Changeset 8788

Timestamp:

Mar 28, 2013, 10:47:22 PM (12 years ago)

Author:

mungkasi

Message:

Automated report for parabolic basin.

Location:

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/parabolic_basin

Files:

• analytical_parabolic_basin.py (modified) (1 diff)
• numerical_parabolic_basin.py (modified) (1 diff)
• plot_results_cross_section.py (modified) (3 diffs)
• produce_report.py (added)
• produce_results.py (modified) (1 diff)
• report.tex (added)
• results.tex (modified) (4 diffs)

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/parabolic_basin/analytical_parabolic_basin.py

@@ -4 +4 @@
 """
 from numpy import zeros,sqrt,sin,cos
+from anuga import g
 
-def analytic_cannal(x,t, D0=4., L=10., A=2., g=9.81):
+def analytic_cannal(x,t, D0=4., L=10., A=2., g=g):
     omega = sqrt(2*D0*g)/L
     N = len(x)

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/parabolic_basin/numerical_parabolic_basin.py

@@ -101 +101 @@
 
 
+#------------------------------------------------------------------------------
+# Produce a documentation of parameters
+#------------------------------------------------------------------------------
+parameter_file=open('parameters.tex', 'w')
+parameter_file.write('\\begin{verbatim}\n')
+from pprint import pprint
+pprint(domain.get_algorithm_parameters(),parameter_file,indent=4)
+parameter_file.write('\\end{verbatim}\n')
+parameter_file.close()
+
+
 #------------------------------
 #Evolve the system through time

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/parabolic_basin/plot_results_cross_section.py

@@ -24 +24 @@
 #Plot stages
 pyplot.clf()
-pyplot.ion()
 pyplot.plot(p2_st.x[v2], p2_st.stage[time_level,v2],'b.', label='numerical stage')
 pyplot.plot(p2_st.x[v2], p2_st.elev[v2],'k-', label='bed elevation')
@@ -37 +36 @@
 #Plot xmomentum
 pyplot.clf()
-pyplot.ion()
 pyplot.plot(p2_st.x[v2], p2_st.xmom[time_level,v2], 'b.', label='numerical')
 pyplot.plot(p2_st.x[v2], u*h,'r-', label='analytical')
@@ -49 +47 @@
 #Plot velocities
 pyplot.clf()
-pyplot.ion()
 pyplot.plot(p2_st.x[v2], p2_st.xvel[time_level,v2], 'b.', label='numerical')
 pyplot.plot(p2_st.x[v2], u,'r-', label='analytical')

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/parabolic_basin/produce_results.py

@@ -12 +12 @@
     run_validation_script('plot_results_cross_section.py')
     run_validation_script('plot_results_origin_wrt_time.py')    
+    run('python', 'produce_report.py')    
 
 def clean():

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/parabolic_basin/results.tex

@@ -1 @@
-\section{1D Parabolic Basin}
-This simulates flow oscillations in a 1D parabolic basin. The analytical solution is described by Thacker (REF), and is periodic. At any instant in time, the free surface elevation is planar, and the velocity is constant (in wet regions). The scenario includes regular wetting and drying, as the flow oscillates back and forth in the basin. As well as testing the ability of the code to do wetting and drying, it will highlight any numerical energy loss or gain, manifest as an increase or decrease in the magnitude of the flow oscillations over long time periods, compared with the analytical solution. 
+\section{Thacker's Planar Oscillations on a Parabolic Basin}
+This test simulates planar oscillations of water in a parabolic basin. The analytical solution was derived by Thacker~\cite{Thacker1981}, and is periodic. At any instant in time, the free surface elevation is planar, and the velocity is constant (in wet regions). The scenario includes regular wetting and drying, as the flow oscillates back and forth in the basin. As well as testing the ability of the code to do wetting and drying, it will highlight any numerical energy loss or gain, and manifest as an increase or decrease in the magnitude of the flow oscillations over long time periods (compared with the analytical solution). 
+
+Consider the topography
+\begin{equation}
+z(x) = D_0 \left(\frac{x}{L}\right)^2
+\end{equation}
+where $D_0$ is the largest depth when water is still and $L$ is the distance between the centre of water surface and the shore when water is still.
+The analytical solution is 
+\begin{equation}
+u(x,t) = -A \omega \sin(\omega t),
+\end{equation}
+\begin{equation}
+w(x,t) = D_0 + \frac{2 A D_0}{L^2} \cos(\omega t) \left( x - \frac{A}{2}\cos(\omega t) \right).
+\end{equation}
+Here $\omega=\sqrt{\frac{2 g D_0)}{L}}$.
+The initial condition is set by taking $t=0$ in the analytical solution.
+
 
 \subsection{Results}
+For our test, we consider $D_0=4$, $L=10$, and $A=2$. After running the simulation for some time, we have Figures~\ref{fig:cross_section_stage}--\ref{fig:cross_section_xvel} showing the stage, $x$-momentum, and $x$-velocity respectively. There should be a good agreement between numerical and analytical solutions.
 
-Figures~\ref{fig:cross_section_stage}--\ref{fig:cross_section_xvel} show a good agreement between analytical and numerical solutions.
-
-\begin{figure}[h]
+\begin{figure}[!h]
 \begin{center}
 \includegraphics[width=0.9\textwidth]{cross_section_stage.png}
-\caption{Stage on a cross section of the basin at time $t=$ ?}
+\caption{Stage on a cross section of the basin at time $t=10$.}
 \label{fig:cross_section_stage}
 \end{center}
 \end{figure}
 
-\begin{figure}[h]
+\begin{figure}
 \begin{center}
 \includegraphics[width=0.9\textwidth]{cross_section_xmom.png}
-\caption{Xmomentum on a cross section of the basin at time $t=$ ?}
+\caption{Xmomentum on a cross section of the basin at time $t=10$.}
 \label{fig:cross_section_xmom}
 \end{center}
 \end{figure}
 
-\begin{figure}[h]
+\begin{figure}
 \begin{center}
 \includegraphics[width=0.9\textwidth]{cross_section_xvel.png}
-\caption{Xvelocity on a cross section of the basin at time $t=$ ?}
+\caption{Xvelocity on a cross section of the basin at time $t=10$.}
 \label{fig:cross_section_xvel}
 \end{center}
@@ -31 +46 @@
 
 
-There should be a good agreement with the analytical solution, although as time goes on, some deviations may appear.  See Figures~\ref{fig:Stage_centre}--\ref{fig:Xvel_centre}.
+As time goes on, some small deviations may appear. These are shown in Figures~\ref{fig:Stage_centre}--\ref{fig:Xvel_centre}, which illustrate the stage, $x$-momentum, and $x$-velocity at the centroid of the domain.
 
-\begin{figure}[h]
+\begin{figure}[!h]
 \begin{center}
 \includegraphics[width=0.9\textwidth]{Stage_centre.png}
@@ -41 +56 @@
 \end{figure}
 
-\begin{figure}[h]
+\begin{figure}
 \begin{center}
 \includegraphics[width=0.9\textwidth]{Xmom_centre.png}
@@ -49 +64 @@
 \end{figure}
 
-\begin{figure}[h]
+\begin{figure}
 \begin{center}
 \includegraphics[width=0.9\textwidth]{Xvel_centre.png}