  We compare gravitational-wave (GW) signals from eight three-dimensional
simulations of core-collapse supernovae, using two different progenitors with
zero-age main sequence masses of 9 and 20 solar masses. The collapse of each
progenitor was simulated four times, at two different grid resolutions and with
two different neutrino transport methods, using the Aenus-Alcar code. The main
goal of this study is to assess the validity of recent concerns that the
so-called "Ray-by-Ray+" (RbR+) approximation is problematic in core-collapse
simulations and can adversely affect theoretical GW predictions. Therefore,
signals from simulations using RbR+ are compared to signals from corresponding
simulations using a fully multidimensional (FMD) transport scheme. The 9
solar-mass progenitor successfully explodes, whereas the 20 solar-mass model
does not. Both the standing accretion shock instability and hot-bubble
convection develop in the postshock layer of the non-exploding models. In the
exploding models, neutrino-driven convection in the postshock flow is
established around 100 ms after core bounce and lasts until the onset of shock
revival. We can, therefore, judge the impact of the numerical resolution and
neutrino transport under all conditions typically seen in non-rotating
core-collapse simulations. We find excellent qualitative agreement in all GW
features. We find minor quantitative differences between simulations, but find
no systematic differences between simulations using different transport
schemes. Resolution-dependent differences in the hydrodynamic behaviour of
low-resolution and high-resolution models have a greater impact on the GW
signals than consequences of the different transport methods. Furthermore,
increasing the resolution decreases the discrepancies between models with
different neutrino transport.
