--- manual/s_algorithm/text/notation.tex 2001/08/08 18:28:56 1.2 +++ manual/s_algorithm/text/notation.tex 2001/09/11 16:05:00 1.5 @@ -1,7 +1,7 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/notation.tex,v 1.2 2001/08/08 18:28:56 adcroft Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/notation.tex,v 1.5 2001/09/11 16:05:00 cnh Exp $ % $Name: $ -\section{Notations} +\subsection{Notation} The notations we use to discribe the discrete formulation of the model are summarised hereafter:\\ @@ -13,15 +13,21 @@ \\ $i,j,k$ : current index relative to X,Y,R directions; \\basic operator: \\ $\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 A} \{ \delta_i \Delta y \mathrm{f}_x + \delta_j \Delta x \mathrm{f}_y \} $ +\label{eq:d_div} \\ $\overline{\nabla}^2 $ = Laplacien operator : $ \overline{\nabla}^2 \Phi = \overline{\nabla}\cdot \overline{\nabla}\Phi $ +\label{eq:d_lap}