Project (25% of your grade): Solve the unsteady heat conduction
in a plate of length and height h, and a heat conduction
coefficient . Assume that the plate is initially at zero
temperature, but at time t=0, the temperature of the right-hand
boundary is raised to , and the top and bottom sides
to .
- Read the values of , h, , and from an input file, along with the values of and
and the parameter that determines the time step.
In the input file, specify the values to be , h=1,
, , and try various values for
, selecting to give square mesh
cells. In the input file, also put the number of desired output
times followed by the output times .
- Write a subroutine that computes the exact solution.
- Write a Peaceman-Rachford scheme to compute a finite difference
solution.
- Optimize the ratio of mesh size to time step for a given
computational effort (= points computed) to give best results
for a given effort.
- Create a Mitchell-Fairweather scheme from the Peaceman-Rachford
one.
- Optimize the ratio of square mesh size to time step
for the same computational effort as for the Peaceman-Rachford
scheme to give the best results.
- See whether the Mitchwell-Fairweather scheme gives better results
than the Peaceman-Rachford
- Increase the effort by a factor 10 and compare again.
Contour lines of constant temperature are a good way to plot the
temperature evolution. Otherwise you might want to plot the
temperature evolution at x=1 and the one at .
The program must meet the neatness recommendations of the handout or
significant credit (30%) will be lost.