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ABSTRACT We performed 3D hydrodynamic simulations of the inner $$\approx 50{{\ \rm per\ cent}}$$ radial extent of a $$25\,\,\mathrm{\mathrm{M}_\odot }$$ star in the early phase of the main sequence and investigate core convection and internal gravity waves in the core-envelope boundary region. Simulations for different grid resolutions and driving luminosities establish scaling relations to constrain models of mixing for 1D applications. As in previous works, the turbulent mass entrainment rate extrapolated to nominal heating is unrealistically high ($$1.58\times 10^{-4}\,\,\mathrm{\mathrm{M}_\odot \, {\mathrm{yr}}^{-1}}$$), which is discussed in terms of the non-equilibrium response of the simulations to the initial stratification. We measure quantitatively the effect of mixing due to internal gravity waves excited by core convection interacting with the boundary in our simulations. The wave power spectral density as a function of frequency and wavelength agrees well with the GYRE eigenmode predictions based on the 1D spherically averaged radial profile. A diffusion coefficient profile that reproduces the spherically averaged abundance distribution evolution is determined for each simulation. Through a combination of eigenmode analysis and scaling relations it is shown that in the N2-peak region, mixing is due to internal gravity waves and follows the scaling relation DIGW-hydro ∝ L4/3 over a $$\gtrapprox 2\,\,\mathrm{\mathrm{dex}}$$ range of heating factors. Different extrapolations of the mixing efficiency down to nominal heating are discussed. If internal gravity wave mixing is due to thermally enhanced shear mixing, an upper limit is $$D_\mathrm{IGW}\lessapprox 2$$ to $$3\times 10^{4}\,\,\mathrm{cm^2\, s^{-1}}$$ at nominal heating in the N2-peak region above the convective core. 

ABSTRACT We present two mixing models for post-processing of 3D hydrodynamic simulations applied to convective–reactive i-process nucleosynthesis in a rapidly accreting white dwarf (RAWD) with [Fe/H] = −2.6, in which H is ingested into a convective He shell. A 1D advective two-stream model adopts physically motivated radial and horizontal mixing coefficients constrained by 3D hydrodynamic simulations. A simpler approach uses diffusion coefficients calculated from the same simulations. All 3D simulations include the energy feedback of the 12C(p, γ)13N reaction from the H entrainment. Global oscillations of shell H ingestion in two of the RAWD simulations cause bursts of entrainment of H and non-radial hydrodynamic feedback. With the same nuclear network as in the 3D simulations, the 1D advective two-stream model reproduces the rate and location of the H burning within the He shell closely matching the 3D simulation predictions, as well as qualitatively displaying the asymmetry of the XH profiles between the upstream and downstream. With a full i-process network the advective mixing model captures the difference in the n-capture nucleosynthesis in the upstream and downstream. For example, 89Kr and 90Kr with half-lives of $$3.18\,\,\mathrm{\mathrm{min}}$$ and $$32.3\,\,\mathrm{\mathrm{s}}$$ differ by a factor 2–10 in the two streams. In this particular application the diffusion approach provides globally the same abundance distribution as the advective two-stream mixing model. The resulting i-process yields are in excellent agreement with observations of the exemplary CEMP-r/s star CS31062-050. 

ABSTRACT 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 ≤ MRAWD/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 Nn, max ≈ 1013–1015 cm−3. The H-ingestion rate and the convective boundary mixing (CBM) parameter ftop adopted in the one-dimensional nucleosynthesis and stellar evolution models are constrained through three-dimensional (3D) hydrodynamic simulations. The mass ingestion rate and, for the first time, the scaling laws for the CBM parameter ftop have been determined from 3D hydrodynamic simulations. We confirm our previous result that the high-metallicity RAWDs have a low mass retention efficiency ($$\eta \lesssim 10{{\ \rm per\ cent}}$$). A new result is that RAWDs with [Fe/H] $$\lesssim -2$$ have $$\eta \gtrsim 20{{\ \rm per\ cent}}$$; 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. 

The special computational challenges of simulating 3-D hydrodynamics in deep stellar interiors are discussed, and numerical algorithmic responses described. Results of recent simulations carried out at scale on the NSF's Blue Waters machine at the University of Illinois are presented, with a special focus on the computational challenges they address. Prospects for future work using GPU-accelerated nodes such as those on the DoE's new Summit machine at Oak Ridge National Laboratory are described, with a focus on numerical algorithmic accommodations that we believe will be necessary.