Streamfunction and Complex Potential - Environmental Modeling - page 286

With the wellvort switch the user decides if wells or vortices are considered.
The mirrorx switch enables the user to make the x-axis a symmetry boundary;
analogously, the value stored in mirrory decides about the y-axis. It is possible to
decide about the x- and y-axis independently: either option may be 'on' or 'off'
independent of the other. In both cases the symmetry may result in an impermeable
boundary or an open boundary. For the latter alternative the mirror switch is
responsible: if it is 'on' (1), the well or vortex on the other side of the symmetry
line is of identical strength; if it is 'off' (0), the mirror object has opposite strength.
In the latter case the pumping well is vis-`-vis of a recharge well, and a clockwise
circulating vortex is vis-`-vis of another one circulating counter-clockwise.
Under xspace and yspace the x- and y-values of the mesh are specified.
Moreover, the user can choose the number of vortices or wells. There are two
options: randomly distributed wells and manual input. For the first option the user
has to choose a value N greater than 0. Otherwise the locations of the wells/vortices
are specified in the zloc vector and their strengths in the s vector. The positions are
given as complex numbers.
There are some further options. The number of start positions around the well is
required. For well systems the starting positions concern streamlines, for vortices
iso-potentials. There is the number of filled contour lines that represent streamlines
for vortices plots and iso-potentials for well galleries. Finally, there is the option
to switch on / off the output of arrow fields.
The next commands compute some auxiliary variables, which are needed in the
following. xrange and yrange represent the length of the model region on both
coordinate axes. x and y are the mesh variables in real numbers, z in complex
numbers. zloc is a vector containing randomly determined positions of the vortices
and wells. s is a vector containing the strength of all, also randomly determined.
With the final command the minimum absolute value of all the vortices or wells
strengths is computed and divided by the integer K .
Note that the contents of the two vectors zloc and s are displayed in the command
window. The user is thus able to find the exact data for the output in case she/he is
interested to reproduce interesting results. In the next command lines virtual wells or
image vortices are introduced depending on the options set in the specification part of
the M-file. The position given by conj(zloc) is the mirror location of a well with
respect to the x -axis, the conjugate complex . It is easy to check that the commands in
the nested if -blocks fulfill the task, which is explained above.