# GfsFunction

### From Gerris

Functions can be used in most objects which require a numerical parameter. A function can be a constant or a piece of C code taking coordinates (x,y,z), time t or any of the domain variables as arguments and returning a floating-point value.

The syntax in parameter files is as follows:

-1.78e-3

or a C function

{ double a = sin (x + y); double b = cos (x - z); double c = sin (M_PI*t); return a + b + c; }

or a C expression

40.*(P - 1.)

or a GTS file

myfunction.gts

The GTS file must be a planar (preferably Delaunay) triangulation of a set of points. The value of the function at a given (x,y) coordinate is then calculated by computing the z-coordinate of the intersection of a vertical line passing through the point at (x,y,0) with the triangulation defined by the GTS file.

or a CDG file

myfile.cdg

The CDG file contain cartesian data. This type of file can be used to introduce 1 to 4 spacial time dimensions data. The first line define the structure of grid for example :

3 x y t

Here 3 show the number of dimension. x, y and t show the structure of data : 2 spacial dimensions and 1 temporal dimension. The data is structured according to space vectors first and according to time vector finaly. The 3 next lines defines the grid : each line contain one vector witch define the position of each point in space-time. The rest of file contain the data. More information in this page.

Gradients of variables can be computed using the `dx()`

, `dy()`

and `dz()`

functions. For example, the z-component of the vorticity would be computed as:

(dx("V") - dy("U"))

## More details on C functions

Comments should use the C syntax; i.e. opening `/*`

and closing
`*/`

not necessarily on the same line rather than the usual parameter file syntax of a line beginning with a `#`

. This is to allow the use of C preprocessor directives in C functions in GfsFunctions.

Example:

- Coalescence of a pair of Gaussian vortices (Gerris logo), in the InitVorticity command.