Ecole doctorale de Physique de la région Parisienne (ED107)

120 Inertial modes in slowly rotating stars : An evolutionary description
V θ
1
0
-1
V θ versus time for 100 oscillations (without any correction)
m=2 r-mode with grid 8 x 6 x 4
0 10 20 30 40 50 60 70
t Ω
Figure 4.1 – Time evolution of the ϑ component of velocity on the equator for the linear
m = 2 r-mode in an incompressible and rigidly rotating fluid. The run is supposed to last
exactly 100 times the period of this mode which is 3 . The beating phenomenon which
4Ω
can be seen is due to the resolution of the graphical tool. See the power spectrum in
Figure 4.3.
δΕ / Ε
0.08
0.06
0.04
0.02
δE/E versus t for 100 oscillations (without any correction)
m=2 r-mode with grid 8 x 6 x 4
100 steps per oscillation
150 steps per oscillation
200 steps per oscillation
0
0 10 20 30 40 50 60 70
t Ω
Figure 4.2 – Time evolution of the relative error in the energy before any improvement
of the conservation of energy. The different straight lines correspond to runs with the
same duration (100 periods of the m = 2 linear r-mode), same spatial grid (8 × 6 × 4
points) but different time steps. We see the linear variation of these errors with time. It
shows that with the exception done of round-off errors (which are so small that they do
not appear here), the main error is deterministic and then well controlled.