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diff --git a/doc/documentation.tex b/doc/documentation.tex new file mode 100644 index 0000000..04d7f8f --- /dev/null +++ b/doc/documentation.tex @@ -0,0 +1,56 @@ +\documentclass{article} +\begin{document} + +\title{ADMConstraints} +\author{Gabrielle Allen} +\date{April 2002} +\maketitle + +\abstract{Calculate the values of the Hamiltonian and Momentum Constraints on the computational grid for output.} + +\section{Physics} + +This analysis thorn calculates the values of the Hamiltonian and +momentum constraint equations on the computational grid during a spacetime +evolution. The Hamiltonian Constraint (grid function: ham) is given by + +\begin{equation} + H = R - K^{i}_{\;\;j} K^{j}_{\;\;i} + trK^2 - 16 \pi \rho +\end{equation} + +The Momentum Constraints (grid functions momx, momy, momz) are given by + +\begin{equation} +M_i = \nabla_j K_i^{\;\;j} - \nabla_i trK - 8 \pi S_i +\end{equation} + +where + +\begin{equation} +S_i = -g_{ia} n_b T^{ab} = - g_i^a n^b T_{ab} = -\frac{1}{\alpha} (T_{i0} - \beta^j T_{ij}) +\end{equation} + +\section{Comments} + +\begin{itemize} + +\item Symmetry boundary conditions ({\tt CactusBase/CartGrid3D}) are implemented. + +\item Default behaviour is to apply so called flat boundary conditions to the calculated values of the constraint equations. + +\item Excision ({\tt Excision/LegoExcision}) is included. + +\item The 3-metric is only included through the Macros in {\tt CactusEinstein/Einstein} and as such the physical metric is used. + +\item Matter is included using the {\tt CalcTmuNu} mechanism. + +\item The constraint calculation is default performed at the ANALYSIS time bin, if the constraint values are needed at every iteration, the parameter {\tt constraints\_persist} should be used to schedule the calculation instead at POSTSTEP. + +\end{itemize} + +% Automatically created from the ccl files by using gmake thorndoc +\include{interface} +\include{param} +\include{schedule} + +\end{document} |