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Diffstat (limited to 'doc')
| -rw-r--r-- | doc/documentation.tex | 189 | ||||
| -rw-r--r-- | doc/domain-external-shiftout.eps | 133 | ||||
| -rw-r--r-- | doc/domain-external-shiftout.fig | 17 | ||||
| -rw-r--r-- | doc/domain-external-staggered.eps | 130 | ||||
| -rw-r--r-- | doc/domain-external-staggered.fig | 16 | ||||
| -rw-r--r-- | doc/domain-external.eps | 130 | ||||
| -rw-r--r-- | doc/domain-external.fig | 16 | ||||
| -rw-r--r-- | doc/domain-internal-staggered.eps | 127 | ||||
| -rw-r--r-- | doc/domain-internal-staggered.fig | 15 | ||||
| -rw-r--r-- | doc/domain-internal.eps | 127 | ||||
| -rw-r--r-- | doc/domain-internal.fig | 15 | ||||
| -rw-r--r-- | doc/domain.eps | 127 | ||||
| -rw-r--r-- | doc/domain.fig | 15 |
13 files changed, 1057 insertions, 0 deletions
diff --git a/doc/documentation.tex b/doc/documentation.tex index b289d1b..ab06462 100644 --- a/doc/documentation.tex +++ b/doc/documentation.tex @@ -100,6 +100,11 @@ CoordBase provides a mechanism for registering coordinate systems, and maintaining a database of coordinate systems and their coordinates, using key-value tables. + +CoordBase also provides a way for specifying the extent of the +simulation domain that is independent of the actual coordinate and +symmetry thorns, and for specifying the discretisation of the boundary +that is independent of the actual boundary thorns. \end{abstract} @@ -402,6 +407,190 @@ Even though another thorn has set a default for all 2D grid variables to something else, Coord\_GroupSystem() will always return the handle for sphere2d when called on this group. + +\section{Specifying the extent of the physical domain} +\label{CactusBase:CoordBase:domain} + +CoordBase provides a way for specifying the extent of the simulation +domain that is independent of the actual coordinate and symmetry +thorns. This is necessary because the size of the physical domain is +not necessarily the same as the size of the computational grid, which +is usually enlarged by symmetry zones and/or boundary zones. + +The physical domain is characterised by the location of its lower and +upper boundary and by its grid spacing. These quantities are related +to the extent and the number of grid cells that span the domain. The +relation between the size of the domain and the size of the +computational grid is defined in section +{\ref{CactusBase:CoordBase:domain}} below. The domain extent as +defined in this section is the continuum extent and is independent of +the actual discretisation. This makes it possible to adapt the same +domain specification for different resolutions by changing only a +single parameter. + +The domain is specified in one of the following ways, which is +selected by the keyword parameter {\texttt{domainsize}}: +\begin{description} +\item[{\texttt{minmax}}:] +by the location of its lower and upper boundary +\item[{\texttt{extent}}:] +by its extent, i.e.\ its width +\item[{\texttt{spacing}}:] +by grid spacing and the number of grid cells +\end{description} +The domain specification uses the number of grid cells instead of the +number of grid points because the latter can easily lead to one-off +errors. + +The domain size in each dimension is specificied in equivalent ways. +For example, the $x$-dimension is specified by a set of some of the +following parameters: +\begin{description} +\item[{\texttt{zero\_origin\_x}} (boolean):] +When the domain size is specified by extent or by spacing, then the +origin (lower boundary) can either be located at $x=0$, which leads to +the domain $x \in [0,L]$ with the extent $L$, or the domain can be +symmetric with respect to $x=0$, which leads to $x \in [-L/2,L/2]$. +\item[{\texttt{xmin}} and {\texttt{xmax}}:] +When the domain is specified by the location of its lower and upper +boundary, then these specify the locations. +\item[{\texttt{xextent}}:] +When the domain is specified by its extent, then this specifies the +extent. +\item[{\texttt{dx}} (real) and {\texttt{ncells\_x}} (int):] +When the domain is specified by grid spacing and the number of grid +cells, then these specify the grid spacing and the number of grid +cells. +\end{description} + + +\section{Specifying the location of the boundary points} +\label{CactusBase:CoordBase:boundary} + +CoordBase also provides a way for specifying the discretisation of the +boundary that is independent of the actual boundary thorns. This +defines the locations of the boundary points and thus the extent of +the computational grid. + +Each face of the grid is specified independently. The specification +does not depend on the resolution, so that it need not be adapted when +the resolution is changed. Figure +{\ref{CactusBase:CoordBase:fig-domain}} shows a domain with several +interior grid points and one boundary point. + +\begin{figure} +\begin{center} +\includegraphics[scale=0.75]{domain} +\end{center} +\caption{A domain (rectangle) with three interior points (empty +circles) and one boundary point (full circle).} +\label{CactusBase:CoordBase:fig-domain} +\end{figure} + +While the physical boundary has a width of zero, the computational +grid can have more than one boundary points. This {\emph{boundary +size}} is defined by the integer parameter +{\texttt{boundary\_size\_x\_lower}} for the lower $x$ boundary (and +similarly for the other boundaries). Figure +{\ref{CactusBase:CoordBase:fig-domain-external}} shows an example +where there are two boundary points. When it is necessary to increase +the number of boundary points (e.g., to accommodate a larger stencil), +then this is the only parameter that needs to be changed. + +\begin{figure} +\begin{center} +\includegraphics[scale=0.75]{domain-external} +\end{center} +\caption{A domain (rectangle) with three interior points (empty +circles) and two boundary points (full circles). This is an exterior +boundary, i.e.\ the boundary points are located outside of the +physical domain.} +\label{CactusBase:CoordBase:fig-domain-external} +\end{figure} + +Depending on the physical setup --- and depending on the personal +taste --- the boundary points should be located either inside or +outside of the physical boundary. The boolean parameter +{\texttt{boundary\_internal\_x\_lower}} specifies whether the boundary +points extend inwards at the lower $x$ face. Figure +{\ref{CactusBase:CoordBase:fig-domain-internal}} shows the same +example, but with internal boundary points. + +\begin{figure} +\begin{center} +\includegraphics[scale=0.75]{domain-internal} +\end{center} +\caption{A domain (rectangle) with two interior points (empty circles) +and two boundary points (full circles). This is an interior boundary, +i.e.\ the boundary points are located inside of the physical domain.} +\label{CactusBase:CoordBase:fig-domain-internal} +\end{figure} + +Depending on the physical setup --- and depending on the personal +taste --- the boundary points should either be staggered about the +physical boundary, or the last boundary point should be located +exactly on the physical boundary. This is specified by the boolean +parameter {\texttt{boundary\_staggered\_x\_lower}}. Figures +{\ref{CactusBase:CoordBase:fig-domain-external-staggered}} and +{\ref{CactusBase:CoordBase:fig-domain-internal-staggered}} show +exampled of external and internal staggered boundary points. + +\begin{figure} +\begin{center} +\includegraphics[scale=0.75]{domain-external-staggered} +\end{center} +\caption{A domain (rectangle) with three interior points (empty circles) +and two boundary points (full circles) which are staggered about the +physical boundary. (This is an exterior boundary.)} +\label{CactusBase:CoordBase:fig-domain-external-staggered} +\end{figure} + +\begin{figure} +\begin{center} +\includegraphics[scale=0.75]{domain-internal-staggered} +\end{center} +\caption{A domain (rectangle) with two interior points (empty circles) +and two boundary points (full circles) which are staggered about the +physical boundary. (This is an interior boundary.)} +\label{CactusBase:CoordBase:fig-domain-internal-staggered} +\end{figure} + +Finally, the integer parameter {\texttt{boundary\_shiftout\_x\_lower}} +can be used to shift the boundary points outwards (or inwards with +negative values) by multiples of the grid spacing. Figure +{\ref{CactusBase:CoordBase:fig-domain-external-shiftout}} shows an +example of an exterior, non-staggered boundary with a shiftout of one. + +\begin{figure} +\begin{center} +\includegraphics[scale=0.75]{domain-external-shiftout} +\end{center} +\caption{A domain (rectangle) with four interior points (empty circles) +and two boundary points (full circles) which are shifted outwards by +one grid point. (This is an exterior, non-staggered boundary.)} +\label{CactusBase:CoordBase:fig-domain-external-shiftout} +\end{figure} + +The following table gives examples for common situations: + +\begin{tabular}{l|ccc|l} +Boundary condition & internal? & staggered? & shiftout & example \\\hline +reflection symmetry, not staggered & no & no & 1 + & figure {\ref{CactusBase:CoordBase:fig-domain-external-shiftout}} \\ +reflection symmetry, staggered & no & yes & 0 + & figure {\ref{CactusBase:CoordBase:fig-domain-external-staggered}} \\ +periodicity, closed boundary & no & no & 1 + & figure {\ref{CactusBase:CoordBase:fig-domain-external-shiftout}} \\ +periodicity, open boundary & no & no & 0 + & figure {\ref{CactusBase:CoordBase:fig-domain-external}} \\ +periodicity, staggered boundary & no & yes & 0 + & figure {\ref{CactusBase:CoordBase:fig-domain-external-staggered}} +\end{tabular} + +For other boundary conditions such as Dirichlet or Robin, one can +choose these parameters freely. + + % Do not delete next line % END CACTUS THORNGUIDE diff --git a/doc/domain-external-shiftout.eps b/doc/domain-external-shiftout.eps new file mode 100644 index 0000000..42003a1 --- /dev/null +++ b/doc/domain-external-shiftout.eps @@ -0,0 +1,133 @@ +%!PS-Adobe-2.0 EPSF-2.0 +%%Title: domain-external-shiftout.fig +%%Creator: fig2dev Version 3.2 Patchlevel 4 +%%CreationDate: Mon Jan 19 23:46:16 2004 +%%For: eschnett@because (Erik Schnetter,AEI 2.27,+49 331 567 7357,) +%%BoundingBox: 0 0 207 87 +%%Magnification: 1.0000 +%%EndComments +/$F2psDict 200 dict def +$F2psDict begin +$F2psDict /mtrx matrix put +/col-1 {0 setgray} bind def +/col0 {0.000 0.000 0.000 srgb} bind def +/col1 {0.000 0.000 1.000 srgb} bind def +/col2 {0.000 1.000 0.000 srgb} bind def +/col3 {0.000 1.000 1.000 srgb} bind def +/col4 {1.000 0.000 0.000 srgb} bind def +/col5 {1.000 0.000 1.000 srgb} bind def +/col6 {1.000 1.000 0.000 srgb} bind def +/col7 {1.000 1.000 1.000 srgb} bind def +/col8 {0.000 0.000 0.560 srgb} bind def +/col9 {0.000 0.000 0.690 srgb} bind def +/col10 {0.000 0.000 0.820 srgb} bind def +/col11 {0.530 0.810 1.000 srgb} bind def +/col12 {0.000 0.560 0.000 srgb} bind def +/col13 {0.000 0.690 0.000 srgb} bind def +/col14 {0.000 0.820 0.000 srgb} bind def +/col15 {0.000 0.560 0.560 srgb} bind def +/col16 {0.000 0.690 0.690 srgb} bind def +/col17 {0.000 0.820 0.820 srgb} bind def +/col18 {0.560 0.000 0.000 srgb} bind def +/col19 {0.690 0.000 0.000 srgb} bind def +/col20 {0.820 0.000 0.000 srgb} bind def +/col21 {0.560 0.000 0.560 srgb} bind def +/col22 {0.690 0.000 0.690 srgb} bind def +/col23 {0.820 0.000 0.820 srgb} bind def +/col24 {0.500 0.190 0.000 srgb} bind def +/col25 {0.630 0.250 0.000 srgb} bind def +/col26 {0.750 0.380 0.000 srgb} bind def +/col27 {1.000 0.500 0.500 srgb} bind def +/col28 {1.000 0.630 0.630 srgb} bind def +/col29 {1.000 0.750 0.750 srgb} bind def +/col30 {1.000 0.880 0.880 srgb} bind def +/col31 {1.000 0.840 0.000 srgb} bind def + +end +save +newpath 0 87 moveto 0 0 lineto 207 0 lineto 207 87 lineto closepath clip newpath +-20.7 114.1 translate +1 -1 scale + +/cp {closepath} bind def +/ef {eofill} bind def +/gr {grestore} bind def +/gs {gsave} bind def +/sa {save} bind def +/rs {restore} bind def +/l {lineto} bind def +/m {moveto} bind def +/rm {rmoveto} bind def +/n {newpath} bind def +/s {stroke} bind def +/sh {show} bind def +/slc {setlinecap} bind def +/slj {setlinejoin} bind def +/slw {setlinewidth} bind def +/srgb {setrgbcolor} bind def +/rot {rotate} bind def +/sc {scale} bind def +/sd {setdash} bind def +/ff {findfont} bind def +/sf {setfont} bind def +/scf {scalefont} bind def +/sw {stringwidth} bind def +/tr {translate} bind def +/tnt {dup dup currentrgbcolor + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add + 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} + bind def +/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul + 4 -2 roll mul srgb} bind def + /DrawEllipse { + /endangle exch def + /startangle exch def + /yrad exch def + /xrad exch def + /y exch def + /x exch def + /savematrix mtrx currentmatrix def + x y tr xrad yrad sc 0 0 1 startangle endangle arc + closepath + savematrix setmatrix + } def + +/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def +/$F2psEnd {$F2psEnteredState restore end} def + +$F2psBegin +10 setmiterlimit +0 slj 0 slc + 0.06299 0.06299 sc +% +% Fig objects follow +% +% +% here starts figure with depth 50 +% Ellipse +7.500 slw +n 1800 1125 113 113 0 360 DrawEllipse gs col0 s gr + +% Ellipse +n 1350 1125 113 113 0 360 DrawEllipse gs col0 s gr + +% Ellipse +n 450 1125 113 113 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr + +% Ellipse +n 2250 1125 113 113 0 360 DrawEllipse gs col0 s gr + +% Ellipse +n 900 1125 113 113 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr + +% Ellipse +n 2700 1125 113 113 0 360 DrawEllipse gs col0 s gr + +% Polyline +n 1350 450 m 3600 450 l 3600 1800 l 1350 1800 l + cp gs col0 s gr +% here ends figure; 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