Changeset 8719 for trunk

Timestamp:

Mar 3, 2013, 11:23:04 PM (12 years ago)

Author:

mungkasi

Message:

Update the report for dry dam break and the code.

Location:

trunk/anuga_core/validation_tests/Tests/Analytical_exact/dam_break_dry

Files:

• numerical_dam_break_dry.py (modified) (3 diffs)
• results.tex (modified) (3 diffs)

trunk/anuga_core/validation_tests/Tests/Analytical_exact/dam_break_dry/numerical_dam_break_dry.py

@@ -54 +54 @@
 domain.set_CFL(cfl)
 
-print 'cfl ',cfl
-print 'alg ',alg
-
 #------------------------------------------------------------------------------
 # Setup initial conditions
@@ -87 +84 @@
 
 
-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()
-
-
 #===============================================================================
 ##from anuga.visualiser import RealtimeVisualiser
@@ -103 +92 @@
 #===============================================================================
 
+
+#------------------------------------------------------------------------------
+# 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()
 
 #------------------------------------------------------------------------------

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

@@ -1 +1 @@
 
-\section{Dam Break}
+\section{Dam Break Involving a Dry Area}
 
-Standard dam break test problem involving a dry area. Should show a rarefaction fan and wetting process. 
+The dam break problem involving a dry area was solved analytically by Ritter~\cite{Ritter1892} as well as Stoker~\cite{Stoker1948, Stoker1957}. The analytical solution exhibits a rarefaction fan as a parabolic curve. As water moves, it involves wetting process over the dry area. This is a one-dimensional-type problem. 
+
+The initial condition is
+\begin{equation} \label{eq:rdbp}
+u(x,0)=0~~, v(x,y)=0, ~~\textrm{and}~~
+h(x,0) = \left\{ \begin{array}{ll}
+h_1 & \textrm{if $x < x_0$}\\
+0 & \textrm{if $x > x_0$}\\
+\end{array} \right.
+\end{equation}
+where $h_1>0$. 
+
+The analytical solution at time $t>0$ is~\cite{Ritter1892, Stoker1948, Stoker1957}
+\begin{equation} \label{eq:h_sol_dry}
+h(x) = \left\{ \begin{array}{ll}
+h_1 & \textrm{if $x \leq -t \sqrt{gh_1}$}\\
+h_R=\frac{4}{9g}(\sqrt{gh_1}-\frac{x}{2t})^2 & \textrm{if $-t \sqrt{gh_1} <x \leq 2t\sqrt{gh_1}$}\\
+0 & \textrm{if $x \geq 2t\sqrt{gh_1}$}\\
+\end{array} \right.
+\end{equation}
+which is the free surface and
+\begin{equation} \label{eq:u_sol_dry}
+u(x) = \left\{ \begin{array}{ll}
+0 & \textrm{if $x \leq -t \sqrt{gh_1}$}\\
+u_R=\frac{2}{3}(\sqrt{gh_1}+\frac{x}{t}) & \textrm{if $-t \sqrt{gh_1} <x \leq 2t\sqrt{gh_1}$}\\
+0 & \textrm{if $x \geq 2t\sqrt{gh_1}$}\\
+\end{array} \right.
+\end{equation}
+which is the velocity.
+
+
 
 \subsection{Results}
-
-
-We should see excellent agreement between the analytical and numerical solutions.
+For our test, we consider $x_0=0$ and $h_1=10$ in (\ref{eq:rdbp}).
+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. The wet/dry interface is difficult to resolve and it usually produces large errors.
 
 \begin{figure}[h]
 \begin{center}
 \includegraphics[width=0.8\textwidth]{stage_plot.png}
+%\label{fig:db_dry_stage}
 \end{center}
 \caption{Stage results}
@@ -20 +50 @@
 \begin{center}
 \includegraphics[width=0.8\textwidth]{xmom_plot.png}
+%\label{fig:db_dry_xmom}
 \end{center}
 \caption{Xmomentum results}
@@ -28 +59 @@
 \begin{center}
 \includegraphics[width=0.8\textwidth]{xvel_plot.png}
+%\label{fig:db_dry_xvel}
 \end{center}
 \caption{Xvelocity results}