Changeset 8724

Timestamp:

Mar 5, 2013, 1:44:12 AM (12 years ago)

Author:

mungkasi

Message:

Updating report/results.tex for dam break dry.

File:

• trunk/anuga_core/validation_tests/Tests/Analytical_exact/dam_break_dry/results.tex (modified) (3 diffs)

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

@@ -1 +1 @@
 
-\section{Dam Break Involving a Dry Area}
+\section{Dam break involving a dry area}
 
-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 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.
 
 The initial condition is
-\begin{equation} \label{eq:rdbp}
-u(x,0)=0~~, v(x,y)=0, ~~\textrm{and}~~
+\begin{equation} \label{eq:db_dry_init}
+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 $x > x_0$}\\
+h_1 & \textrm{if $x < 0$}\\
+0 & \textrm{if $x > 0$}\\
 \end{array} \right.
 \end{equation}
-where $h_1>0$. 
+where $h_1>0$. The topography is a horizontal flat bed.
 
-The analytical solution at time $t>0$ is~\cite{Ritter1892, Stoker1948, Stoker1957}
-\begin{equation} \label{eq:h_sol_dry}
+
+The analytical solution~\cite{Ritter1892, Stoker1948, Stoker1957} at time $t>0$ is
+\begin{equation}
 h(x) = \left\{ \begin{array}{ll}
 h_1 & \textrm{if $x \leq -t \sqrt{gh_1}$}\\
@@ -23 +24 @@
 \end{equation}
 which is the free surface and
-\begin{equation} \label{eq:u_sol_dry}
+\begin{equation}
 u(x) = \left\{ \begin{array}{ll}
 0 & \textrm{if $x \leq -t \sqrt{gh_1}$}\\
@@ -35 +36 @@
 
 \subsection{Results}
-For our test, we consider $x_0=0$ and $h_1=10$ in (\ref{eq:rdbp}).
+For our test, we consider $h_1=10$ in (\ref{eq:db_dry_init}).
 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.