--- manual/s_algorithm/text/notation.tex 2001/08/08 18:28:56 1.2 +++ 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 1.2 2001/08/08 18:28:56 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 ...). @@ -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 \} $ -\\ $\overline{\nabla}^2 $ = Laplacien operator : +\label{eq:d_div} +\\ $\overline{\nabla}^2 $ = Laplacian operator : $ \overline{\nabla}^2 \Phi = \overline{\nabla}\cdot \overline{\nabla}\Phi $ +\label{eq:d_lap}