This work investigates the properties of convection in stars with particular emphasis on entrainment across the upper convective boundary (CB). Idealised simulations of turbulent convection in the O-burning shell of a massive star are performed in 4π geometry on 768 3 and 1536 3 grids, driven by a representative heating rate. A heating series is also performed on the 768 3 grid. The 1536 3 simulation exhibits an entrainment rate at the upper CB of 1.33 × 10 −6 M s −1 . The 768 3 simulation with the same heating rate agrees within 17 per cent. The entrainment rate at the upper convective boundary is found to scale linearly with the driving luminosity and with the cube of the shear velocity at the upper boundary, while the radial RMS fluid velocity scales with the cube root of the driving luminosity, as expected. The mixing is analysed in a 1D diffusion framework, resulting in a simple model for CB mixing. The analysis confirms previous findings that limiting the MLT mixing length to the distance to the CB in 1D simulations better represents the spherically-averaged radial velocity profiles from the 3D simulations and provides an improved determination of the reference diffusion coefficient D 0 for the exponential diffusion CB mixing model in 1D. From the 3D simulation data we adopt as the convective boundary the location of the maximum gradient in the horizontal velocity component which has 2σ spatial fluctuations of ≈ 0.17H P . The exponentially decaying diffusion CB mixing model with f = 0.03 reproduces the spherically-averaged 3D abundance profiles.

We have modelled the multicycle evolution of rapidly-accreting CO white dwarfs (RAWDs) with stable H burning intermittent with strong He-shell flashes on their surfaces for 0.7 ≤ M RAWD /M ≤ 0.75 and [Fe/H] ranging from 0 to −2.6. We have also computed the i-process nucleosynthesis yields for these models. The i process occurs when convection driven by the He-shell flash ingests protons from the accreted H-rich surface layer, which results in maximum neutron densities N n,max ≈ 10 13 -10 15 cm −3 . The H-ingestion rate and the convective boundary mixing (CBM) parameter f top adopted in the one-dimensional nucleosynthesis and stellar evolution models are constrained through 3D hydrodynamic simulations. The mass ingestion rate and, for the first time, the scaling laws for the CBM parameter f top have been determined from 3D hydrodynamic simulations. We confirm our previous result that the highmetallicity RAWDs have a low mass retention efficiency (η < ∼ 10%). A new result is that RAWDs with [Fe/H] < ∼ − 2 have η > ∼ 20%, therefore their masses may reach the Chandrasekhar limit and they may eventually explode as SNeIa. This result and the good fits of the i-process yields from the metal-poor RAWDs to the observed chemical composition of the CEMP-r/s stars suggest that some of the present-day CEMP-r/s stars could be former distant members of triple systems, orbiting close binary systems with RAWDs that may have later exploded as SNeIa.