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OpenFOAM-dev / data /doc /Doxygen /Macros /tensorOperator.sty

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%------------------------------------------------------------------------------
% =========                 |
% \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
%  \\    /   O peration     | Website:  https://openfoam.org
%   \\  /    A nd           | Copyright (C) 2011-2018 OpenFOAM Foundation
%    \\/     M anipulation  |
%------------------------------------------------------------------------------
% 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/>.
%
% LaTeX Style file
%     tensorOperator.sty
%
% Description
%     Standard OpenFOAM LaTeX macros for typesetting tensor algebra.
%
%------------------------------------------------------------------------------

% tensor style
% ~~~~~~~~~~~~
\renewcommand{\vec}[1] {\ensuremath{\mathbf #1}}
\newcommand{\gvec}[1] {\ensuremath{\mbox{\boldmath$\bf#1$}}}

% products
% ~~~~~~~~
\newcommand{\anyprod}{\star}
\newcommand{\cprod} {\times}
\newcommand{\dprod} {\,{\scriptscriptstyle \stackrel{\bullet}{{}}}\,}
\newcommand{\ddprod} {\,{\scriptscriptstyle \stackrel{\bullet}{\bullet}}\,}
\newcommand{\tdprod} {\,{\scriptscriptstyle \stackrel{3}{\bullet}}\,}
\newcommand{\tprod} {\,{\scriptscriptstyle \stackrel{\otimes}{{}}}\,}

% operations
% ~~~~~~~~~~
\newcommand{\adj} {\ensuremath{\operatorname{adj}}}
\newcommand{\cof} {\ensuremath{\operatorname{cof}}}
\newcommand{\diag} {\ensuremath{\operatorname{diag}}}
\newcommand{\dev} {\ensuremath{\operatorname{dev}}}

\newcommand{\Hodge} {\ensuremath{\operatorname{\stackrel{\displaystyle \ast}{}}}}
\newcommand{\hyd} {\ensuremath{\operatorname{hyd}}}
\renewcommand{\max} {\ensuremath{\operatorname{max}}}
\renewcommand{\min} {\ensuremath{\operatorname{min}}}
\newcommand{\inv} {\ensuremath{\operatorname{inv}}}
\newcommand{\sym} {\ensuremath{\operatorname{symm}}}    % symm ?
\newcommand{\skw} {\ensuremath{\operatorname{skew}}}    % skew already defined
\newcommand{\tr} {\ensuremath{\operatorname{tr}}}
\newcommand{\trans}[1] {\ensuremath{#1^{\operatorname{T}}}}

% alternative tensor operators for hypersonics etc.
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
\newcommand{\devs}[1] {\overset{\scriptscriptstyle\circ}{#1}}
%\newcommand{\trans}[1] {\ensuremath{#1^{\operatorname{T}}}}
\newcommand{\symms}[1] {\overleftrightarrow{#1}}
\newlength{\skewslength}
\newlength{\skewsheight}
\newcommand{\skews}[1]{
    \settowidth{\skewslength}{#1}%
    \settoheight{\skewsheight}{#1}%
    \addtolength{\skewsheight}{0.4mm}%
    {\overleftrightarrow{#1}\hspace{-.5\skewslength}%
    \rule[\skewsheight]{.4pt}{1.4mm}
    \hspace{.5\skewslength}%
}}
%\newcommand{\skew}[1] {\ensuremath{#1^{\operatorname{A}}}}

% spatial derivatives
% ~~~~~~~~~~~~~~~~~~~
\newcommand{\curl}{\ensuremath{\nabla\cprod}}
\renewcommand{\div} {\ensuremath{\nabla\dprod}}
\newcommand{\grad}{\ensuremath{\nabla}}
\newcommand{\laplacian}{\ensuremath{\nabla^{2}}}

% temporal derivatives
% ~~~~~~~~~~~~~~~~~~~~
\newcommand{\ddt}[1] {\ensuremath{\frac{\partial #1}{\partial t }}}
\newcommand{\DDt}[1] {\ensuremath{\frac{D #1}{D t}}}
\newcommand{\DpDt}[2] {\ensuremath{\frac{d_{#1} #2}{d t }}}
\newcommand{\dsdts}[1] {\ensuremath{\frac{\partial ^2 #1}{\partial t^2}}}
\newcommand{\rate}[1] {\ensuremath{\dot{#1}}}

\newcommand{\genDer}{\mathcal{L}}

% time average symbols
% ~~~~~~~~~~~~~~~~~~~~
\newcommand{\av}[1] {\ensuremath{\overline{#1}}}
\newcommand{\corrtwo}[2] {{\dwea{\dprime{#1} \dprime{#2}}}}
\newcommand{\curly}[1] {{\cal #1}}
\newcommand{\dprime}[1] {\ensuremath{{#1}^{^{\prime \prime}}}}
\newcommand{\dwea}[1] {\ensuremath{\widetilde{#1}}}
\newcommand{\dweafluc}[1] {\ensuremath{\dprime{#1}}}
\newcommand{\fluc}[1] {\ensuremath{#1^{\prime}}}

% index style
% ~~~~~~~~~~~
\newcommand{\veci}[2][i] {\ensuremath{#2_{#1}}}
\newcommand{\teni}[2][ij] {\ensuremath{#2_{#1}}}
\newcommand{\tenTi}[2][ji] {\ensuremath{#2_{#1}}}

% index operations
% ~~~~~~~~~~~~~~~~
\newcommand{\deltai}[1] {\ensuremath{\partial_{#1}}}

% Sub-subscripts
% ~~~~~~~~~~~~~~
\newcommand{\eff} {{\scriptscriptstyle e\!f\!\!f\!}}

% unknown use
% ~~~~~~~~~~~
%\font\bigtenrm=cmr12 scaled 1200
%\newcommand{\eexp}[1]{{\hbox{$\textfont1=\bigtenrm e$}}^{\raise3pt
%\hbox{$#1$}}}


% ------------------------------------------------------------------------------

	%------------------------------------------------------------------------------
	% ========= \|
	% \\ / F ield \| OpenFOAM: The Open Source CFD Toolbox
	% \\ / O peration \| Website: https://openfoam.org
	% \\ / A nd \| Copyright (C) 2011-2018 OpenFOAM Foundation
	% \\/ M anipulation \|
	%------------------------------------------------------------------------------
	% 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/>.
	%
	% LaTeX Style file
	% tensorOperator.sty
	%
	% Description
	% Standard OpenFOAM LaTeX macros for typesetting tensor algebra.
	%
	%------------------------------------------------------------------------------

	% tensor style
	% ~~~~~~~~~~~~
	\renewcommand{\vec}[1] {\ensuremath{\mathbf #1}}
	\newcommand{\gvec}[1] {\ensuremath{\mbox{\boldmath$\bf#1$}}}

	% products
	% ~~~~~~~~
	\newcommand{\anyprod}{\star}
	\newcommand{\cprod} {\times}
	\newcommand{\dprod} {\,{\scriptscriptstyle \stackrel{\bullet}{{}}}\,}
	\newcommand{\ddprod} {\,{\scriptscriptstyle \stackrel{\bullet}{\bullet}}\,}
	\newcommand{\tdprod} {\,{\scriptscriptstyle \stackrel{3}{\bullet}}\,}
	\newcommand{\tprod} {\,{\scriptscriptstyle \stackrel{\otimes}{{}}}\,}

	% operations
	% ~~~~~~~~~~
	\newcommand{\adj} {\ensuremath{\operatorname{adj}}}
	\newcommand{\cof} {\ensuremath{\operatorname{cof}}}
	\newcommand{\diag} {\ensuremath{\operatorname{diag}}}
	\newcommand{\dev} {\ensuremath{\operatorname{dev}}}

	\newcommand{\Hodge} {\ensuremath{\operatorname{\stackrel{\displaystyle \ast}{}}}}
	\newcommand{\hyd} {\ensuremath{\operatorname{hyd}}}
	\renewcommand{\max} {\ensuremath{\operatorname{max}}}
	\renewcommand{\min} {\ensuremath{\operatorname{min}}}
	\newcommand{\inv} {\ensuremath{\operatorname{inv}}}
	\newcommand{\sym} {\ensuremath{\operatorname{symm}}} % symm ?
	\newcommand{\skw} {\ensuremath{\operatorname{skew}}} % skew already defined
	\newcommand{\tr} {\ensuremath{\operatorname{tr}}}
	\newcommand{\trans}[1] {\ensuremath{#1^{\operatorname{T}}}}

	% alternative tensor operators for hypersonics etc.
	% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
	\newcommand{\devs}[1] {\overset{\scriptscriptstyle\circ}{#1}}
	%\newcommand{\trans}[1] {\ensuremath{#1^{\operatorname{T}}}}
	\newcommand{\symms}[1] {\overleftrightarrow{#1}}
	\newlength{\skewslength}
	\newlength{\skewsheight}
	\newcommand{\skews}[1]{
	\settowidth{\skewslength}{#1}%
	\settoheight{\skewsheight}{#1}%
	\addtolength{\skewsheight}{0.4mm}%
	{\overleftrightarrow{#1}\hspace{-.5\skewslength}%
	\rule[\skewsheight]{.4pt}{1.4mm}
	\hspace{.5\skewslength}%
	}}
	%\newcommand{\skew}[1] {\ensuremath{#1^{\operatorname{A}}}}

	% spatial derivatives
	% ~~~~~~~~~~~~~~~~~~~
	\newcommand{\curl}{\ensuremath{\nabla\cprod}}
	\renewcommand{\div} {\ensuremath{\nabla\dprod}}
	\newcommand{\grad}{\ensuremath{\nabla}}
	\newcommand{\laplacian}{\ensuremath{\nabla^{2}}}

	% temporal derivatives
	% ~~~~~~~~~~~~~~~~~~~~
	\newcommand{\ddt}[1] {\ensuremath{\frac{\partial #1}{\partial t }}}
	\newcommand{\DDt}[1] {\ensuremath{\frac{D #1}{D t}}}
	\newcommand{\DpDt}[2] {\ensuremath{\frac{d_{#1} #2}{d t }}}
	\newcommand{\dsdts}[1] {\ensuremath{\frac{\partial ^2 #1}{\partial t^2}}}
	\newcommand{\rate}[1] {\ensuremath{\dot{#1}}}

	\newcommand{\genDer}{\mathcal{L}}

	% time average symbols
	% ~~~~~~~~~~~~~~~~~~~~
	\newcommand{\av}[1] {\ensuremath{\overline{#1}}}
	\newcommand{\corrtwo}[2] {{\dwea{\dprime{#1} \dprime{#2}}}}
	\newcommand{\curly}[1] {{\cal #1}}
	\newcommand{\dprime}[1] {\ensuremath{{#1}^{^{\prime \prime}}}}
	\newcommand{\dwea}[1] {\ensuremath{\widetilde{#1}}}
	\newcommand{\dweafluc}[1] {\ensuremath{\dprime{#1}}}
	\newcommand{\fluc}[1] {\ensuremath{#1^{\prime}}}

	% index style
	% ~~~~~~~~~~~
	\newcommand{\veci}[2][i] {\ensuremath{#2_{#1}}}
	\newcommand{\teni}[2][ij] {\ensuremath{#2_{#1}}}
	\newcommand{\tenTi}[2][ji] {\ensuremath{#2_{#1}}}

	% index operations
	% ~~~~~~~~~~~~~~~~
	\newcommand{\deltai}[1] {\ensuremath{\partial_{#1}}}

	% Sub-subscripts
	% ~~~~~~~~~~~~~~
	\newcommand{\eff} {{\scriptscriptstyle e\!f\!\!f\!}}

	% unknown use
	% ~~~~~~~~~~~
	%\font\bigtenrm=cmr12 scaled 1200
	%\newcommand{\eexp}[1]{{\hbox{$\textfont1=\bigtenrm e$}}^{\raise3pt
	%\hbox{$#1$}}}


	% ------------------------------------------------------------------------------