foam-extend4.1-coherent-io/Macros/tensorOperator.sty

%-----------------------------------------------------------------------------
% =========                 |
% \\      /  F ield         | foam-extend: Open Source CFD
%  \\    /   O peration     | Version:     4.0
%   \\  /    A nd           | Web:         http://www.foam-extend.org
%    \\/     M anipulation  | For copyright notice see file Copyright
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%     This file is part of foam-extend.
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%     You should have received a copy of the GNU General Public License
%     along with foam-extend.  If not, see <http://www.gnu.org/licenses/>.
%
% LaTeX Style file
%     tensorOperator.sty
%
% Description
%     Standard OpenCFD 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{$#1$}}}


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