The production of the neutron-capture isotopes beyond iron that we observe today in the Solar system is the result of the combined contribution of the r-process, the s-process, and possibly the i-process. Low-mass asymptotic giant branch (AGB) (1.5 < M/M⊙ < 3) and massive (M > 10 M⊙) stars have been identified as the main site of the s-process. In this work we consider the evolution and nucleosynthesis of low-mass AGB stars. We provide an update of the NuGrid Set models, adopting the same general physics assumptions but using an updated convective-boundary-mixing model accounting for the contribution from internal gravity waves. The combined data set includes the initial masses MZAMS/M⊙ = 2, 3 for Z = 0.03, 0.02, 0.01. These new models are computed with the mesa stellar code and the evolution is followed up to the end of the AGB phase. The nucleosynthesis was calculated for all isotopes in post-processing with the NuGrid mppnp code. The convective-boundary-mixing model leads to the formation of a 13C-pocket three times wider compared to the one obtained in the previous set of models, bringing the simulation results now in closer agreement with observations. Using these new models, we discuss the potential impact of other processes inducing mixing, like rotation, adopting parametric models compatible with theory and observations. Complete yield data tables, derived data products, and online analytic data access are provided.