[Commits] [svn:einsteintoolkit] Workshop_Spring_2012/numerical_relativity/ (Rev. 45)

[bcmsma at astro.rit.edu]

User: bmundim
Date: 2012/04/04 10:55 AM

Modified:
 /numerical_relativity/
  numerical_relativity.tex

Log:
 burgers eqn

File Changes:

Directory: /numerical_relativity/
=================================

File [modified]: numerical_relativity.tex
Delta lines: +21 -0
===================================================================
--- numerical_relativity/numerical_relativity.tex	2012-04-04 15:40:22 UTC (rev 44)
+++ numerical_relativity/numerical_relativity.tex	2012-04-04 15:55:15 UTC (rev 45)
@@ -591,4 +591,25 @@
 
 }
 
+\frame{\frametitle{Example: Burgers Equation}
+\begin{equation}
+u_t + f(u)_x = 0, \qquad f(u)=\frac{1}{2}u^2
+\end{equation}
+with 
+\[
+u(x,0) = \left\{ \begin{array}{ll}
+                  u_l & \mbox{if $x<0$}\\ 
+                  u_r & \mbox{if $x>0$}
+                 \end{array}
+         \right.
+\]\pause
+
+\begin{figure}
+    \includegraphics[width=6cm]{shock.pdf}
+    \includegraphics[width=6cm]{rarefaction.pdf}
+\end{figure}
+
+
+}
+
 \end{document}