[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 16)

[diener at cct.lsu.edu]

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

Modified:
 /
  ET.tex

Log:
 Some text about Object tracking.

File Changes:

Directory: /
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File [modified]: ET.tex
Delta lines: +17 -0
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--- 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}