The Coordinates Section

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The optional COORDINATES section defines the coordinate geometry of the problem.  The basic form of the section is:

       

COORDINATES  geometry

 

where geometry may be any of the following:

 

Name

Meaning

 

 

CARTESIAN1

1D Cartesian coordinate named 'X'

CYLINDER1

1D Cylindrical coordinate named 'R'

SPHERE1

1D Spherical coordinate named 'R'

 

 

CARTESIAN2

2D Cartesian coordinates named 'X' and 'Y'.

XCYLINDER

2D Cylindrical coordinates with axial coordinate 'Z' lying along the horizontal (X) plot axis, and radial coordinate 'R' lying along the vertical(Y) plot axis.

YCYLINDER

2D Cylindrical coordinates with radial coordinate 'R' lying along the horizontal (X) plot axis, and axial coordinate 'Z' lying along the vertical(Y) plot axis.

 

 

CARTESIAN3

3D Cartesian coordinates named 'X', 'Y' and 'Z'.

 

 

Renaming Coordinates

 

A second form of the COORDINATES section allows renaming of the coordinates:

 

COORDINATES  geometry ( 'Xname'  [,'Yname'  [,'Zname'] ])

 

In this case, the 'Xname' argument renames the coordinate lying along the horizontal plot axis, and 'Yname' renames the coordinate lying along the vertical plot axis. 'Zname' renames the extrusion coordinate. Names may be quoted strings or unquoted names. 

 

Renaming coordinates causes a redefinition of the differential operators.  DX becomes D<Xname>, etc.

 

The DIV, GRAD, and CURL operators are expanded correctly for the designated geometry.  Use of these operators in the EQUATIONS section can considerably simplify problem specification.

 

IF no COORDINATES section is specified, a CARTESIAN2 coordinate system is assumed.