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revision 2974 by artak, Thu Mar 4 01:33:38 2010 UTC revision 2975 by ahallam, Thu Mar 4 05:44:12 2010 UTC
# Line 14  Line 14 
14  \section{Steady-state Heat Refraction}  \section{Steady-state Heat Refraction}
15  \label{STEADY-STATE HEAT REFRACTION}  \label{STEADY-STATE HEAT REFRACTION}
16    
17  In this chapter we show how to handle more complex geometries.  In this chapter we demonstrate how to handle more complex geometries.
18    
19  Steady-state heat refraction will give us an opportunity to investigate some of the richer features that the \esc package has to offer. One of these is \pycad . The advantage of using \pycad is that it offers an easy method for developing and manipulating complex domains. In conjunction with \gmsh we can generate finite element meshes that conform to our domain's shape providing accurate modelling of interfaces and boundaries. Another useful function of \pycad is that we can tag specific areas of our domain with labels as we construct them. These labels can then be used in \esc to define properties like material constants and source locations.  Steady-state heat refraction will give us an opportunity to investigate some of the richer features that the \esc package has to offer. One of these is \pycad . The advantage of using \pycad is that it offers an easy method for developing and manipulating complex domains. In conjunction with \gmsh we can generate finite element meshes that conform to our domain's shape providing accurate modelling of interfaces and boundaries. Another useful function of \pycad is that we can tag specific areas of our domain with labels as we construct them. These labels can then be used in \esc to define properties like material constants and source locations.
20    
# Line 30  the steady-state heat equation over a re Line 30  the steady-state heat equation over a re
30  \section{Example 4: Creating the domain with \pycad}  \section{Example 4: Creating the domain with \pycad}
31  \sslist{example04a.py}  \sslist{example04a.py}
32    
33  We modify the example in Chapter~\ref{CHAP HEAT 2a} in two ways: we look the steady state  We modify the example in Chapter~\ref{CHAP HEAT 2a} in two ways. Firstly, we look at the steady state
34  case with slightly modified boundary conditions and use a more flexible tool  case with slightly modified boundary conditions and then we use a more flexible tool
35  to generate to generate the geometry. Lets look at the geometry first.  to generate the geometry. Lets look at the geometry first.
36    
37  We want to define a rectangular domain of width $5 km$ and depth $6 km$ below the surface of the Earth. Under the assumption of a known temperature at the surface, a known heat flux at the bottom and  We want to define a rectangular domain of width $5 km$ and depth $6 km$ below the surface of the Earth. The domain is subject to a few conditions. The temperature is known at the surface and the basement has a known heat flux. Each side of the domain is insulated and the aim is to calculate the final temperature distribution.
 insulation to both sides we want to calculate the steady-state temperature distribution.  
38    
39  In \pycad there are a few primary constructors that build upon each other to define domains and boundaries;  In \pycad there are a few primary constructors that build upon each other to define domains and boundaries;
40  the ones we use are:  the ones we use are:
# Line 46  Line() #Creates a line from a number of Line 45  Line() #Creates a line from a number of
45  CurveLoop() #Creates a closed loop from a number of lines.  CurveLoop() #Creates a closed loop from a number of lines.
46  PlaneSurface() #Creates a surface based on a CurveLoop  PlaneSurface() #Creates a surface based on a CurveLoop
47  \end{python}  \end{python}
48  So to build-up our domain as shown in \reffig{fig:pycad rec} we first need to create  So to construct our domain as shown in \reffig{fig:pycad rec}, we first need to create
49  the corner points. From the corner points we build the four edges of the rectangle. The four edges  the corner points. From the corner points we build the four edges of the rectangle. The four edges
50  form then a closed loop which defines our domain as a surface.  then form a closed loop which defines our domain as a surface.
51  We start by inputting the variables we need to construct the model.  We start by inputting the variables we need to construct the model.
52  \begin{python}  \begin{python}
53  width=5000.0*m   #width of model  width=5000.0*m   #width of model

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