Macros/tensorOperator.sty

   1 %-----------------------------------------------------------------------------
   2 % =========                 |
   3 % \\      /  F ield         | foam-extend: Open Source CFD
   4 %  \\    /   O peration     | Version:     3.2
   5 %   \\  /    A nd           | Web:         http://www.foam-extend.org
   6 %    \\/     M anipulation  | For copyright notice see file Copyright
   7 %------------------------------------------------------------------------------
   8 % License
   9 %     This file is part of foam-extend.
  10 %
  11 %     foam-extend 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 3 of the License, or (at your
  14 %     option) any later version.
  15 %
  16 %     foam-extend is distributed in the hope that it will be useful, but
  17 %     WITHOUT ANY WARRANTY; without even the implied warranty of
  18 %     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  19 %     General Public License for more details.
  20 %
  21 %     You should have received a copy of the GNU General Public License
  22 %     along with foam-extend.  If not, see <http://www.gnu.org/licenses/>.
  23 %
  24 % LaTeX Style file
  25 %     tensorOperator.sty
  26 %
  27 % Description
  28 %     Standard OpenCFD LaTeX macros for typesetting tensor algebra.
  29 %
  30 %------------------------------------------------------------------------------
  31
  32 % tensor style
  33 % ~~~~~~~~~~~~
  34 \renewcommand{\vec}[1] {\ensuremath{\mathbf #1}}
  35 \newcommand{\gvec}[1] {\ensuremath{\mbox{\boldmath$\bf#1$}}}
  36
  37 % products
  38 % ~~~~~~~~
  39 \newcommand{\anyprod}{\star}
  40 \newcommand{\cprod} {\times}
  41 \newcommand{\dprod} {\,{\scriptscriptstyle \stackrel{\bullet}{{}}}\,}
  42 \newcommand{\ddprod} {\,{\scriptscriptstyle \stackrel{\bullet}{\bullet}}\,}
  43 \newcommand{\tdprod} {\,{\scriptscriptstyle \stackrel{3}{\bullet}}\,}
  44 \newcommand{\tprod} {\,{\scriptscriptstyle \stackrel{\otimes}{{}}}\,}
  45
  46 % operations
  47 % ~~~~~~~~~~
  48 \newcommand{\adj} {\ensuremath{\operatorname{adj}}}
  49 \newcommand{\cof} {\ensuremath{\operatorname{cof}}}
  50 \newcommand{\diag} {\ensuremath{\operatorname{diag}}}
  51 \newcommand{\dev} {\ensuremath{\operatorname{dev}}}
  52
  53 \newcommand{\Hodge} {\ensuremath{\operatorname{\stackrel{\displaystyle \ast}{}}}}
  54 \newcommand{\hyd} {\ensuremath{\operatorname{hyd}}}
  55 \renewcommand{\max} {\ensuremath{\operatorname{max}}}
  56 \renewcommand{\min} {\ensuremath{\operatorname{min}}}
  57 \newcommand{\inv} {\ensuremath{\operatorname{inv}}}
  58 \newcommand{\sym} {\ensuremath{\operatorname{symm}}}    % symm ?
  59 \newcommand{\skw} {\ensuremath{\operatorname{skew}}}    % skew already defined
  60 \newcommand{\tr} {\ensuremath{\operatorname{tr}}}
  61 \newcommand{\trans}[1] {\ensuremath{#1^{\operatorname{T}}}}
  62
  63 % alternative tensor operators for hypersonics etc.
  64 % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  65 \newcommand{\devs}[1] {\overset{\scriptscriptstyle\circ}{#1}}
  66 %\newcommand{\trans}[1] {\ensuremath{#1^{\operatorname{T}}}}
  67 \newcommand{\symms}[1] {\overleftrightarrow{#1}}
  68 \newlength{\skewslength}
  69 \newlength{\skewsheight}
  70 \newcommand{\skews}[1]{
  71     \settowidth{\skewslength}{#1}%
  72     \settoheight{\skewsheight}{#1}%
  73     \addtolength{\skewsheight}{0.4mm}%
  74     {\overleftrightarrow{#1}\hspace{-.5\skewslength}%
  75     \rule[\skewsheight]{.4pt}{1.4mm}
  76     \hspace{.5\skewslength}%
  77 }}
  78 %\newcommand{\skew}[1] {\ensuremath{#1^{\operatorname{A}}}}
  79
  80 % spatial derivatives
  81 % ~~~~~~~~~~~~~~~~~~~
  82 \newcommand{\curl}{\ensuremath{\nabla\cprod}}
  83 \renewcommand{\div} {\ensuremath{\nabla\dprod}}
  84 \newcommand{\grad}{\ensuremath{\nabla}}
  85 \newcommand{\laplacian}{\ensuremath{\nabla^{2}}}
  86
  87 % temporal derivatives
  88 % ~~~~~~~~~~~~~~~~~~~~
  89 \newcommand{\ddt}[1] {\ensuremath{\frac{\partial #1}{\partial t }}}
  90 \newcommand{\DDt}[1] {\ensuremath{\frac{D #1}{D t}}}
  91 \newcommand{\DpDt}[2] {\ensuremath{\frac{d_{#1} #2}{d t }}}
  92 \newcommand{\dsdts}[1] {\ensuremath{\frac{\partial ^2 #1}{\partial t^2}}}
  93 \newcommand{\rate}[1] {\ensuremath{\dot{#1}}}
  94
  95 \newcommand{\genDer}{\mathcal{L}}
  96
  97 % time average symbols
  98 % ~~~~~~~~~~~~~~~~~~~~
  99 \newcommand{\av}[1] {\ensuremath{\overline{#1}}}
 100 \newcommand{\corrtwo}[2] {{\dwea{\dprime{#1} \dprime{#2}}}}
 101 \newcommand{\curly}[1] {{\cal #1}}
 102 \newcommand{\dprime}[1] {\ensuremath{{#1}^{^{\prime \prime}}}}
 103 \newcommand{\dwea}[1] {\ensuremath{\widetilde{#1}}}
 104 \newcommand{\dweafluc}[1] {\ensuremath{\dprime{#1}}}
 105 \newcommand{\fluc}[1] {\ensuremath{#1^{\prime}}}
 106
 107 % index style
 108 % ~~~~~~~~~~~
 109 \newcommand{\veci}[2][i] {\ensuremath{#2_{#1}}}
 110 \newcommand{\teni}[2][ij] {\ensuremath{#2_{#1}}}
 111 \newcommand{\tenTi}[2][ji] {\ensuremath{#2_{#1}}}
 112
 113 % index operations
 114 % ~~~~~~~~~~~~~~~~
 115 \newcommand{\deltai}[1] {\ensuremath{\partial_{#1}}}
 116
 117 % Sub-subscripts
 118 % ~~~~~~~~~~~~~~
 119 \newcommand{\eff} {{\scriptscriptstyle e\!f\!\!f\!}}
 120
 121 % unknown use
 122 % ~~~~~~~~~~~
 123 %\font\bigtenrm=cmr12 scaled 1200
 124 %\newcommand{\eexp}[1]{{\hbox{$\textfont1=\bigtenrm e$}}^{\raise3pt
 125 %\hbox{$#1$}}}
 126
 127
 128 % ------------------------------------------------------------------------------