dimension

The dimension block contains information about the grid and the size of the domain $\Omega$. The following keywords are allowed:

length <$x$,$y$,$z$>

defines the domain $\Omega$ as

$$\Omega=[0,x]\times [0,y]\times [0,z]\subset\mathbb{R}^3.$$

If not specified, the default domain is $\Omega=[0,1]^3$.

resolution <$M$,$N$,$K$>

defines the number of cells in each direction, numbered from 1 to $M$, 1 to $N$ and from 1 to $K$. The program will add ''ghost cells'' in each direction, so the exact number of cells is $N+2$, respectively numbered from 0 to $N+1$. If not specified, the default number of cells will be $M=N=K=15$. This parameter has to be specified before one of the following parameters x, y or z.

x $k_0$ $x_0\dots k_M$ $x_M$

defines a non-equidistant grid, where the $x_l$ values define the positions of the grid lines and the $k_l$ values are optional numbers of the grid lines. These values are ignored by the parser and only serve for compatibility with gnuplot's data format. The program will compute the width of every cell from $x_l$. Thus the first grid line does not need to be positioned at 0. Furthermore, the width of the ''ghost cells'' will be the same as the width of the adjacent inner cell. If not specified, the grid will be equidistant and the widths are calculated using resolution and length.

y $k_0$ $y_0\dots k_N$ $y_N$

See x $k_0$ $x_0\dots k_M$ $x_M$.

z $k_0$ $z_0\dots k_K$ $z_K$

See x $k_0$ $x_0\dots k_M$ $x_M$.

Example:

dimension {
   resolution <5, 4, 1>
   length <3.0, 2.0, 0.5>
 x 0  0.0
   1  0.5
   2  1.1
   3  1.9
   4  2.5
   5  3.0
}

generates the grid shown in figure .

Figure: Ghost cells are bounded by thin lines and inner cells are bounded by thick lines.