5.4. TEMPORAL RESOLUTION 49
Figure 5.3: Numerical convergence and temporal resolution. (a) Graphs of the build-up of acoustic
energy Eac(t) in the time-domain simulations calculated with dierent
xed time steps t. The energy of
the time-domain simulations is normalized with respect to the energy
Efd
ac(1)
of the steady solution in
the frequency domain, and should thus converge towards unity. In all simulations the actuation frequency
equals the numerically
determined resonance frequency. (b) Acoustic energy Eac(1000 t0) at t = 1000 t0,
normalized by
Efd
, and plotted versus the temporal resolution t0=t of the oscillation. The inset
ac(1)
is a semilog plot of the relative deviation of Eac(1000 t0) from
Efd
ac(1)
. The circled point in each graph
indicates the time step t = t0=256 used in all subsequent simulations. Figure adapted from Ref. 30
Appendix E.
