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Timestamp:
2012-01-18T11:28:11+01:00 (9 years ago)
Author:
agn
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dev_NEMO_MERGE_2011:(DOC) Finish griffies description, remove need for pstricks

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  • branches/2011/dev_NEMO_MERGE_2011/DOC/TexFiles/Chapters/Chap_DOM.tex

    r3221 r3267  
    123123the following discrete forms in the curvilinear $s$-coordinate system: 
    124124\begin{equation} \label{Eq_DOM_grad} 
    125 \nabla q\equiv    \frac{1}{e_{1u} } \delta _{i+1/2 } [q] \;\,{\rm {\bf i}} 
    126       +  \frac{1}{e_{2v} } \delta _{j+1/2 } [q] \;\,{\rm {\bf j}} 
    127       +  \frac{1}{e_{3w}} \delta _{k+1/2} [q] \;\,{\rm {\bf k}} 
     125\nabla q\equiv    \frac{1}{e_{1u} } \delta _{i+1/2 } [q] \;\,\mathbf{i} 
     126      +  \frac{1}{e_{2v} } \delta _{j+1/2 } [q] \;\,\mathbf{j} 
     127      +  \frac{1}{e_{3w}} \delta _{k+1/2} [q] \;\,\mathbf{k} 
    128128\end{equation} 
    129129\begin{multline} \label{Eq_DOM_lap} 
    130 \Delta q\equiv \frac{1}{e_{1t}\,e_{2t}\,e_{3t} }  
     130\Delta q\equiv \frac{1}{e_{1t}\,e_{2t}\,e_{3t} } 
    131131       \;\left(          \delta_i  \left[ \frac{e_{2u}\,e_{3u}} {e_{1u}} \;\delta_{i+1/2} [q] \right] 
    132132+                        \delta_j  \left[ \frac{e_{1v}\,e_{3v}}  {e_{2v}} \;\delta_{j+1/2} [q] \right] \;  \right)      \\ 
     
    139139\begin{eqnarray}  \label{Eq_DOM_curl} 
    140140 \nabla \times {\rm {\bf A}}\equiv & 
    141       \frac{1}{e_{2v}\,e_{3vw} } \ \left( \delta_{j +1/2} \left[e_{3w}\,a_3 \right] -\delta_{k+1/2} \left[e_{2v} \,a_2 \right] \right)  &\ \rm{\bf i} \\  
    142  +& \frac{1}{e_{2u}\,e_{3uw}} \ \left( \delta_{k+1/2} \left[e_{1u}\,a_1  \right] -\delta_{i +1/2} \left[e_{3w}\,a_3 \right] \right)  &\ \rm{\bf j} \\  
    143  +& \frac{1}{e_{1f} \,e_{2f}    } \ \left( \delta_{i +1/2} \left[e_{2v}\,a_2  \right] -\delta_{j +1/2} \left[e_{1u}\,a_1 \right] \right)  &\ \rm{\bf k} 
     141      \frac{1}{e_{2v}\,e_{3vw} } \ \left( \delta_{j +1/2} \left[e_{3w}\,a_3 \right] -\delta_{k+1/2} \left[e_{2v} \,a_2 \right] \right)  &\ \mathbf{i} \\  
     142 +& \frac{1}{e_{2u}\,e_{3uw}} \ \left( \delta_{k+1/2} \left[e_{1u}\,a_1  \right] -\delta_{i +1/2} \left[e_{3w}\,a_3 \right] \right)  &\ \mathbf{j} \\ 
     143 +& \frac{1}{e_{1f} \,e_{2f}    } \ \left( \delta_{i +1/2} \left[e_{2v}\,a_2  \right] -\delta_{j +1/2} \left[e_{1u}\,a_1 \right] \right)  &\ \mathbf{k} 
    144144 \end{eqnarray} 
    145145\begin{equation} \label{Eq_DOM_div} 
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