Changeset 14644 for NEMO/branches/2020/dev_r14116_HPC-04_mcastril_Mixed_Precision_implementation_final/doc/latex/NEMO/subfiles/chap_time_domain.tex

Timestamp:

2021-03-26T15:33:49+01:00 (3 years ago)

Author:

sparonuz

Message:

Merge trunk -r14642:HEAD

Location:

NEMO/branches/2020/dev_r14116_HPC-04_mcastril_Mixed_Precision_implementation_final

Files:

• . (modified) (1 prop)
• doc/latex/NEMO/subfiles (modified) (1 prop)
• doc/latex/NEMO/subfiles/chap_time_domain.tex (modified) (12 diffs)

NEMO/branches/2020/dev_r14116_HPC-04_mcastril_Mixed_Precision_implementation_final

@@ -9 +9 @@
 
 # SETTE
-^/utils/CI/sette_wave@13990         sette
+^/utils/CI/sette@14244        sette

@@ -9 +9 @@
 
 # SETTE
-^/utils/CI/sette_wave@13990         sette
+^/utils/CI/sette@14244        sette

NEMO/branches/2020/dev_r14116_HPC-04_mcastril_Mixed_Precision_implementation_final/doc/latex/NEMO/subfiles

@@ +1 @@
+*.aux
+*.bbl
+*.blg
+*.fdb*
+*.fls
+*.idx
+*.ilg
 *.ind
-*.ilg
+*.lo*
+*.out
+*.pdf
+*.pyg
+*.tdo
+*.toc
+*.xdv
+cache*

@@ +1 @@
+*.aux
+*.bbl
+*.blg
+*.fdb*
+*.fls
+*.idx
+*.ilg
 *.ind
-*.ilg
+*.lo*
+*.out
+*.pdf
+*.pyg
+*.tdo
+*.toc
+*.xdv
+cache*

NEMO/branches/2020/dev_r14116_HPC-04_mcastril_Mixed_Precision_implementation_final/doc/latex/NEMO/subfiles/chap_time_domain.tex

@@ -6 +6 @@
 \label{chap:TD}
 
-\thispagestyle{plain}
-
 \chaptertoc
 
@@ -14 +12 @@
 {\footnotesize
   \begin{tabularx}{0.5\textwidth}{l||X|X}
-    Release          & Author(s)                                       &
+    Release          & Author(s)                                       & 
     Modifications                                                      \\
     \hline
-    {\em        4.0} & {\em J\'{e}r\^{o}me Chanut \newline Tim Graham} &
+    {\em        4.0} & {\em J\'{e}r\^{o}me Chanut \newline Tim Graham} & 
     {\em Review \newline Update                                      } \\
-    {\em        3.6} & {\em Christian \'{E}th\'{e}                   } &
+    {\em        3.6} & {\em Christian \'{E}th\'{e}                   } & 
     {\em Update                                                      } \\
-    {\em $\leq$ 3.4} & {\em Gurvan Madec                             } &
+    {\em $\leq$ 3.4} & {\em Gurvan Madec                             } & 
     {\em First version                                               } \\
   \end{tabularx}
@@ -46 +44 @@
 
 The time stepping used in \NEMO\ is a three level scheme that can be represented as follows:
+
 \begin{equation}
   \label{eq:TD}
   x^{t + \rdt} = x^{t - \rdt} + 2 \, \rdt \ \text{RHS}_x^{t - \rdt, \, t, \, t + \rdt}
 \end{equation}
+
 where $x$ stands for $u$, $v$, $T$ or $S$;
 RHS is the \textbf{R}ight-\textbf{H}and-\textbf{S}ide of the corresponding time evolution equation;
@@ -99 +99 @@
 first designed by \citet{robert_JMSJ66} and more comprehensively studied by \citet{asselin_MWR72},
 is a kind of laplacian diffusion in time that mixes odd and even time steps:
+
 \begin{equation}
   \label{eq:TD_asselin}
   x_F^t = x^t + \gamma \, \lt[ x_F^{t - \rdt} - 2 x^t + x^{t + \rdt} \rt]
 \end{equation}
+
 where the subscript $F$ denotes filtered values and $\gamma$ is the Asselin coefficient.
 $\gamma$ is initialized as \np{rn_atfp}{rn\_atfp} (namelist parameter).
@@ -134 +136 @@
 The conditions for stability of second and fourth order horizontal diffusion schemes are
 \citep{griffies_bk04}:
+
 \begin{equation}
   \label{eq:TD_euler_stability}
@@ -142 +145 @@
   \end{cases}
 \end{equation}
+
 where $e$ is the smallest grid size in the two horizontal directions and
 $A^h$ is the mixing coefficient.
@@ -153 +157 @@
 To overcome the stability constraint, a backward (or implicit) time differencing scheme is used.
 This scheme is unconditionally stable but diffusive and can be written as follows:
+
 \begin{equation}
   \label{eq:TD_imp}
@@ -170 +175 @@
 where RHS is the right hand side of the equation except for the vertical diffusion term.
 We rewrite \autoref{eq:TD_imp} as:
+
 \begin{equation}
   \label{eq:TD_imp_mat}
   -c(k + 1) \; T^{t + 1}(k + 1) + d(k) \; T^{t + 1}(k) - \; c(k) \; T^{t + 1}(k - 1) \equiv b(k)
 \end{equation}
+
 where
+
 \[
   c(k) = A_w^{vT} (k) \, / \, e_{3w} (k) \text{,} \quad
@@ -241 +249 @@
 $Q$ is redistributed over several time step.
 In the modified LF-RA environment, these two formulations have been replaced by:
+
 \begin{gather}
   \label{eq:TD_forcing}
@@ -248 +257 @@
                     - \gamma \, \rdt \, \lt( Q^{t + \rdt / 2} - Q^{t - \rdt / 2} \rt)
 \end{gather}
+
 The change in the forcing formulation given by \autoref{eq:TD_forcing}
 (see \autoref{fig:TD_MLF_forcing}) has a significant effect:
@@ -377 +387 @@
   %
 \end{flalign*}
+
 \begin{flalign*}
   \allowdisplaybreaks
@@ -389 +400 @@
   %
 \end{flalign*}
+
 \begin{flalign*}
   \allowdisplaybreaks

@@ -9 +9 @@
 
 # SETTE
-^/utils/CI/sette_wave@13990         sette
+^/utils/CI/sette@14244        sette

@@ +1 @@
+*.aux
+*.bbl
+*.blg
+*.fdb*
+*.fls
+*.idx
+*.ilg
 *.ind
-*.ilg
+*.lo*
+*.out
+*.pdf
+*.pyg
+*.tdo
+*.toc
+*.xdv
+cache*