Macros/tensorOperator.sty

   1 %-----------------------------------------------------------------------------
   2 % =========                 |
   3 % \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   4 %  \\    /   O peration     |
   5 %   \\  /    A nd           | Copyright held by original author
   6 %    \\/     M anipulation  |
   7 %------------------------------------------------------------------------------
   8 % License
   9 %     This file is part of OpenFOAM.
  10 %
  11 %     OpenFOAM is free software; you can redistribute it and/or modify it
  12 %     under the terms of the GNU General Public License as published by the
  13 %     Free Software Foundation; either version 2 of the License, or (at your
  14 %     option) any later version.
  15 %
  16 %     OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
  17 %     ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  18 %     FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  19 %     for more details.
  20 %
  21 %     You should have received a copy of the GNU General Public License
  22 %     along with OpenFOAM; if not, write to the Free Software Foundation,
  23 %     Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
  24 %
  25 % LaTeX Style file
  26 %     tensorOperator.sty
  27 %
  28 % Description
  29 %     Standard OpenCFD LaTeX macros for typesetting tensor algebra.
  30 %
  31 %------------------------------------------------------------------------------
  32
  33 % tensor style
  34 % ~~~~~~~~~~~~
  35 \renewcommand{\vec}[1] {\ensuremath{\mathbf #1}}
  36 \newcommand{\gvec}[1] {\ensuremath{\mbox{\boldmath$\bf#1$}}}
  37
  38 % products
  39 % ~~~~~~~~
  40 \newcommand{\anyprod}{\star}
  41 \newcommand{\cprod} {\times}
  42 \newcommand{\dprod} {\,{\scriptscriptstyle \stackrel{\bullet}{{}}}\,}
  43 \newcommand{\ddprod} {\,{\scriptscriptstyle \stackrel{\bullet}{\bullet}}\,}
  44 \newcommand{\tdprod} {\,{\scriptscriptstyle \stackrel{3}{\bullet}}\,}
  45 \newcommand{\tprod} {\,{\scriptscriptstyle \stackrel{\otimes}{{}}}\,}
  46
  47 % operations
  48 % ~~~~~~~~~~
  49 \newcommand{\adj} {\ensuremath{\operatorname{adj}}}
  50 \newcommand{\cof} {\ensuremath{\operatorname{cof}}}
  51 \newcommand{\diag} {\ensuremath{\operatorname{diag}}}
  52 \newcommand{\dev} {\ensuremath{\operatorname{dev}}}
  53
  54 \newcommand{\Hodge} {\ensuremath{\operatorname{\stackrel{\displaystyle \ast}{}}}}
  55 \newcommand{\hyd} {\ensuremath{\operatorname{hyd}}}
  56 \renewcommand{\max} {\ensuremath{\operatorname{max}}}
  57 \renewcommand{\min} {\ensuremath{\operatorname{min}}}
  58 \newcommand{\inv} {\ensuremath{\operatorname{inv}}}
  59 \newcommand{\sym} {\ensuremath{\operatorname{symm}}}    % symm ?
  60 \newcommand{\skw} {\ensuremath{\operatorname{skew}}}    % skew already defined
  61 \newcommand{\tr} {\ensuremath{\operatorname{tr}}}
  62 \newcommand{\trans}[1] {\ensuremath{#1^{\operatorname{T}}}}
  63
  64 % alternative tensor operators for hypersonics etc.
  65 % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  66 \newcommand{\devs}[1] {\overset{\scriptscriptstyle\circ}{#1}}
  67 %\newcommand{\trans}[1] {\ensuremath{#1^{\operatorname{T}}}}
  68 \newcommand{\symms}[1] {\overleftrightarrow{#1}}
  69 \newlength{\skewslength}
  70 \newlength{\skewsheight}
  71 \newcommand{\skews}[1]{
  72     \settowidth{\skewslength}{#1}%
  73     \settoheight{\skewsheight}{#1}%
  74     \addtolength{\skewsheight}{0.4mm}%
  75     {\overleftrightarrow{#1}\hspace{-.5\skewslength}%
  76     \rule[\skewsheight]{.4pt}{1.4mm}
  77     \hspace{.5\skewslength}%
  78 }}
  79 %\newcommand{\skew}[1] {\ensuremath{#1^{\operatorname{A}}}}
  80
  81 % spatial derivatives
  82 % ~~~~~~~~~~~~~~~~~~~
  83 \newcommand{\curl}{\ensuremath{\nabla\cprod}}
  84 \renewcommand{\div} {\ensuremath{\nabla\dprod}}
  85 \newcommand{\grad}{\ensuremath{\nabla}}
  86 \newcommand{\laplacian}{\ensuremath{\nabla^{2}}}
  87
  88 % temporal derivatives
  89 % ~~~~~~~~~~~~~~~~~~~~
  90 \newcommand{\ddt}[1] {\ensuremath{\frac{\partial #1}{\partial t }}}
  91 \newcommand{\DDt}[1] {\ensuremath{\frac{D #1}{D t}}}
  92 \newcommand{\DpDt}[2] {\ensuremath{\frac{d_{#1} #2}{d t }}}
  93 \newcommand{\dsdts}[1] {\ensuremath{\frac{\partial ^2 #1}{\partial t^2}}}
  94 \newcommand{\rate}[1] {\ensuremath{\dot{#1}}}
  95
  96 \newcommand{\genDer}{\mathcal{L}}
  97
  98 % time average symbols
  99 % ~~~~~~~~~~~~~~~~~~~~
 100 \newcommand{\av}[1] {\ensuremath{\overline{#1}}}
 101 \newcommand{\corrtwo}[2] {{\dwea{\dprime{#1} \dprime{#2}}}}
 102 \newcommand{\curly}[1] {{\cal #1}}
 103 \newcommand{\dprime}[1] {\ensuremath{{#1}^{^{\prime \prime}}}}
 104 \newcommand{\dwea}[1] {\ensuremath{\widetilde{#1}}}
 105 \newcommand{\dweafluc}[1] {\ensuremath{\dprime{#1}}}
 106 \newcommand{\fluc}[1] {\ensuremath{#1^{\prime}}}
 107
 108 % index style
 109 % ~~~~~~~~~~~
 110 \newcommand{\veci}[2][i] {\ensuremath{#2_{#1}}}
 111 \newcommand{\teni}[2][ij] {\ensuremath{#2_{#1}}}
 112 \newcommand{\tenTi}[2][ji] {\ensuremath{#2_{#1}}}
 113
 114 % index operations
 115 % ~~~~~~~~~~~~~~~~
 116 \newcommand{\deltai}[1] {\ensuremath{\partial_{#1}}}
 117
 118 % Sub-subscripts
 119 % ~~~~~~~~~~~~~~
 120 \newcommand{\eff} {{\scriptscriptstyle e\!f\!\!f\!}}
 121
 122 % unknown use
 123 % ~~~~~~~~~~~
 124 %\font\bigtenrm=cmr12 scaled 1200
 125 %\newcommand{\eexp}[1]{{\hbox{$\textfont1=\bigtenrm e$}}^{\raise3pt
 126 %\hbox{$#1$}}}
 127
 128
 129 % ------------------------------------------------------------------------------