% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/notation.tex,v 1.1 2001/08/08 16:15:21 adcroft Exp $ % $Name: $ \section{Notations} The notations we use to discribe the discrete formulation of the model are summarised 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 ...). \\ ${\cal V}_u , {\cal V}_v , {\cal V}_v , {\cal V}_\theta$ : 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_x $ : $\delta_x \Phi = \frac{1}{\Delta x} \delta_i \Phi $ \\ \\ $\overline{\nabla}$ = gradient operator : $\overline{\nabla} \Phi = \{ \delta_x \Phi , \delta_y \Phi \}$ \\ $\overline{\nabla} \cdot$ = 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 : $ \overline{\nabla}^2 \Phi = \overline{\nabla}\cdot \overline{\nabla}\Phi $