Changeset 8725 for trunk/anuga_core/validation_tests

Timestamp:

Mar 5, 2013, 1:45:06 AM (12 years ago)

Author:

mungkasi

Message:

Updating codes and reports for dam break wet.

Location:

trunk/anuga_core/validation_tests/Tests/Analytical_exact/dam_break_wet

Files:

• numerical_dam_break_wet.py (modified) (1 diff)
• report.tex (modified) (2 diffs)
• results.tex (modified) (1 diff)

trunk/anuga_core/validation_tests/Tests/Analytical_exact/dam_break_wet/numerical_dam_break_wet.py

@@ -98 +98 @@
 
 #------------------------------------------------------------------------------
+# 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/validation_tests/Tests/Analytical_exact/dam_break_wet/report.tex

@@ -1 @@
-\documentclass[11pt,a4paper]{report}
+\documentclass[11pt,a4paper]{article}
 
 \usepackage{graphicx}
@@ -17 +17 @@
 
 \title{Automated Report on the Performance of \anuga{} on Wet Dam Break}
-%\maketitle
+\maketitle
 %\tableofcontents
 
 %======================
-\chapter{Wet Dam Break}
+%\chapter{Wet Dam Break}
 %======================
 
 \input{results}
 
+\section{Parameters used for this simulation}
+
+\input{parameters}
+
+%======================
+% bibliography
+%======================
+\bibliographystyle{plain}
+\bibliography{../../../bibliography}
 
 \end{document}

trunk/anuga_core/validation_tests/Tests/Analytical_exact/dam_break_wet/results.tex

@@ -1 +1 @@
 
-\section{Dam Break}
+\section{Dam break on wet areas}
 
-Standard dam break test problem on wet areas. Should show a rarefaction fan and a shock. 
+The dam break problem on wet areas was solved analytically by Stoker~\cite{Stoker1948, Stoker1957}. The analytical solution exhibits a rarefaction and involves a shock. Generally this problem is easier to solve numerically than the dry dam break (the dam break on a dry area).
+
+The initial condition is
+\begin{equation} \label{eq:dbp_init_wet}
+u(x,0)=0, ~~v(x,y)=0, ~~\textrm{and}~~
+h(x,0) = \left\{ \begin{array}{ll}
+h_1 & \textrm{if $x < 0$}\\
+h_0 & \textrm{if $x > 0$}\\
+\end{array} \right.
+\end{equation}
+where $h_1>h_0>0$. The topography is a horizontal flat bed.
+
+The analytical solution~\cite{Stoker1948, Stoker1957} to the wet dam break problem is
+\begin{equation}
+h(x) = \left\{ \begin{array}{ll}
+h_1 & \textrm{if $x \leq -t \sqrt{gh_1}$}\\
+h_3=\frac{4}{9g}(\sqrt{gh_1}-\frac{x}{2t})^2 & \textrm{if $-t \sqrt{gh_1} <x \leq t(u_2-\sqrt{gh_2}$})\\
+h_2=\frac{h_0}{2}\bigg(\sqrt{1+\frac{8\dot{\xi}^2}{gh_0}}-1\bigg) & \textrm{if $ t(u_2-\sqrt{gh_2}) <x < t\dot{\xi}$}\\
+h_0 & \textrm{if $x \geq t\dot{\xi}$}\\
+\end{array} \right.
+\end{equation}
+and
+\begin{equation}
+u(x) = \left\{ \begin{array}{ll}
+0 & \textrm{if $x \leq -t \sqrt{gh_1}$}\\
+u_3=\frac{2}{3}(\sqrt{gh_1}+\frac{x}{t}) & \textrm{if $-t \sqrt{gh_1} <x \leq t(u_2-\sqrt{gh_2}$})\\
+u_2=\dot{\xi}-\frac{gh_0}{4\dot{\xi}}\bigg(1+\sqrt{1+\frac{8\dot{\xi}^2}{gh_0}} \bigg) & \textrm{if $ t(u_2-\sqrt{gh_2}) <x < t\dot{\xi}$}\\
+0 & \textrm{if $x \geq t\dot{\xi}$}\\
+\end{array} \right.
+\end{equation}
+at any time $t>0$, where $\dot{\xi}$ is the shock speed constant given by 
+\begin{equation} \label{eq:shock}
+\dot{\xi}=2\sqrt{gh_1}+\frac{gh_0}{4\dot{\xi}}\bigg( 1+\sqrt{1+\frac{8\dot{\xi}^2}{gh_0}}\bigg)-\bigg( 2gh_0 \sqrt{1+\frac{8\dot{\xi}^2}{gh_0}}-2gh_0\bigg)^\frac{1}{2}.
+\end{equation}
+
 
 \subsection{Results}
 
-
-We should see excellent agreement between the analytical and numerical solutions.
+For our test, we consider $h_1=10$ and $h_0=1$ in (\ref{eq:dbp_init_wet}).
+The following figures show the stage, $x$-momentum, and $x$-velocity at several instants of time.
+We should see excellent agreement between the analytical and numerical solutions. 
 
 \begin{figure}[h]