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    The inner structure of core helium burning (CHeB) stars remains uncertain due to the yet unknown nature of mixing at the boundary of their cores. Large convective cores beyond a bare Schwarzschild model are favoured both from theoretical arguments and from asteroseismological constraints. However, the exact nature of this extra mixing, and in particular the possible presence of semiconvective layers, is still debated. In this work, we approach this problem through a new avenue by performing the first full-sphere 3D hydrodynamics simulations of the interiors of CHeB stars. We use the ppmstar explicit gas dynamics code to simulate the inner 0.45$\, {\rm M}_{\odot }$ of a 3 M⊙ CHeB star. Simulations are performed using different Cartesian grid resolutions (7683, 11523, and 17283) and heating rates. We use two different initial states, one based on mesas's predictive mixing scheme (which significantly extends the core beyond the Schwarzschild boundary) and one based on the convective premixing approach (which exhibits a semiconvective interface). The general behaviour of the flow in the convective core and in the stable envelope (where internal gravity waves are observed) is consistent with our recent simulations of core convection in massive main-sequence stars, and so are the various luminosity scaling relations. The semiconvective layers are dominated by strong internal gravity waves that do not produce measurable species mixing, but overshooting motions from the convective core gradually homogenize the semiconvective interface. This process can possibly completely erase the semiconvective layers, which would imply that CHeB stars do not harbour a semiconvection zone.

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    We present the first 3D hydrodynamics simulations of the excitation and propagation of internal gravity waves (IGWs) in the radiative interiors of low-mass stars on the red giant branch (RGB). We use the ppmstar explicit gas dynamics code to simulate a portion of the convective envelope and all the radiative zone down to the hydrogen-burning shell of a $1.2\, {\rm M}_{\odot }$ upper RGB star. We perform simulations for different grid resolutions (7683, 15363, and 28803), a range of driving luminosities, and two different stratifications (corresponding to the bump luminosity and the tip of the RGB). Our RGB tip simulations can be directly performed at the nominal luminosity, circumventing the need for extrapolations to lower luminosities. A rich, continuous spectrum of IGWs is observed, with a significant amount of total power contained at high wavenumbers. By following the time evolution of a passive dye in the stable layers, we find that IGW mixing in our simulations is weaker than predicted by a simple analytical prescription based on shear mixing and not efficient enough to explain the missing RGB extra mixing. However, we may be underestimating the efficiency of IGW mixing given that our simulations include a limited portion of the convective envelope. Quadrupling its radial extent compared to our fiducial set-up increases convective velocities by up to a factor 2 and IGW velocities by up to a factor 4. We also report the formation of a $\sim 0.2\, H_P$ penetration zone and evidence that IGWs are excited by plumes that overshoot into the stable layers.

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    Supermassive stars are Population III stars with masses exceeding $10^4\, {\rm M}_{\odot }$ that could be the progenitors of the first supermassive black holes. Their interiors are in a regime where radiation pressure dominates the equation of state. In this work, we use the explicit gas dynamics code ppmstar to simulate the hydrogen-burning core of a $10^4\, {\rm M}_{\odot }$ supermassive main-sequence star. These are the first three-dimensional hydrodynamics simulations of core convection in supermassive stars. We perform a series of 10 simulations at different heating rates and on Cartesian grids with resolutions of 7683, 11523, and 17283. We examine different properties of the convective flow, including its large-scale morphology, its velocity spectrum, and its mixing properties. We conclude that the radiation pressure-dominated nature of the interior does not noticeably affect the behaviour of convection compared to the case of core convection in a massive main-sequence star where gas pressure dominates. Our simulations also offer support for the use of mixing-length theory in one-dimensional models of supermassive stars.

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  4. 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. 
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