
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% index style
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% ~~~~~~~~~~~
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\newcommand{\veci}[2][i] {\ensuremath{#2_{#1}}}
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\newcommand{\teni}[2][ij] {\ensuremath{#2_{#1}}}
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\newcommand{\tenTi}[2][ji] {\ensuremath{#2_{#1}}}
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% index operations
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% ~~~~~~~~~~~~~~~~
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\newcommand{\deltai}[1] {\ensuremath{\partial_{#1}}}
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% Sub-subscripts
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% ~~~~~~~~~~~~~~
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\newcommand{\eff} {{\scriptscriptstyle e\!f\!\!f\!}}
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% unknown use
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% ~~~~~~~~~~~
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%\font\bigtenrm=cmr12 scaled 1200
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%\newcommand{\eexp}[1]{{\hbox{$\textfont1=\bigtenrm e$}}^{\raise3pt
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%\hbox{$#1$}}}
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% ------------------------------------------------------------------------------
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