Project 6
Wave Equation in one dimension on moving grid
Implicit Method (9 point)
with Radiation Boundary Conditions
General Results
- Radiation boundary conditions were implemented for the
one dimensional wave equation with constant shift vector (beta) only
if the magnitude of the shift was less than one.
- When the magnitude of the shift is greater than one, the
boundary conditions must be changed.
- The convergance factor is very low (hovering around 1)
when the shift equals one. This is because the solution
is exactly stationary, and only round-off error contributes
to the convergance factor.
- The convergance factor is sensitive to the sign of beta. The
convergance factor for negative betas is slightly less than
for positive betas, all other factors held constant.
- The convergance factor is essentially independent of CFL number.
I generated fewer plots for this project because after a while they
all look the same. On this page I concentrate on convergance factors
- Click here
to see that the CFL number really does not affect
the convergance factor. In this plot beta is +0.9 and solutions
are plotted for CFL = 0.3, 0.9, and 1.4. The different factor
are so close in value that they are not distingiushable except
that CFL = 1.4 has the large jump after the wave leaves the
grid.
- Click here
to see how bad things get when the shift is precisely one.
Here you see convergance factors for CFL = 0.3, 0.9, 1.0, 1.4
- And what happens when beta is negative?