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.
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