--- manual/s_algorithm/text/notation.tex	2001/08/08 16:15:21	1.1.1.1
+++ manual/s_algorithm/text/notation.tex	2001/10/25 18:36:53	1.6
@@ -1,10 +1,10 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/notation.tex,v 1.1.1.1 2001/08/08 16:15:21 adcroft Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/notation.tex,v 1.6 2001/10/25 18:36:53 cnh Exp $
 % $Name:  $
 
-\section{Notations} 
+\subsection{Notation} 
 
-The notations we use to discribe the discrete formulation 
-of the model are summarised hereafter:\\
+The notations we use to describe the discrete formulation 
+of the model are summarized hereafter:\\
 general notation:
 \\ $\Delta x, \Delta y, \Delta r$ grid spacing in X,Y,R directions.
 \\ $A_o$ : Area of the face orthogonal to "o" direction (o=u,v,w ...).
@@ -12,16 +12,22 @@
 Volume of the grid box surrounding $u,v,w,\theta$ point;
 \\ $i,j,k$ : current index relative to X,Y,R directions;
 \\basic operator:
-\\ $\delta_i $ : $\delta_i \Phi = \Phi_{i+1} - \Phi_i $
-\\ $\overline{~}i$ : $\overline{\Phi}^i = ( \Phi_{i+1} + \Phi_i ) / 2 $ 
+\\ $\delta_i $ : $\delta_i \Phi = \Phi_{i+1/2} - \Phi_{i-1/2} $
+\label{eq:delta_i}
+\\ $\overline{~}i$ : $\overline{\Phi}^i = ( \Phi_{i+1/2} + \Phi_{i-1/2} ) / 2 $ 
+\label{eq:bar_i}
 \\ $\delta_x $ : $\delta_x \Phi = \frac{1}{\Delta x} \delta_i \Phi $
+\label{eq:delta_x}
 \\
 \\ $\overline{\nabla}$ = gradient operator :  
 $\overline{\nabla} \Phi = \{ \delta_x \Phi , \delta_y \Phi \}$
+\label{eq:d_grad}
 \\ $\overline{\nabla} \cdot$ = divergence operator :  
 $\overline{\nabla}\cdot \vec{\mathrm{f}}  = 
-\frac{1}{\cal V} \{ \delta_i A_x \mathrm{f}_x 
-                  + \delta_j A_y \mathrm{f}_y \} $
-\\ $\overline{\nabla}^2 $ = Laplacien operator :
+\frac{1}{\cal A} \{ \delta_i \Delta y \mathrm{f}_x 
+                  + \delta_j \Delta x \mathrm{f}_y \} $
+\label{eq:d_div}
+\\ $\overline{\nabla}^2 $ = Laplacian operator :
 $ \overline{\nabla}^2 \Phi = 
    \overline{\nabla}\cdot \overline{\nabla}\Phi $
+\label{eq:d_lap}