Changeset 11598 for NEMO/trunk/doc/latex/NEMO/subfiles/apdx_algos.tex

Timestamp:

2019-09-25T22:00:42+02:00 (5 years ago)

Author:

nicolasmartin

Message:

Add template of versioning record at the beginning of chapters

File:

• NEMO/trunk/doc/latex/NEMO/subfiles/apdx_algos.tex (modified) (8 diffs)

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

@@ -2 +2 @@
 
 \begin{document}
+
 \chapter{Note on some algorithms}
 \label{apdx:ALGOS}
 
+\thispagestyle{plain}
+
 \chaptertoc
+
+\paragraph{Changes record} ~\\
+
+{\footnotesize
+  \begin{tabularx}{\textwidth}{l||X|X}
+    Release & Author(s) & Modifications \\
+    \hline
+    {\em   4.0} & {\em ...} & {\em ...} \\
+    {\em   3.6} & {\em ...} & {\em ...} \\
+    {\em   3.4} & {\em ...} & {\em ...} \\
+    {\em <=3.4} & {\em ...} & {\em ...}
+  \end{tabularx}
+}
+
+\clearpage
 
 This appendix some on going consideration on algorithms used or planned to be used in \NEMO.
@@ -356 +374 @@
 This expression of the iso-neutral diffusion has been chosen in order to satisfy the following six properties:
 \begin{description}
-\item [$\bullet$ horizontal diffusion]
-  The discretization of the diffusion operator recovers the traditional five-point Laplacian in
-  the limit of flat iso-neutral direction:
+\item [Horizontal diffusion] The discretization of the diffusion operator recovers the traditional five-point Laplacian in the limit of flat iso-neutral direction:
   \[
     % \label{eq:ALGOS_Gf_property1a}
@@ -366 +382 @@
     { _i^k \mathbb{R}_{i_p}^{k_p} }=0
   \]
-
-\item [$\bullet$ implicit treatment in the vertical]
-  In the diagonal term associated with the vertical divergence of the iso-neutral fluxes
+\item [Implicit treatment in the vertical] In the diagonal term associated with the vertical divergence of the iso-neutral fluxes
   \ie\ the term associated with a second order vertical derivative)
   appears only tracer values associated with a single water column.
@@ -380 +394 @@
   \]
   can be quite large.
-
-\item [$\bullet$ pure iso-neutral operator]
-  The iso-neutral flux of locally referenced potential density is zero, \ie
+\item [Pure iso-neutral operator] The iso-neutral flux of locally referenced potential density is zero, \ie
   \begin{align*}
     % \label{eq:ALGOS_Gf_property2}
@@ -396 +408 @@
   This result is trivially obtained using the \autoref{eq:ALGOS_Gf_triads} applied to $T$ and $S$ and
   the definition of the triads' slopes \autoref{eq:ALGOS_Gf_slopes}.
-
-\item [$\bullet$ conservation of tracer]
-  The iso-neutral diffusion term conserve the total tracer content, \ie
+\item [Conservation of tracer] The iso-neutral diffusion term conserve the total tracer content, \ie
   \[
     % \label{eq:ALGOS_Gf_property1}
@@ -404 +414 @@
   \]
 This property is trivially satisfied since the iso-neutral diffusive operator is written in flux form.
-
-\item [$\bullet$ decrease of tracer variance]
-  The iso-neutral diffusion term does not increase the total tracer variance, \ie
+\item [Decrease of tracer variance] The iso-neutral diffusion term does not increase the total tracer variance, \ie
   \[
     % \label{eq:ALGOS_Gf_property1}
@@ -417 +425 @@
 It therfore ensures that, when the diffusivity coefficient is large enough,
 the field on which it is applied become free of grid-point noise.
-
-\item [$\bullet$ self-adjoint operator]
-  The iso-neutral diffusion operator is self-adjoint, \ie
+\item [Self-adjoint operator] The iso-neutral diffusion operator is self-adjoint, \ie
   \[
     % \label{eq:ALGOS_Gf_property1}
@@ -583 +589 @@
 \ie\ it does not include a diffusive component but is a "pure" advection term.
 
-$\ $\newpage      %force an empty line
 %% =================================================================================================
 \subsection{Discrete invariants of the iso-neutral diffrusion}