/[escript]/trunk/doc/cookbook/twodheatdiff001.tex
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revision 2947 by gross, Mon Feb 8 06:45:41 2010 UTC revision 2948 by gross, Thu Feb 25 04:54:30 2010 UTC
# Line 115  Before we turn the question how we set $ Line 115  Before we turn the question how we set $
115  pointed out in \refEq{NEUMAN 2} makes certain assumptions on the boundary conditions. In our case  pointed out in \refEq{NEUMAN 2} makes certain assumptions on the boundary conditions. In our case
116  this assumptions translates to;  this assumptions translates to;
117  \begin{equation}  \begin{equation}
118    -n \cdot \kappa \nabla T^{(n)} =
119  -n\hackscore{0} \cdot \kappa \frac{\partial T^{(n)}}{\partial x} - n\hackscore{1} \cdot  \kappa \frac{\partial T^{(n)}}{\partial y} = 0  -n\hackscore{0} \cdot \kappa \frac{\partial T^{(n)}}{\partial x} - n\hackscore{1} \cdot  \kappa \frac{\partial T^{(n)}}{\partial y} = 0
120    \label{eq:hom flux}
121  \end{equation}  \end{equation}
122  which sets the normal component of the heat flux $- \kappa \cdot (\frac{\partial T^{(n)}}{\partial x}, \frac{\partial T^{(n)}}{\partial y})$ to zero. This means that the regions is insulated which is what we want.  which sets the normal component of the heat flux $- \kappa \cdot (\frac{\partial T^{(n)}}{\partial x}, \frac{\partial T^{(n)}}{\partial y})$ to zero. This means that the regions is insulated which is what we want.
123  On the left and right face of the domain where we have $(n\hackscore{0},n\hackscore{1} ) = (\mp 1,0)$  On the left and right face of the domain where we have $(n\hackscore{0},n\hackscore{1} ) = (\mp 1,0)$
# Line 177  sample points of a PDE solution\footnote Line 179  sample points of a PDE solution\footnote
179  \end{figure}  \end{figure}
180    
181  \section{Contouring \esc data using \modmpl.}  \section{Contouring \esc data using \modmpl.}
182    \label{Sec:2DHD plot}
183  To complete our transition from a 1D to a 2D model we also need to modify the  To complete our transition from a 1D to a 2D model we also need to modify the
184  plotting procedure. As before we use the  \modmpl to do the plotting  plotting procedure. As before we use the  \modmpl to do the plotting
185  in this case a contour plot. For 2D contour plots \modmpl expects that the  in this case a contour plot. For 2D contour plots \modmpl expects that the
# Line 266  visualize the temperature and can direct Line 269  visualize the temperature and can direct
269  regridding required. It is recommended to use the file extension \file{.vtu} for files  regridding required. It is recommended to use the file extension \file{.vtu} for files
270  created by \verb|saveVTK|.  created by \verb|saveVTK|.
271    
272  \begin{figure}[h]  \begin{figure}[ht]
273  \centerline{\includegraphics[width=4.in]{figures/ScreeshotMayavi2n1}}  \centerline{\includegraphics[width=4.in]{figures/ScreeshotMayavi2n1}}
274  \caption{\mayavi start up Window.}  \caption{\mayavi start up Window.}
275  \label{fig:mayavi window}  \label{fig:mayavi window}
276  \end{figure}  \end{figure}
277    
278  \begin{figure}[h]  \begin{figure}[ht]
279  \centerline{\includegraphics[width=4.in]{figures/ScreeshotMayavi2n2}}  \centerline{\includegraphics[width=4.in]{figures/ScreeshotMayavi2n2}}
280  \caption{\mayavi data control window.}  \caption{\mayavi data control window.}
281  \label{fig:mayavi window2}  \label{fig:mayavi window2}

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