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| -rw-r--r-- | doc/rotating_sym.tex | 9 |
1 files changed, 5 insertions, 4 deletions
diff --git a/doc/rotating_sym.tex b/doc/rotating_sym.tex index e5ef6b7..02c9371 100644 --- a/doc/rotating_sym.tex +++ b/doc/rotating_sym.tex @@ -44,7 +44,7 @@ These notes describe the implentation of rotating symmetry conditions for \emph{bitant} and \emph{quadrant} domains in \texttt{CartGrid3D}. For these particular domain types, the condition that fields on the -grid are have a rotational symmetry in a plane along one of the +grid have a rotational symmetry in a plane along one of the coordinate axes can be simply implemented with minor extensions to the already existing symmetry mechanism, which copies the components of a given field to the required ghost-zones with a possible plus-minus @@ -146,7 +146,8 @@ rotation.\\ The first of these issues is not difficult to resolve. As an example, consider the half-plane rotational symmetry about the $z$-axis applied -in the $x=0$ plane, as depicted in Figure \ref{fig:rs_grid}. The has +in the $x=0$ plane, as depicted in Figure \ref{fig:rs_grid}. The +Figure has $j=0\ldots m$ in the $y$ direction, an arbitrary number of points in the $x$ and $z$ directions, and some ghostzones whose $j$ coordinates are labelled $j=-1,-2,\ldots$. Then for the ghost-zone point $(n-i, -j, @@ -361,7 +362,7 @@ symmetries.} We note the following useful fact: The transformation factor $s_i$ for a rotation about the axis $i$ is given by $s_j \times s_k$ where $i\neq j\neq k$. For example, for a rotation about the $z$-axis, the -transformation factor for the is given by +transformation factor is given by \begin{equation} s_x \times s_y = -1 \times -1 = 1. \end{equation} @@ -447,7 +448,7 @@ standard reflection symmetry is applied to one of the half-planes, while the physical fields are assumed to rotate in the other plane. To set up such a grid which rotates about the $z$-axis and which is reflection symmetric in the $z=0$ plane, the following parameters -could be used: +would be used: \begin{verbatim} grid::domain = "quadrant_rotate_reflect" grid::quadrant_direction = "x" |