Changeset 3754

Timestamp:

Oct 11, 2006, 4:45:01 PM (18 years ago)

Author:

ole

Message:

Added channel examples to user manual

Location:

anuga_core/documentation/user_manual

Files:

• anuga_user_manual.tex (modified) (1 diff)
• examples/channel1.py (moved) (moved from anuga_core/documentation/user_manual/examples/channel_1.py) (1 diff)
• examples/channel2.py (moved) (moved from anuga_core/documentation/user_manual/examples/channel_2.py)
• examples/channel3.py (moved) (moved from anuga_core/documentation/user_manual/examples/channel_3.py) (2 diffs)
• examples/runup.py (modified) (2 diffs)

anuga_core/documentation/user_manual/anuga_user_manual.tex

@@ -658 +658 @@
   \caption{Bedslope example viewed with Swollen}
   \label{fig:bedslope2}
+\end{figure}
+
+
+
+\clearpage
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{A slightly more complex example}
+\label{sec:channelexample}
+
+\subsection{Overview}
+
+The next example is about waterflow in a channel with varying boundary conditions and 
+more complex topograhies. These examples build on the
+concepts introduced through the \file{runup.py} in Section \ref{sec:simpleexample}.
+The example will be built up through three progressively more complex scripts.
+
+\subsection{Overview}
+As in the case of \file{runup.py}, the actions carried
+out by the program can be organised according to this outline:
+
+\begin{enumerate}
+
+   \item Set up a triangular mesh.
+
+   \item Set certain parameters governing the mode of
+operation of the model---specifying, for instance, where to store the
+model output.
+
+   \item Set up initial conditions for various quantities such as the elevation, to be specified at each mesh point (vertex).
+
+   \item Set up the boundary conditions.
+
+   \item Carry out the evolution of the model through a series of time
+steps and output the results, providing a results file that can be
+visualised.
+
+\end{enumerate}
+
+
+\subsection{The Code}
+
+Here is the code for the first version of the channel flow \file{channel1.py}:
+
+\verbatiminput{examples/channel1.py}
+
+In discussing the details of this example, we follow the outline
+given above, discussing each major step of the code in turn.
+
+\subsection{Establishing the Mesh}\index{mesh, establishing}
+
+In this example we use a similar simple structured triangular mesh as in \code{runup.py} 
+for simplicity, but this time we will use a symmetric one and also 
+change the physical extent of the domain. The assignment
+
+{\small \begin{verbatim}
+    points, vertices, boundary = rectangular_cross(m, n, 
+                                                   len1=length, len2=width)
+\end{verbatim}}
+returns a m x n mesh similar to the one used in the previous example, except that now the 
+extent in the x and y directions are given by the value of \code{length} and \code{width} 
+respectively.
+
+Defining m and n in terms of the extent as in this example provides a convenient way of 
+controlling the resolution: By defining dx and dy to be the desired size of each hypothenuse in the mesh we can write the mesh generation as follows:
+
+{\small \begin{verbatim}
+length = 10.
+width = 5.
+dx = dy = 1           # Resolution: Length of subdivisions on both axes
+
+points, vertices, boundary = rectangular_cross(int(length/dx), int(width/dy),
+                                               len1=length, len2=width)
+\end{verbatim}}
+which yields a mesh of length=10m, width=5m with 1m spacings. To increase the resolution, as we will later in this example, one merely decrease the values of dx and dy.
+
+The rest of this script is as in the previous example.
+% except for an application of the 'expression' form of \code{set\_quantity} where we use the value of \code{elevation} to define the (dry) initial condition for \code{stage}:
+%{\small \begin{verbatim}
+%  domain.set_quantity('stage', expression='elevation')
+%\end{verbatim}}
+
+\section{Model Output}
+
+The following figures are screenshots from the \anuga visualisation
+tool \code{swollen} of output from this example.
+%\begin{figure}[hbt]
+%  \centerline{\includegraphics[width=75mm, height=75mm]
+%    {examples/runupstart.eps}}%
+%
+%  \caption{Bedslope example viewed with Swollen}
+%  \label{fig:runupstart}
+%\end{figure}
+
+
+\subsection{Changing boundary conditions on the fly}
+
+Here is the code for the second version of the channel flow \file{channel2.py}:
+\verbatiminput{examples/channel2.py}
+This example differs from the first version in that a constant outflow boundary condition has 
+been defined 
+{\small \begin{verbatim}
+    Bo = Dirichlet_boundary([-5, 0, 0]) # Outflow
+\end{verbatim}}
+and that it is applied to the right hand side boundary when the water level there exceeds 0m.
+{\small \begin{verbatim}
+for t in domain.evolve(yieldstep = 0.2, finaltime = 40.0):
+    domain.write_time()
+
+    if domain.get_quantity('stage').get_values(interpolation_points=[[10, 2.5]]) > 0:        
+        print 'Stage > 0: Changing to outflow boundary'
+        domain.modify_boundary({'right': Bo})
+\end{verbatim}}
+
+The if statement in the timestepping loop (evolve) gets the quantity
+\code{stage} and obtain the interpolated value at the point (10m,
+2.5m) which is on the right boundary. If the stage exceeds 0m a
+message is printed and the old boundary condition at tag 'right' is
+replaced by the outflow boundary using the method 
+{\small \begin{verbatim} 
+    domain.modify_boundary({'right': Bo})
+\end{verbatim}}
+This type of dynamically varying boundary could for example be used to model the 
+breakdown of a sluice door when water exceeds a certain level. 
+
+\subsection{Output}
+
+The text output from this example looks like this
+{\small \begin{verbatim} 
+...
+Time = 15.4000, delta t in [0.03789902, 0.03789916], steps=6 (6)
+Time = 15.6000, delta t in [0.03789896, 0.03789908], steps=6 (6)
+Time = 15.8000, delta t in [0.03789891, 0.03789903], steps=6 (6)
+Stage > 0: Changing to outflow boundary
+Time = 16.0000, delta t in [0.02709050, 0.03789898], steps=6 (6)
+Time = 16.2000, delta t in [0.03789892, 0.03789904], steps=6 (6)
+...
+\end{verbatim}}
+
+
+\subsection{Flow through more complex topograhies}
+
+Here is the code for the third version of the channel flow \file{channel3.py}:
+\verbatiminput{examples/channel3.py}
+
+This example differs from the first two versions in that the topography 
+contains obstacles.
+
+This is accomplished here by defining the function \code{topography} as follows
+{\small \begin{verbatim}
+def topography(x,y):
+    """Complex topography defined by a function of vectors x and y
+    """
+    
+    z = -x/10                                
+
+    N = len(x)
+    for i in range(N):
+
+        # Step
+        if 10 < x[i] < 12:
+            z[i] += 0.4 - 0.05*y[i]        
+        
+        # Constriction
+        if 27 < x[i] < 29 and y[i] > 3:
+            z[i] += 2        
+        
+        # Pole
+        if (x[i] - 34)**2 + (y[i] - 2)**2 < 0.4**2:
+            z[i] += 2
+
+    return z
+\end{verbatim}}
+
+In addition, changing the resolution to dx=dy=0.1 creates a finer mesh resolving the new featurse better.
+
+A screenshot of this model at time == ... is
+\begin{figure}[hbt]
+
+  \centerline{\includegraphics[width=75mm, height=75mm]
+    {examples/runupstart.eps}}
+
+  \caption{Channel3 example viewed with Swollen}
+  \label{fig:channel3}
 \end{figure}
 

anuga_core/documentation/user_manual/examples/channel1.py

@@ -38 +38 @@
                     expression='elevation')        # Dry
 #domain.set_quantity('stage',
-                     expression='elevation + 0.1') # Wet
+#                     expression='elevation + 0.1') # Wet
 
 

anuga_core/documentation/user_manual/examples/channel3.py

@@ -19 +19 @@
 length = 40.
 width = 5.
-dx = dy = 1           # Resolution: Length of subdivisions on both axes
-#dx = dy = .1           # Resolution: Length of subdivisions on both axes
+#dx = dy = 1           # Resolution: Length of subdivisions on both axes
+dx = dy = .1           # Resolution: Length of subdivisions on both axes
 
 points, vertices, boundary = rectangular_cross(int(length/dx), int(width/dy),
@@ -78 +78 @@
 
 
+    if domain.get_quantity('stage').\
+           get_values(interpolation_points=[[10, 2.5]]) > 0:        
+        print 'Stage > 0: Changing to outflow boundary'
+        domain.modify_boundary({'right': Bo})

anuga_core/documentation/user_manual/examples/runup.py

@@ -10 +10 @@
 #------------------------------------------------------------------------------
 
-from anuga.abstract_2d_finite_volumes.mesh_factory import rectangular_cross
+from anuga.abstract_2d_finite_volumes.mesh_factory import rectangular
 from anuga.shallow_water import Domain
 from anuga.shallow_water import Reflective_boundary
@@ -22 +22 @@
 #------------------------------------------------------------------------------
 
-points, vertices, boundary = rectangular_cross(10, 10) # Basic mesh
+points, vertices, boundary = rectangular(10, 10) # Basic mesh
 
 domain = Domain(points, vertices, boundary) # Create domain