Ignore:
Timestamp:
2019-09-25T22:00:42+02:00 (16 months ago)
Author:
nicolasmartin
Message:

Add template of versioning record at the beginning of chapters

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1 edited

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  • NEMO/trunk/doc/latex/NEMO/subfiles/apdx_algos.tex

    r11597 r11598  
    22 
    33\begin{document} 
     4 
    45\chapter{Note on some algorithms} 
    56\label{apdx:ALGOS} 
    67 
     8\thispagestyle{plain} 
     9 
    710\chaptertoc 
     11 
     12\paragraph{Changes record} ~\\ 
     13 
     14{\footnotesize 
     15  \begin{tabularx}{\textwidth}{l||X|X} 
     16    Release & Author(s) & Modifications \\ 
     17    \hline 
     18    {\em   4.0} & {\em ...} & {\em ...} \\ 
     19    {\em   3.6} & {\em ...} & {\em ...} \\ 
     20    {\em   3.4} & {\em ...} & {\em ...} \\ 
     21    {\em <=3.4} & {\em ...} & {\em ...} 
     22  \end{tabularx} 
     23} 
     24 
     25\clearpage 
    826 
    927This appendix some on going consideration on algorithms used or planned to be used in \NEMO. 
     
    356374This expression of the iso-neutral diffusion has been chosen in order to satisfy the following six properties: 
    357375\begin{description} 
    358 \item [$\bullet$ horizontal diffusion] 
    359   The discretization of the diffusion operator recovers the traditional five-point Laplacian in 
    360   the limit of flat iso-neutral direction: 
     376\item [Horizontal diffusion] The discretization of the diffusion operator recovers the traditional five-point Laplacian in the limit of flat iso-neutral direction: 
    361377  \[ 
    362378    % \label{eq:ALGOS_Gf_property1a} 
     
    366382    { _i^k \mathbb{R}_{i_p}^{k_p} }=0 
    367383  \] 
    368  
    369 \item [$\bullet$ implicit treatment in the vertical] 
    370   In the diagonal term associated with the vertical divergence of the iso-neutral fluxes 
     384\item [Implicit treatment in the vertical] In the diagonal term associated with the vertical divergence of the iso-neutral fluxes 
    371385  \ie\ the term associated with a second order vertical derivative) 
    372386  appears only tracer values associated with a single water column. 
     
    380394  \] 
    381395  can be quite large. 
    382  
    383 \item [$\bullet$ pure iso-neutral operator] 
    384   The iso-neutral flux of locally referenced potential density is zero, \ie 
     396\item [Pure iso-neutral operator] The iso-neutral flux of locally referenced potential density is zero, \ie 
    385397  \begin{align*} 
    386398    % \label{eq:ALGOS_Gf_property2} 
     
    396408  This result is trivially obtained using the \autoref{eq:ALGOS_Gf_triads} applied to $T$ and $S$ and 
    397409  the definition of the triads' slopes \autoref{eq:ALGOS_Gf_slopes}. 
    398  
    399 \item [$\bullet$ conservation of tracer] 
    400   The iso-neutral diffusion term conserve the total tracer content, \ie 
     410\item [Conservation of tracer] The iso-neutral diffusion term conserve the total tracer content, \ie 
    401411  \[ 
    402412    % \label{eq:ALGOS_Gf_property1} 
     
    404414  \] 
    405415This property is trivially satisfied since the iso-neutral diffusive operator is written in flux form. 
    406  
    407 \item [$\bullet$ decrease of tracer variance] 
    408   The iso-neutral diffusion term does not increase the total tracer variance, \ie 
     416\item [Decrease of tracer variance] The iso-neutral diffusion term does not increase the total tracer variance, \ie 
    409417  \[ 
    410418    % \label{eq:ALGOS_Gf_property1} 
     
    417425It therfore ensures that, when the diffusivity coefficient is large enough, 
    418426the field on which it is applied become free of grid-point noise. 
    419  
    420 \item [$\bullet$ self-adjoint operator] 
    421   The iso-neutral diffusion operator is self-adjoint, \ie 
     427\item [Self-adjoint operator] The iso-neutral diffusion operator is self-adjoint, \ie 
    422428  \[ 
    423429    % \label{eq:ALGOS_Gf_property1} 
     
    583589\ie\ it does not include a diffusive component but is a "pure" advection term. 
    584590 
    585 $\ $\newpage      %force an empty line 
    586591%% ================================================================================================= 
    587592\subsection{Discrete invariants of the iso-neutral diffrusion} 
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