We compute the temperature over time of a thin square steel strip with a heat source at its center. Initially, the steel strip is at 0 degrees. The heat source within the steel strip generates heat with increasing intensity as time increases.
The PDE is given by
We solve this parabolic problem on a 25 x 25 uniform grid,
using PDELab's 5-Point Star inside a time loop, where
the time variable is discretized. We
take advantage of the symbolic manipulation available in PDELab:
MAXIMA is accessed to discretize the time variable
via Crank-Nicolson, and
then GENCRAY generates the mix of
PDELab language and fortran code
required for the problem definition.
The linear system is solved using the direct Band GE. The PDELab
output can be animated in with the OutputTool using Visual2D. The
solution U, as well as its derivatives Ux and
Uy are saved at every
iteration of the time loop.
Use PDELab to ...
Step 14: The PDELab .e file is loaded
Click on the Run button
The trace of the process for compiling and linking the PDELab executable appears
in the trace window. When the compiling and
linking process is complete, the executable program is run and the solution and
trance files are generated and placed in your user directory.
Click on Quit to exit the ExecuteTool.
Click on the OutputTool in the
Session toolkit. Select PDELab Solution
in the File menu. Select the output file that was generated by your program
when the OutputTool requests the filename. The Select Solution Box is
displayed after the file is loaded.
The selection box contains a list of the computed solutions, one for
each time step. You can choose any or all of the solutions. If more
than one solution is selected, PDELab will animate the solution