Changeset 6055

Timestamp:

2015-12-15T17:19:09+01:00 (8 years ago)

Author:

gm

Message:

#1613: vvl by default : update DOC on TRA advection + change in namelist comment

Location:

branches/2015/dev_r5836_NOC3_vvl_by_default

Files:

• DOC/TexFiles/Biblio/Biblio.bib (modified) (5 diffs)
• DOC/TexFiles/Chapters/Chap_TRA.tex (modified) (15 diffs)
• DOC/TexFiles/Namelist/namtra_adv (modified) (1 diff)
• NEMOGCM/CONFIG/SHARED/namelist_ref (modified) (1 diff)

branches/2015/dev_r5836_NOC3_vvl_by_default/DOC/TexFiles/Biblio/Biblio.bib

@@ -763 +763 @@
 }
 
+@PHDTHESIS{Demange_PhD2014,
+  author = {J. Farge},
+  title = {Sch\'{e}́mas num\'{e}́riques d’advection et de propagation d’ondes de gravit\'{e}́ 
+           dans les mod\`{e}les de circulation oc\'{e}́anique.},
+  school = {Doctorat es Applied Mathematiques, Grenoble University, France},
+  year = {2014},
+  pages = {138pp}
+}
 
 @ARTICLE{Dobricic_al_OS07,
@@ -983 +991 @@
   author = {M. Farge},
   title = {Dynamique non lineaire des ondes et des tourbillons dans les equations de Saint Venant},
-  school = {Doctorat es Mathematiques, Paris VI University},
+  school = {Doctorat es Mathematiques, Paris VI University, France},
   year = {1987},
   pages = {401pp}
@@ -1663 +1671 @@
 }
 
+
+@ARTICLE{Lemarie_OM2015,
+  author = {F. Lemari\'{e} and L. Debreu and J. Demange and  G. Madec and J.M. Molines and M. Honnorat},
+  title = {Stability Constraints for Oceanic Numerical Models: 
+           Implications for the Formulation of time and space Discretizations},
+  journal = OM,
+  year = {2015},
+  volume = {92}, 
+  pages = {124--148},
+  doi = {10.1016/j.ocemod.2015.06.006},
+  url = {http://dx.doi.org/10.1016/j.ocemod.2015.06.006}
+}
+
 @ARTICLE{Lermusiaux2001,
   author = {P. F. J. Lermusiaux},
@@ -1675 +1696 @@
   author = {M. L\'{e}vy},
   title = {Mod\'{e}lisation des processus biog\'{e}ochimiques en M\'{e}diterran\'{e}e
-   nord-occidentale. Cycle saisonnier et variabilit\'{e} m\'{e}so\'{e}chelle},
+           nord-occidentale. Cycle saisonnier et variabilit\'{e} m\'{e}so\'{e}chelle},
   school = {Universit\'{e} Pierre et Marie Curie, Paris, France, 207pp},
   year = {1996}
@@ -1814 +1835 @@
   year = {2010},
   pages = {submitted},
+}
+
+@ARTICLE{Lele_JCP1992,
+  author = {S.K. Lele},
+  title = {Compact finite difference schemes with spectral-like resolution},
+  journal = JCP,
+  year = {1992},
+  volume = {103}
+  pages = {16--42}
 }
 

branches/2015/dev_r5836_NOC3_vvl_by_default/DOC/TexFiles/Chapters/Chap_TRA.tex

@@ -135 +135 @@
 when those parameterisations are used (see Chap.~\ref{LDF}).
 
-The choice of an advection scheme is made in the \textit{\ngn{namtra\_adv}} namelist, by 
-setting to \textit{true} one of the logicals \textit{ln\_traadv\_xxx}. The 
-corresponding code can be found in the \textit{traadv\_xxx.F90} module, where 
-\textit{xxx} is a 3 or 4 letter acronym corresponding to each scheme. 
+Several tracer advection scheme are proposed, namely 
+a $2^{nd}$ or $4^{th}$ order centred schemes (CEN), 
+a $2^{nd}$ or $4^{th}$ order Flux Corrected Transport scheme (FCT),
+a Monotone Upstream Scheme for Conservative Laws scheme (MUSCL),
+a $3^{rd}$ Upstream Biased Scheme (UBS, also often called UP3), and
+a Quadratic Upstream Interpolation for Convective Kinematics with 
+Estimated Streaming Terms scheme (QUICKEST).
+The choice is made in the \textit{\ngn{namtra\_adv}} namelist, by 
+setting to \textit{true} one of the logicals \textit{ln\_traadv\_xxx}. 
+The corresponding code can be found in the \textit{traadv\_xxx.F90} module, 
+where \textit{xxx} is a 3 or 4 letter acronym corresponding to each scheme. 
 By default ($i.e.$ in the reference namelist, \ngn{namelist\_ref}), all the logicals 
 are set to \textit{false}. If the user does not select an advection scheme 
-in the configuration namelist (\ngn{namelist\_cfg}), the tracers will not be advected !
-
-Details of the advection schemes are given below. The choice of an advection scheme 
+in the configuration namelist (\ngn{namelist\_cfg}), the tracers will \textit{not} be advected !
+
+Details of the advection schemes are given below. The choosing an advection scheme 
 is a complex matter which depends on the model physics, model resolution, 
-type of tracer, as well as the issue of numerical cost. 
-
-Note that 
+type of tracer, as well as the issue of numerical cost. In particular, we note that
 (1) CEN and FCT schemes require an explicit diffusion operator 
-while the other schemes are diffusive enough so that they do not necessarily require additional diffusion ; 
+while the other schemes are diffusive enough so that they do not necessarily need additional diffusion ; 
 (2) CEN and UBS are not \textit{positive} schemes
 \footnote{negative values can appear in an initially strictly positive tracer field 
@@ -166 +171 @@
 %        2nd and 4th order centred schemes
 % -------------------------------------------------------------------------------------------------------------
-\subsection   [$2^{nd}$ and $4^{th}$ order centred schemes (CEN) (\np{ln\_traadv\_cen})]
-         {$2^{nd}$ and $4^{th}$ order centred schemes (CEN) (\np{ln\_traadv\_cen}=true)}
+\subsection [centred schemes (CEN) (\np{ln\_traadv\_cen})]
+            {centred schemes (CEN) (\np{ln\_traadv\_cen}=true)}
 \label{TRA_adv_cen}
 
 %        2nd order centred scheme  
 
-In the $2^{nd}$ order centred formulation (CEN2), the tracer at velocity points is 
-evaluated as the mean of the two neighbouring $T$-point values. 
+The centred advection scheme (CEN) is used when \np{ln\_traadv\_cen}~=~\textit{true}. 
+Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) 
+and vertical direction by setting \np{nn\_cen\_h} and \np{nn\_cen\_v} to $2$ or $4$. 
+CEN implementation can be found in the \mdl{traadv\_cen} module.
+
+In the $2^{nd}$ order centred formulation (CEN2), the tracer at velocity points 
+is evaluated as the mean of the two neighbouring $T$-point values. 
 For example, in the $i$-direction :
 \begin{equation} \label{Eq_tra_adv_cen2}
@@ -185 +195 @@
 a leapfrog scheme in conjunction with an Asselin time-filter, so $T$ in 
 (\ref{Eq_tra_adv_cen2}) is the \textit{now} tracer value. 
-CEN2 is computed in the \mdl{traadv\_cen} module.
 
 Note that using the CEN2, the overall tracer advection is of second 
 order accuracy since both (\ref{Eq_tra_adv}) and (\ref{Eq_tra_adv_cen2}) 
-have this order of accuracy. \gmcomment{Note also that ... blah, blah}
+have this order of accuracy.
 
 %        4nd order centred scheme  
 
-In the $4^{th}$ order formulation (CEN4), tracer values are evaluated at velocity points as 
+In the $4^{th}$ order formulation (CEN4), tracer values are evaluated at u- and v-points as 
 a $4^{th}$ order interpolation, and thus depend on the four neighbouring $T$-points. 
 For example, in the $i$-direction:
@@ -200 +209 @@
 =\overline{   T - \frac{1}{6}\,\delta _i \left[ \delta_{i+1/2}[T] \,\right]   }^{\,i+1/2}
 \end{equation}
+In the vertical direction (\np{nn\_cen\_v}=$4$), a $4^{th}$ COMPACT interpolation 
+has been prefered \citep{Demange_PhD2014}.
+In the COMPACT scheme, both the field and its derivative are interpolated, 
+which leads, after a matrix inversion, spectral characteristics 
+similar to schemes of higher order \citep{Lele_JCP1992}.
+ 
 
 Strictly speaking, the CEN4 scheme is not a $4^{th}$ order advection scheme 
@@ -212 +227 @@
 
 A direct consequence of the pseudo-fourth order nature of the scheme is that 
-it is not non-diffusive, $i.e.$ the global variance of a tracer is not preserved using 
-CEN4. Furthermore, it must be used in conjunction with an explicit 
-diffusion operator to produce a sensible solution. As in CEN2 case, the time-stepping is  
-performed using a leapfrog scheme in conjunction with an Asselin time-filter, 
-so $T$ in (\ref{Eq_tra_adv_cen4}) is the \textit{now} tracer.
-
-At a $T$-grid cell adjacent to a boundary (coastline, bottom and surface), an 
-additional hypothesis must be made to evaluate $\tau _u^{cen4}$. This 
-hypothesis usually reduces the order of the scheme. Here we choose to set 
-the gradient of $T$ across the boundary to zero. Alternative conditions can be 
-specified, such as a reduction to a second order scheme for these near boundary 
-grid points.
+it is not non-diffusive, $i.e.$ the global variance of a tracer is not preserved using CEN4. 
+Furthermore, it must be used in conjunction with an explicit diffusion operator 
+to produce a sensible solution. 
+As in CEN2 case, the time-stepping is performed using a leapfrog scheme in conjunction 
+with an Asselin time-filter, so $T$ in (\ref{Eq_tra_adv_cen4}) is the \textit{now} tracer.
+
+At a $T$-grid cell adjacent to a boundary (coastline, bottom and surface), 
+an additional hypothesis must be made to evaluate $\tau _u^{cen4}$. 
+This hypothesis usually reduces the order of the scheme. 
+Here we choose to set the gradient of $T$ across the boundary to zero. 
+Alternative conditions can be specified, such as a reduction to a second order scheme 
+for these near boundary grid points.
 
 % -------------------------------------------------------------------------------------------------------------
 %        FCT scheme  
 % -------------------------------------------------------------------------------------------------------------
-\subsection   [$2^{nd}$ and $4^{th}$ Flux Corrected Transport schemes (FCT) (\np{ln\_traadv\_fct})]
-         {$2^{nd}$ and $4^{th}$ Flux Corrected Transport schemes (FCT) (\np{ln\_traadv\_fct}=true)}
+\subsection   [Flux Corrected Transport schemes (FCT) (\np{ln\_traadv\_fct})]
+         {Flux Corrected Transport schemes (FCT) (\np{ln\_traadv\_fct}=true)}
 \label{TRA_adv_tvd}
 
-In the Flux Corrected Transport formulation, the tracer at velocity 
-points is evaluated using a combination of an upstream and a centred scheme. 
-For example, in the $i$-direction :
+The Flux Corrected Transport schemes (FCT) is used when \np{ln\_traadv\_fct}~=~\textit{true}. 
+Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) 
+and vertical direction by setting \np{nn\_fct\_h} and \np{nn\_fct\_v} to $2$ or $4$.
+FCT implementation can be found in the \mdl{traadv\_fct} module.
+
+In FCT formulation, the tracer at velocity points is evaluated using a combination of 
+an upstream and a centred scheme. For example, in the $i$-direction :
 \begin{equation} \label{Eq_tra_adv_fct}
 \begin{split}
@@ -246 +265 @@
 \end{equation}
 where $c_u$ is a flux limiter function taking values between 0 and 1. 
+The FCT order is the one of the centred scheme used ($i.e.$ it depends on the setting of
+\np{nn\_fct\_h} and \np{nn\_fct\_v}.
 There exist many ways to define $c_u$, each corresponding to a different 
-total variance decreasing scheme. The one chosen in \NEMO is described in 
-\citet{Zalesak_JCP79}. $c_u$ only departs from $1$ when the advective term 
-produces a local extremum in the tracer field. The resulting scheme is quite 
-expensive but \emph{positive}. It can be used on both active and passive tracers. 
-This scheme is tested and compared with MUSCL and a MPDATA scheme in \citet{Levy_al_GRL01}. 
-The FCT scheme is implemented in the \mdl{traadv\_fct} module.
-
-For stability reasons (see \S\ref{STP}),
-$\tau _u^{cen}$ is evaluated  in (\ref{Eq_tra_adv_fct}) using the \textit{now} tracer 
-while $\tau _u^{ups}$ is evaluated using the \textit{before} tracer. In other words, 
+FCT scheme. The one chosen in \NEMO is described in \citet{Zalesak_JCP79}. 
+$c_u$ only departs from $1$ when the advective term produces a local extremum in the tracer field. 
+The resulting scheme is quite expensive but \emph{positive}. 
+It can be used on both active and passive tracers. 
+A comparison of FCT-2 with MUSCL and a MPDATA scheme can be found in \citet{Levy_al_GRL01}. 
+
+An additional option has been added controlled by \np{nn\_fct\_zts}. By setting this integer to 
+a value larger than zero, a $2^{nd}$ order FCT scheme is used on both horizontal and vertical direction, 
+but on the latter, a split-explicit time stepping is used, with a number of sub-timestep equals
+to \np{nn\_fct\_zts}. This option can be useful when the size of the timestep is limited 
+by vertical advection \citep{Lemarie_OM2015)}. Note that in this case, a similar split-explicit 
+time stepping should be used on vertical advection of momentum to insure a better stability
+(see \S\ref{DYN_zad}).
+
+For stability reasons (see \S\ref{STP}), $\tau _u^{cen}$ is evaluated in (\ref{Eq_tra_adv_fct}) 
+using the \textit{now} tracer while $\tau _u^{ups}$ is evaluated using the \textit{before} tracer. In other words, 
 the advective part of the scheme is time stepped with a leap-frog scheme 
 while a forward scheme is used for the diffusive part. 
@@ -267 +294 @@
 \label{TRA_adv_mus}
 
-The Monotone Upstream Scheme for Conservative Laws (MUSCL) has been 
-implemented by \citet{Levy_al_GRL01}. In its formulation, the tracer at velocity points 
+The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np{ln\_traadv\_mus}~=~\textit{true}. 
+MUSCL implementation can be found in the \mdl{traadv\_mus} module.
+
+MUSCL has been first implemented in \NEMO by \citet{Levy_al_GRL01}. In its formulation, the tracer at velocity points 
 is evaluated assuming a linear tracer variation between two $T$-points 
 (Fig.\ref{Fig_adv_scheme}). For example, in the $i$-direction :
@@ -288 +317 @@
 directed toward land, an upstream flux is used. This choice ensure 
 the \textit{positive} character of the scheme. 
+In addition, fluxes round a grid-point where a runoff is applied can optionally be 
+computed using upstream fluxes (\np{ln\_mus\_ups}~=~\textit{true}).
 
 % -------------------------------------------------------------------------------------------------------------
@@ -296 +327 @@
 \label{TRA_adv_ubs}
 
-The UBS advection scheme (also often called UP3) is an upstream-biased third order 
-scheme based on an upstream-biased parabolic interpolation. It is also known as 
-the Cell Averaged QUICK scheme (Quadratic Upstream Interpolation for Convective 
-Kinematics). For example, in the $i$-direction :
+The Upstream-Biased Scheme (UBS) is used when \np{ln\_traadv\_ubs}~=~\textit{true}. 
+UBS implementation can be found in the \mdl{traadv\_mus} module.
+
+The UBS scheme, often called UP3, is also known as the Cell Averaged QUICK scheme 
+(Quadratic Upstream Interpolation for Convective Kinematics). It is an upstream-biased 
+third order scheme based on an upstream-biased parabolic interpolation.  
+For example, in the $i$-direction :
 \begin{equation} \label{Eq_tra_adv_ubs}
    \tau _u^{ubs} =\overline T ^{i+1/2}-\;\frac{1}{6} \left\{      
@@ -313 +347 @@
  the advection scheme is similar to that reported in \cite{Farrow1995}. 
 It is a relatively good compromise between accuracy and smoothness. 
-It is not a \emph{positive} scheme, meaning that false extrema are permitted, 
+Nevertheless the scheme is not \emph{positive}, meaning that false extrema are permitted, 
 but the amplitude of such are significantly reduced over the centred second 
-or fourth order method. Nevertheless it is not recommended that it should be 
+or fourth order method. therefore it is not recommended that it should be 
 applied to a passive tracer that requires positivity. 
 
 The intrinsic diffusion of UBS makes its use risky in the vertical direction 
-where the control of artificial diapycnal fluxes is of paramount importance. 
-Therefore the vertical flux is evaluated using either a 2nd order FCT scheme 
-or a 4th order COMPACT scheme (\np{nn\_cen\_v}=2 or 4).
+where the control of artificial diapycnal fluxes is of paramount importance \citep{Shchepetkin_McWilliams_OM05, Demange_PhD2014}. 
+Therefore the vertical flux is evaluated using either a $2^nd$ order FCT scheme 
+or a $4^th$ order COMPACT scheme (\np{nn\_cen\_v}=2 or 4).
 
 For stability reasons  (see \S\ref{STP}),
@@ -336 +370 @@
 substitution in the \mdl{traadv\_ubs} module and obtain a QUICK scheme.
 
-???
-
-Four different options are possible for the vertical 
-component used in the UBS scheme. $\tau _w^{ubs}$ can be evaluated 
-using either \textit{(a)} a centred $2^{nd}$ order scheme, or  \textit{(b)} 
-a FCT scheme, or  \textit{(c)} an interpolation based on conservative 
-parabolic splines following the \citet{Shchepetkin_McWilliams_OM05} 
-implementation of UBS in ROMS, or  \textit{(d)} a UBS. The $3^{rd}$ case 
-has dispersion properties similar to an eighth-order accurate conventional scheme.
-The current reference version uses method (b).
-
-???
-
-Note that :
-
-(1) When a high vertical resolution $O(1m)$ is used, the model stability can 
-be controlled by vertical advection (not vertical diffusion which is usually 
-solved using an implicit scheme). Computer time can be saved by using a 
-time-splitting technique on vertical advection. Such a technique has been 
-implemented and validated in ORCA05 with 301 levels. It is not available 
-in the current reference version. 
-
-(2) It is straightforward to rewrite \eqref{Eq_tra_adv_ubs} as follows:
+Note that it is straightforward to rewrite \eqref{Eq_tra_adv_ubs} as follows:
 \begin{equation} \label{Eq_traadv_ubs2}
 \tau _u^{ubs} = \tau _u^{cen4} + \frac{1}{12} \left\{  
@@ -380 +392 @@
 Thirdly, the diffusion term is in fact a biharmonic operator with an eddy 
 coefficient which is simply proportional to the velocity:
- $A_u^{lm}= \frac{1}{12}\,{e_{1u}}^3\,|u|$. Note the current version of NEMO still uses 
- \eqref{Eq_tra_adv_ubs}, not \eqref{Eq_traadv_ubs2}.
- %%%
- \gmcomment{the change in UBS scheme has to be done}
- %%%
+ $A_u^{lm}= \frac{1}{12}\,{e_{1u}}^3\,|u|$. Note the current version of NEMO uses 
+the computationally more efficient formulation \eqref{Eq_tra_adv_ubs}.
 
 % -------------------------------------------------------------------------------------------------------------
@@ -395 +404 @@
 The Quadratic Upstream Interpolation for Convective Kinematics with 
 Estimated Streaming Terms (QUICKEST) scheme proposed by \citet{Leonard1979} 
-is the third order Godunov scheme. It is associated with the ULTIMATE QUICKEST 
+is used when \np{ln\_traadv\_qck}~=~\textit{true}. 
+QUICKEST implementation can be found in the \mdl{traadv\_mus} module.
+
+QUICKEST is the third order Godunov scheme which is associated with the ULTIMATE QUICKEST 
 limiter \citep{Leonard1991}. It has been implemented in NEMO by G. Reffray 
 (MERCATOR-ocean) and can be found in the \mdl{traadv\_qck} module.
@@ -405 +417 @@
 This no longer guarantees the positivity of the scheme. The use of TVD in the vertical 
 direction (as for the UBS case) should be implemented to restore this property.
+
+%%%gmcomment   :  Cross term are missing in the current implementation....
 
 
@@ -1241 +1255 @@
 \hline
 coeff.   & computer name   & S-EOS     &  description                      \\ \hline
-$a_0$       & \np{nn\_a0}     & 1.6550 $10^{-1}$ &  linear thermal expansion coeff.    \\ \hline
-$b_0$       & \np{nn\_b0}     & 7.6554 $10^{-1}$ &  linear haline  expansion coeff.    \\ \hline
-$\lambda_1$ & \np{nn\_lambda1}& 5.9520 $10^{-2}$ &  cabbeling coeff. in $T^2$          \\ \hline
-$\lambda_2$ & \np{nn\_lambda2}& 5.4914 $10^{-4}$ &  cabbeling coeff. in $S^2$       \\ \hline
-$\nu$       & \np{nn\_nu}     & 2.4341 $10^{-3}$ &  cabbeling coeff. in $T \, S$       \\ \hline
-$\mu_1$     & \np{nn\_mu1}    & 1.4970 $10^{-4}$ &  thermobaric coeff. in T         \\ \hline
-$\mu_2$     & \np{nn\_mu2}    & 1.1090 $10^{-5}$ &  thermobaric coeff. in S            \\ \hline
+$a_0$       & \np{rn\_a0}     & 1.6550 $10^{-1}$ &  linear thermal expansion coeff.    \\ \hline
+$b_0$       & \np{rn\_b0}     & 7.6554 $10^{-1}$ &  linear haline  expansion coeff.    \\ \hline
+$\lambda_1$ & \np{rn\_lambda1}& 5.9520 $10^{-2}$ &  cabbeling coeff. in $T^2$          \\ \hline
+$\lambda_2$ & \np{rn\_lambda2}& 5.4914 $10^{-4}$ &  cabbeling coeff. in $S^2$       \\ \hline
+$\nu$       & \np{rn\_nu}     & 2.4341 $10^{-3}$ &  cabbeling coeff. in $T \, S$       \\ \hline
+$\mu_1$     & \np{rn\_mu1}    & 1.4970 $10^{-4}$ &  thermobaric coeff. in T         \\ \hline
+$\mu_2$     & \np{rn\_mu2}    & 1.1090 $10^{-5}$ &  thermobaric coeff. in S            \\ \hline
 \end{tabular}
 \caption{ \label{Tab_SEOS}

branches/2015/dev_r5836_NOC3_vvl_by_default/DOC/TexFiles/Namelist/namtra_adv

@@ -13 +13 @@
       ln_mus_ups =  .false.         !  use upstream scheme near river mouths
    ln_traadv_ubs =  .false.  !  UBS scheme
-      nn_ubs_v   =  2               !  =2  , vertical 2nd order FCT
+      nn_ubs_v   =  2               !  =2  , vertical 2nd order FCT / COMPACT 4th order
    ln_traadv_qck =  .false.  !  QUICKEST scheme
 /

branches/2015/dev_r5836_NOC3_vvl_by_default/NEMOGCM/CONFIG/SHARED/namelist_ref

@@ -765 +765 @@
       ln_mus_ups =  .false.         !  use upstream scheme near river mouths
    ln_traadv_ubs =  .false.  !  UBS scheme
-      nn_ubs_v   =  2               !  =2  , vertical 2nd order FCT
+      nn_ubs_v   =  2               !  =2  , vertical 2nd order FCT / COMPACT 4th order
    ln_traadv_qck =  .false.  !  QUICKEST scheme
 /