Changeset 8797

Timestamp:

Apr 1, 2013, 10:50:14 AM (12 years ago)

Author:

mungkasi

Message:

Automated report for subcritical flow over a bump.

Location:

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/subcritical_over_bump

Files:

• analytical_subcritical.py (modified) (1 diff)
• numerical_subcritical.py (modified) (1 diff)
• plot_results.py (modified) (3 diffs)
• produce_report.py (added)
• produce_results.py (modified) (1 diff)
• report.tex (added)
• results.tex (modified) (3 diffs)

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/subcritical_over_bump/analytical_subcritical.py

@@ -12 +12 @@
 from scipy.optimize import fsolve
 from pylab import plot, ylim, show
+from anuga import g
 
 qA = 4.42  # This is the imposed momentum
 hx = 2.0   # This is the water height downstream
-g  = 9.81  # Accelleration due to gravity
 
 def analytic_sol(x):    

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/subcritical_over_bump/numerical_subcritical.py

@@ -97 +97 @@
 
 #------------------------------------------------------------------------------
+# 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 system through time
 #------------------------------------------------------------------------------

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/subcritical_over_bump/plot_results.py

@@ -18 +18 @@
 #Plot the stages##############################################################
 pyplot.clf()
-pyplot.ion()
 pyplot.plot(p2_st.x[v2], p2_st.stage[300,v2], 'b.-', label='numerical stage') # 0*T/6
 pyplot.plot(p2_st.x[v2], h+z,'r-', label='analytical stage')
@@ -32 +31 @@
 #Plot the momentums##########################################################
 pyplot.clf()
-pyplot.ion()
 pyplot.plot(p2_st.x[v2], p2_st.xmom[300,v2], 'b.-', label='numerical') # 0*T/6
 pyplot.plot(p2_st.x[v2], 4.42*ones(len(p2_st.x[v2])),'r-', label='analytical')
@@ -46 +44 @@
 #Plot the velocities#########################################################
 pyplot.clf()
-pyplot.ion()
 pyplot.plot(p2_st.x[v2], p2_st.xvel[300,v2], 'b.-', label='numerical') # 0*T/6
 pyplot.plot(p2_st.x[v2], 4.42/h,'r-', label='analytical')

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

@@ -11 +11 @@
     run_validation_script('numerical_subcritical.py')
     run_validation_script('plot_results.py')
+    run('python', 'produce_report.py')     
 
 def clean():

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

@@ -1 +1 @@
 
-\section{Flow over a bump: subcritical flow}
+\section{Subcritical flow over a bump without a shock}
 
-This is a subcritical flow over a bump. No shock occurs.
+This is a subcritical flow over a bump. This test is adapted from Goutal and Maurel~\cite{GM1997}. No shock occurs in this scenario. 
+
+Consider a one dimensional domain $[0,25]$ with topography
+\begin{equation}
+z(x)= \left\{ \begin{array}{ll}
+ 0.2-0.05\left(x-10\right)^2& ~\textrm{if}\quad 8 \leq x \leq 12\,,\\
+ 0 & ~\textrm{otherwise}\,,\\
+\end{array} \right.
+\end{equation}
+together with Dirichlet boundary conditions.
+Physically, the boundary conditions mean that there is a source of flow upstream at the point $x=0^{-}$ and at the same time there exists a sink of flow downstream at the point $x=25^{+}$\,.
+
+
+The analytical height is found by solving the Bernoulli equation. The simplified Bernoulli equation is the following cubic equation
+\begin{equation}
+h^3 + \left(z - \frac{q^2}{2 g H^2} - H \right) h^2 + \frac{q^2}{2 g} = 0\,,
+\end{equation}
+where $H$ is the upstream height and $q=uh$ is the discharge or $x$-momentum. When the height $h$ has been found, the velocity is computed as $u=q/h$\,.
 
 \subsection{Results}
+For our test we consider the initial condition
+\begin{equation}
+u(x,y,0)=v(x,y,0)=0\,, \quad
+w(x,y,0)= 0.2\,,
+\end{equation}
+and the Dirichlet boundary conditions at $x=0^{-}$ and $25^{+}$ to be $[w,hu,hv]=[2, 4.42, 0]$\,.
+Representatives of the simulation results are given in the following three figures. Even though we have small discrepancy in the numerical and analytical momenta, these numerical an analytical solutions should agree quite well.
 
-
-We should see excellent agreement between the analytical and numerical solutions.
-
-\begin{figure}[h]
+\begin{figure}
 \begin{center}
 \includegraphics[width=0.9\textwidth]{stage_plot.png}
@@ -17 +38 @@
 
 
-\begin{figure}[h]
+\begin{figure}
 \begin{center}
 \includegraphics[width=0.9\textwidth]{xmom_plot.png}
@@ -25 +46 @@
 
 
-\begin{figure}[h]
+\begin{figure}
 \begin{center}
 \includegraphics[width=0.9\textwidth]{xvel_plot.png}