Separate shock-response and time-integration errors in coarse-step simulations

Determine whether the non-conservative stabilization caused by coarse temporal resolution in transonic flutter simulations arises from errors in the aerodynamic shock response, from time integration, or from both mechanisms.

Background

The paper finds that using too few time steps per pitch period can reverse the stability label near the flutter boundary, even though the dual-time-stepping iterations converge at every step. A coarse step also slightly lowers the identified frequency, but that effect alone would weaken the quasi-steady damping rather than produce the observed stabilization.

Because the net aerodynamic work near the flutter boundary is small relative to the shock contribution, small errors in shock motion, phase, or temporal integration can change the sign of the damping. The authors identify the possible sources of the error but do not determine how much is attributable to the shock response versus the time-integration procedure.

References

The coarse step stabilises even though it lowers the frequency slightly (0.7--0.8\% with 32 steps), which alone would weaken the quasi-steady loss, so its error must enter through the shock response or the time integration; we have not separated the two.

— How the elastic axis folds the transonic flutter boundary: shock energy transfer and conformally calibrated active learning  (2610.23298 - Saxena et al., 16 Oct 2026) in Section 7, Discussion, subsection “Why all of these are of order one per cent”