  Linear time-domain simulations of acoustic oscillations are unstable in the
stellar convection zone. To overcome this problem it is customary to compute
the oscillations of a stabilized background stellar model. The stabilization,
however, affects the result. Here we propose to use a perturbative approach
(running the simulation twice) to approximately recover the acoustic wave
field, while preserving seismic reciprocity. To test the method we considered a
1D standard solar model. We found that the mode frequencies of the (unstable)
standard solar model are well approximated by the perturbative approach within
$1~\mu$Hz for low-degree modes with frequencies near $3~\mu$Hz. We also show
that the perturbative approach is appropriate for correcting
rotational-frequency kernels. Finally, we comment that the method can be
generalized to wave propagation in 3D magnetized stellar interiors because the
magnetic fields have stabilizing effects on convection.
