--- manual/s_algorithm/text/notation.tex 2001/08/08 16:15:21 1.1.1.1 +++ manual/s_algorithm/text/notation.tex 2001/08/08 18:28:56 1.2 @@ -1,4 +1,4 @@ -% $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 1.2 2001/08/08 18:28:56 adcroft Exp $ % $Name: $ \section{Notations} @@ -12,16 +12,16 @@ 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} $ +\\ $\overline{~}i$ : $\overline{\Phi}^i = ( \Phi_{i+1/2} + \Phi_{i-1/2} ) / 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 \} $ +\frac{1}{\cal A} \{ \delta_i \Delta y \mathrm{f}_x + + \delta_j \Delta x \mathrm{f}_y \} $ \\ $\overline{\nabla}^2 $ = Laplacien operator : $ \overline{\nabla}^2 \Phi = \overline{\nabla}\cdot \overline{\nabla}\Phi $