Changeset 8778

Timestamp:

Mar 26, 2013, 11:59:42 PM (12 years ago)

Author:

mungkasi

Message:

 

Location:

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/lake_at_rest_steep_island

Files:

• numerical_steep_island.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) (1 diff)

trunk/anuga_core/source/anuga_validation_tests/Analytical_exact/lake_at_rest_steep_island/numerical_steep_island.py

@@ -123 +123 @@
 
 #------------------------------------------------------------------------------
+# 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/lake_at_rest_steep_island/plot_results.py

@@ -30 +30 @@
 #Plot stages
 pyplot.clf()
-pyplot.ion()
 pyplot.plot(p2_st.x[v2], p2_st.stage[40,v2],'b.', label='numerical stage')
 pyplot.plot(p2_st.x[v2], p2_st.elev[v2],'k-', label='discretised bed')
@@ -43 +42 @@
 #Plot xmomentum
 pyplot.clf()
-pyplot.ion()
 pyplot.plot(p2_st.x[v2], p2_st.xmom[40,v2], 'b.', label='numerical')
 pyplot.plot(p2_st.x[v2], zeros(len(p2_st.x[v2])),'r-', label='analytical')
@@ -55 +53 @@
 #Plot velocities
 pyplot.clf()
-pyplot.ion()
 pyplot.plot(p2_st.x[v2], p2_st.xvel[40,v2], 'b.', label='numerical')
 pyplot.plot(p2_st.x[v2], zeros(len(p2_st.x[v2])),'r-', label='analytical')

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

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

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

@@ -2 +2 @@
 \section{Lake at rest with a steep island}
 
-This is a test if the method is well-balanced. Furthermore, we test if the wet/dry interface has been correctly treated.
+This is a test if the method is well-balanced. Furthermore, we test if the wet/dry interface has been correctly treated for a steep island. This test is taken from the work of Mungkasi and Roberts~\cite{MR2010}.
+
+The initial condition is a lake at rest with water depth $4.5$. The topography is
+\begin{equation}
+z(x,y)= \left\{ \begin{array}{ll}
+             -0.01(x-200) + 4& ~\textrm{if}\quad 0 \leq x < 200\\
+             -0.02(x-200) + 4& ~\textrm{if}\quad 200 \leq x < 300\\
+             -0.01(x-300) + 2& ~\textrm{if}\quad 300 \leq x < 400\\
+             (-1/75)(x-400) + 2& ~\textrm{if}\quad 400 \leq x < 550\\
+             (1/11250)(x-550)(x-550)& ~\textrm{if}\quad 550 \leq x < 700\\
+             0.03(x-700)& ~\textrm{if}\quad 700 \leq x < 800\\
+             -0.03(x-800) + 3& ~\textrm{if}\quad 800 \leq x < 900\\
+             6& ~\textrm{if}\quad 900 \leq x < 1000\\
+             (-1.0/20000)(x-1000)(x-1400)& ~\textrm{if}\quad 1000 \leq x < 1400\\
+             0& ~\textrm{if}\quad 1400 \leq x < 1500\\
+             3& ~\textrm{if}\quad 1500 \leq x < 1700\\
+             -0.03(x-1700) + 3& ~\textrm{if}\quad 1700 \leq x < 1800\\
+             (4.5/40000)(x-1800)(x-1800) + 2 & ~\textrm{otherwise,}\\
+\end{array} \right.
+\end{equation} 
+The analytical solution is the lake at rest, that is, $w=4.5$ and $u=v=0$.
 
 \subsection{Results}
 
 
-We should see excellent agreement between the analytical and numerical solutions if the method is well-balanced and if the wet/dry interface has been correctly treated.
+Current version of \anuga{} might not handle a discontinuous island perfectly. The following three figures show the stage, $x$-momentum, and $x$-velocity respectively, after we run the simulation for some time. We should see excellent agreement between the analytical and numerical solutions if the method is well-balanced and if the wet/dry interface has been correctly treated.
 
 \begin{figure}[h]