Source Code

The source code used for this project was the same as in project 1 except for additional routines for periodic and radiation boundaries.

Data

The runs that follow were carried out with
****Parameters****
nx(1,2,3) = 401 801 1601
xmin/max= -1.0 1.0
gaussian width = 5.0E-02
gaussian amplitude = 0.5
propagation velocity = 1.0
dt/dx = cfl = 0.5
max no. of iterations to run 500
final time = 1.25

Radiation Boundaries

Evolution with Radiation boundaries
Given the initial data and parameters discussed earlier an evolution is carried out to 500 steps. This corresponds to a time of 1.25 units. The pulse moves to the right and when it hits the boundaries it moves through it as expected.

MPEG movie of evolution of moving pulse with radiation boundaries.

Radiation boundary convergence test
The graph below shows the convergence factor as a function of time. At t=1.0 there is variation due to the boundaries of the convergence factor. Apart from boundary effects the code is always second order.


Periodic Boundaries

Evolution with Periodic boundaries
Given the initial data and parameters discussed earlier an evolution is carried out to 500 steps. This corresponds to a time of 1.25 units. The pulse moves to the right and when it hits the boundaries it moves through and appears on the leftmost boundary is as expected.

MPEG movie of evolution of moving pulse with periodic boundaries.

Periodic boundary convergence test
The graph below shows the convergence factor as a function of time. At t=1.0 there is variation due to the boundaries of the convergence factor. Apart from boundary effects the code is always second order. Note that the variation at t=1.0 is an order of magnitude smaller than in the radiation boundary case.