Imagine being able to predict -with unprecedented accuracy and precision -the structure of the proton and neutron, and the forces between them, directly from the dynamics of quarks and gluons, and then using this information in calculations of the structure and reactions of atomic nuclei and of the properties of dense neutron stars (NSs). Also imagine discovering new and exotic states of matter, and new laws of nature, by being able to collect more experimental data than we dream possible today, analyzing it in real time to feed back into an experiment, and curating the data with full tracking capabilities and with fully distributed data mining capabilities. Making this vision a reality would improve basic scientific understanding, enabling us to precisely calculate, for example, the spectrum of gravity waves emitted during NS coalescence, and would have important societal applications in nuclear energy research, stockpile stewardship, and other areas. This review presents the components and characteristics of the exascale computing ecosystems necessary to realize this vision.Nuclear physics research and its applications, more than many other areas of science, rely heavily on large-scale, high-performance computing (HPC). HPC is integral to (1) the design and optimization of an extensive and vibrant experimental program, (2) acquisition and handling of large volumes of experimental data, and (3) large-scale simulations of emergent complex systems -from the subatomic to the cosmological. Dramatic progress has already been made in enhancing our understanding of strongly-interacting matter across many areas of physics: from the quark and gluon structure of the proton and neutron, the building blocks of atomic nuclei; to relating the hot dense plasma in the early universe to the near-perfect fluid produced at the Relativistic Heavy Ion Collider (RHIC); to the structure of rare isotopes and the reactions required to form all the elements of the universe; to the creation and properties of the dense cold matter formed in supernovae and NSs.In addition to pursuing new analytical and experimental techniques and algorithms and more complete physical models at higher resolution, the following broadly grouped areas relevant to the U.S. Department of Energy (DOE) Office of Advanced Scientific Computing Research (ASCR) and the National Science Foundation (NSF) would directly affect the mission need of the DOE Office of Science (SC) Nuclear Physics (NP) program.Exascale capability computing and associated capacity computing will revolutionize our understanding of nuclear physics and nuclear applications.Closely tied to the needs for exascale hardware are the requirements for new software (codes, algorithms, and workflows) appropriate for the exascale ecosystem, which can be developed through collaborations among ASCR and NSF mathematicians and computer scientists and NP scientists.

We develop implicit-explicit (IMEX) schemes for neutrino transport in a background material in the context of a two-moment model that evolves the angular moments of a neutrino phase-space distribution function. Considering the upper and lower bounds that are introduced by Pauli’s exclusion principle on the moments, an algebraic moment closure based on Fermi-Dirac statistics and a convex-invariant time integrator both are demanded. A finite-volume/first-order discontinuous Galerkin(DG) method is used to illustrate how an algebraic moment closure based on Fermi-Dirac statistics is needed to satisfy the bounds. Several algebraic closures are compared with these bounds in mind, and the Cernohorsky and Bludman closure, which satisfies the bounds, is chosen for our IMEX schemes. For the convex-invariant time integrator, two IMEX schemes named PD-ARS have been proposed. PD-ARS denotes a convex-invariant IMEX Runge-Kutta scheme that is high-order accurate in the streaming limit, and works well in the diffusion limit. Our two PD-ARS schemes use second-and third-order, explicit, strong-stability-preserving Runge-Kutta methods as their explicit part, respectively, and therefore are second-and third-order accurate in the streaming limit, respectively. The accuracy and convex-invariance of our PD-ARS schemes are demonstrated in the numerical tests with a third-order DG method for spatial discretization and a simple Lax-Friedrichs flux. The method has been implemented in our high-order neutrino-radiation hydrodynamics (thornado) toolkit. We show preliminary results employing tabulated neutrino opacities.

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Nuclear electron capture and the nuclear equation of state play important roles during the collapse of a massive star and the subsequent supernova. The nuclear equation of state controls the nature of the bounce which initially forms the supernova shock while electron capture determines the location where the shock forms. Advances in nuclear structure theory have allowed a more realistic treatment of electron capture on heavy nuclei to be developed. We will review how this improvement has led to a change in our understanding of stellar core collapse, with electron capture on nuclei with masses larger than 50 found to dominate electron capture on free protons, resulting is significant changes in the hydrodynamics of core collapse and bounce. We will also demonstrate the impact of a variety of nuclear equations of state on supernova shock propagation. Of particular note is the interplay between the nuclear composition determined by the equation of state and nuclear electron capture. 10th Symposium on Nuclei in the Cosmos

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Unraveling the core-collapse supernovae mechanism is an outstanding computational challenge and the problem remains essentially unsolved despite more than four decades of effort. However, progress in realistic modeling has occurred recently through the availability of petascale platforms and the increasing sophistication of supernova codes. CHIMERA is a code we have developed to simulate core-collapse supernovae in one, two, and three spatial dimensions, incorporating modules for ray-by-ray neutrino transport and nuclear kinetics. In addition to this base functionality, CHIMERA includes several other features designed to provide additional capability. For example, the availability of Lagrangian tracer particles in CHIMERA allows us to produce realistic, post-processed estimates for a variety of multi-messenger observables, including supernova nucleosynthesis and gravitational wave signatures.

Ascertaining the core-collapse supernova mechanism is a complex, and yet unsolved, problem dependent on the interaction of general relativity, hydrodynamics, neutrino transport, neutrinomatter interactions, and nuclear equations of state and reaction kinetics. Ab initio modeling of core-collapse supernovae and their nucleosynthetic outcomes requires care in the coupling and approximations of the physical components. We have built our multi-physics CHIMERA code for supernova modeling in 1-, 2-, and 3-D, using ray-by-ray neutrino transport, approximate general relativity, and detailed neutrino and nuclear physics. We discuss some early results from our current series of exploding 2D simulations and our work to perform computationally tractable simulations in 3D using the "Yin-Yang" grid.

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