[Commits] [svn:einsteintoolkit] Workshop_Spring_2012/numerical_relativity/ (Rev. 48)

[bcmsma at astro.rit.edu]

User: bmundim
Date: 2012/04/04 11:45 AM

Modified:
 /numerical_relativity/
  numerical_relativity.tex

Log:
 algorithm overview.

File Changes:

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

File [modified]: numerical_relativity.tex
Delta lines: +32 -0
===================================================================
--- numerical_relativity/numerical_relativity.tex	2012-04-04 16:29:55 UTC (rev 47)
+++ numerical_relativity/numerical_relativity.tex	2012-04-04 16:45:17 UTC (rev 48)
@@ -658,4 +658,36 @@
 \end{figure}
 
 }
+
+\frame{\frametitle{Algorithm Overview}
+\begin{itemize}
+\item Set boundary conditions or ghost zone values \pause
+\item Calculate numerical flux at every cell interface by 
+solving an approximate Riemann problem \pause
+  \begin{itemize}
+    \item Reconstruct the primitive variables $p_l$ and $p_r$ at the 
+cell interfaces (by using slope limiters for example). \pause
+    \item Find the conservative variables $q_l$ and $q_r$ by using their
+definition \pause
+    \item Calculate the fluxes $f(q_l)$ and $f(q_r)$ \pause
+    \item Calculate $A$, $r_{\alpha}$, $\lambda_{\alpha}$ and use them to
+find $\omega_{\alpha}$ \pause
+    \item Calculate the Roe formula for the numerical flux: $F^{\rm Roe}_{i+1/2}
+$ \pause
+  \end{itemize}
+  \item Evaluate the sources $\Psi(q)$. \pause
+  \item Update the average quantities $Q^n_i$ using method of lines.
+\end{itemize}
+
+}
+
+\frame{\frametitle{Algorithm Overview}
+\begin{figure}
+    \includegraphics[width=10cm]{all_waves.pdf}
+\end{figure}
+
+}
+
+
+
 \end{document}