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}