User: diener Date: 2011/01/24 11:41 AM

Modified: / ET.tex

Log: Some text about Object tracking.

File Changes:

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

File [modified]: ET.tex Delta lines: +17 -0 =================================================================== --- ET.tex 2011-01-24 17:40:13 UTC (rev 15) +++ ET.tex 2011-01-24 17:41:21 UTC (rev 16) @@ -494,7 +494,24 @@ \paragraph{Vacuum-Matter Coupling}

\paragraph{Object tracking} +We provide a module (\codename{PunctureTracker}) for tracking black hole +positions when evolved with the moving puncture technique. This can be used +with (\codename{CarpetTracker}) to have the mesh refinement regions follow the +black holes as they move across the grid. The black hole position is +stored as the centroid of a spherical surface (even though there is no surface) +provided by \codename{SphericalSurface}.

+Since the punctures only move due to the shift advection terms in +the BSSN equations, the puncture location is evolved very simply as +\begin{equation} + \frac{d x^i}{d t} = -\beta^i, \label{eq:puncturetracking} +\end{equation} +where $x^i$ is the puncture location and $\beta^i$ is the shift. Since the +puncture location usually does not coincide with gridpoints, the shift is +interpolated to the location of the puncture. +Equation~(\ref{eq:puncturetracking}) is implemented with a simple first order +Euler scheme, which seems to be accurate enough for controlling the mesh +refinement grids.

\subsection{Infrastructure and Numerical Methods} \todo{1/2 page Erik}