Changeset 11598 for NEMO/trunk/doc/latex/NEMO/subfiles/apdx_algos.tex
 Timestamp:
 20190925T22:00:42+02:00 (16 months ago)
 File:

 1 edited
Legend:
 Unmodified
 Added
 Removed

NEMO/trunk/doc/latex/NEMO/subfiles/apdx_algos.tex
r11597 r11598 2 2 3 3 \begin{document} 4 4 5 \chapter{Note on some algorithms} 5 6 \label{apdx:ALGOS} 6 7 8 \thispagestyle{plain} 9 7 10 \chaptertoc 11 12 \paragraph{Changes record} ~\\ 13 14 {\footnotesize 15 \begin{tabularx}{\textwidth}{lXX} 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 8 26 9 27 This appendix some on going consideration on algorithms used or planned to be used in \NEMO. … … 356 374 This expression of the isoneutral diffusion has been chosen in order to satisfy the following six properties: 357 375 \begin{description} 358 \item [$\bullet$ horizontal diffusion] 359 The discretization of the diffusion operator recovers the traditional fivepoint Laplacian in 360 the limit of flat isoneutral direction: 376 \item [Horizontal diffusion] The discretization of the diffusion operator recovers the traditional fivepoint Laplacian in the limit of flat isoneutral direction: 361 377 \[ 362 378 % \label{eq:ALGOS_Gf_property1a} … … 366 382 { _i^k \mathbb{R}_{i_p}^{k_p} }=0 367 383 \] 368 369 \item [$\bullet$ implicit treatment in the vertical] 370 In the diagonal term associated with the vertical divergence of the isoneutral fluxes 384 \item [Implicit treatment in the vertical] In the diagonal term associated with the vertical divergence of the isoneutral fluxes 371 385 \ie\ the term associated with a second order vertical derivative) 372 386 appears only tracer values associated with a single water column. … … 380 394 \] 381 395 can be quite large. 382 383 \item [$\bullet$ pure isoneutral operator] 384 The isoneutral flux of locally referenced potential density is zero, \ie 396 \item [Pure isoneutral operator] The isoneutral flux of locally referenced potential density is zero, \ie 385 397 \begin{align*} 386 398 % \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 397 409 the definition of the triads' slopes \autoref{eq:ALGOS_Gf_slopes}. 398 399 \item [$\bullet$ conservation of tracer] 400 The isoneutral diffusion term conserve the total tracer content, \ie 410 \item [Conservation of tracer] The isoneutral diffusion term conserve the total tracer content, \ie 401 411 \[ 402 412 % \label{eq:ALGOS_Gf_property1} … … 404 414 \] 405 415 This property is trivially satisfied since the isoneutral diffusive operator is written in flux form. 406 407 \item [$\bullet$ decrease of tracer variance] 408 The isoneutral diffusion term does not increase the total tracer variance, \ie 416 \item [Decrease of tracer variance] The isoneutral diffusion term does not increase the total tracer variance, \ie 409 417 \[ 410 418 % \label{eq:ALGOS_Gf_property1} … … 417 425 It therfore ensures that, when the diffusivity coefficient is large enough, 418 426 the field on which it is applied become free of gridpoint noise. 419 420 \item [$\bullet$ selfadjoint operator] 421 The isoneutral diffusion operator is selfadjoint, \ie 427 \item [Selfadjoint operator] The isoneutral diffusion operator is selfadjoint, \ie 422 428 \[ 423 429 % \label{eq:ALGOS_Gf_property1} … … 583 589 \ie\ it does not include a diffusive component but is a "pure" advection term. 584 590 585 $\ $\newpage %force an empty line586 591 %% ================================================================================================= 587 592 \subsection{Discrete invariants of the isoneutral diffrusion}
Note: See TracChangeset
for help on using the changeset viewer.