Changeset 3267 for branches/2011/dev_NEMO_MERGE_2011/DOC/TexFiles/Chapters/Chap_DOM.tex

Timestamp:

2012-01-18T11:28:11+01:00 (12 years ago)

Author:

agn

Message:

dev_NEMO_MERGE_2011:(DOC) Finish griffies description, remove need for pstricks

File:

• branches/2011/dev_NEMO_MERGE_2011/DOC/TexFiles/Chapters/Chap_DOM.tex (modified) (2 diffs)

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

@@ -123 +123 @@
 the following discrete forms in the curvilinear $s$-coordinate system:
 \begin{equation} \label{Eq_DOM_grad}
-\nabla q\equiv    \frac{1}{e_{1u} } \delta _{i+1/2 } [q] \;\,{\rm {\bf i}}
-      +  \frac{1}{e_{2v} } \delta _{j+1/2 } [q] \;\,{\rm {\bf j}}
-      +  \frac{1}{e_{3w}} \delta _{k+1/2} [q] \;\,{\rm {\bf k}}
+\nabla q\equiv    \frac{1}{e_{1u} } \delta _{i+1/2 } [q] \;\,\mathbf{i}
+      +  \frac{1}{e_{2v} } \delta _{j+1/2 } [q] \;\,\mathbf{j}
+      +  \frac{1}{e_{3w}} \delta _{k+1/2} [q] \;\,\mathbf{k}
 \end{equation}
 \begin{multline} \label{Eq_DOM_lap}
-\Delta q\equiv \frac{1}{e_{1t}\,e_{2t}\,e_{3t} } 
+\Delta q\equiv \frac{1}{e_{1t}\,e_{2t}\,e_{3t} }
        \;\left(          \delta_i  \left[ \frac{e_{2u}\,e_{3u}} {e_{1u}} \;\delta_{i+1/2} [q] \right]
 +                        \delta_j  \left[ \frac{e_{1v}\,e_{3v}}  {e_{2v}} \;\delta_{j+1/2} [q] \right] \;  \right)      \\
@@ -139 +139 @@
 \begin{eqnarray}  \label{Eq_DOM_curl}
  \nabla \times {\rm {\bf A}}\equiv &
-      \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} \\ 
- +& \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} \\ 
- +& \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}
+      \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} \\ 
+ +& \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} \\
+ +& \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}
  \end{eqnarray}
 \begin{equation} \label{Eq_DOM_div}