GenASiS: General Astrophysical Simulation System. II. Self-gravitating Baryonic Matter

GenASiS (General Astrophysical Simulation System) is a code being developed initially and primarily, though not exclusively, for the simulation of core-collapse supernovae on the world’s leading capability supercomputers. This paper – the second in a series – documents capabilities for Newtonian self-gravitating fluid dynamics, including tabulated microphysical equations of state treating nuclei and nuclear matter (`baryonic matter’). Computation of the gravitational potential of a spheroid, and simulation of the gravitational collapse of dust and of an ideal fluid, provide tests of self-gravitation against known solutions. In multidimensional computations of the adiabatic collapse, bounce, and explosion of spherically symmetric pre-supernova progenitors – which we propose become a standard benchmark for code comparisons – we find that the explosions are prompt and remain spherically symmetric (as expected), with an average shock expansion speed and total kinetic energy that are inversely correlated with the progenitor mass at the onset of collapse and the compactness parameter.

💡 Research Summary

This paper presents the second installment of the GenASiS (General Astrophysical Simulation System) development series, focusing on Newtonian self‑gravity coupled to baryonic fluid dynamics. The authors extend the previously described single‑level, centrally refined mesh to a spherical‑coordinate mesh that employs a novel angular‑radial coarsening strategy. Near the origin and polar axis, where conventional spherical cells become prohibitively small, adjacent angular cells are grouped into blocks and averaged, allowing the global time step to be limited by a uniform minimum radial spacing (Δr_min) rather than by vanishing angular widths. This approach mitigates CFL constraints while preserving geometric fidelity and incurs only modest computational overhead (≈10 % of total runtime on GPUs).

The gravitational potential is obtained by solving Poisson’s equation with a multipole expansion. Real‑valued cosine and sine angular kernels derived from spherical harmonics are pre‑computed and stored. For each radial shell the angular moments of the source density are accumulated via outward and inward radial integrations, reducing the naïve O(N²) operation count to O((L+1)² N_r N_θ N_φ), where L≈10–20 suffices for quasi‑spherical mass distributions. GPU acceleration is achieved through OpenMP target directives; the authors collapse the six‑dimensional reduction (kernel type, ℓ, m, radial index, θ‑index, φ‑index) into a two‑dimensional operation by first forming a per‑process angular‑moment index array and then performing an OpenMP reduction on that array. This two‑level parallelism avoids excessive private memory allocation on the device.

The fluid dynamics module incorporates a high‑order parabolic reconstruction scheme and a tabulated microphysical equation of state (EOS) that treats heavy nuclei, a phase transition to nuclear matter, electrons, positrons, and photons. The EOS tables are interpolated on‑the‑fly, enabling accurate treatment of strong pressure gradients and phase changes that occur during core bounce. The finite‑volume solver is also GPU‑offloaded using the same OpenMP target model, yielding a 5–7× speedup relative to CPU‑only execution.

A suite of verification tests validates the implementation. The authors compute the potential of a homogeneous spheroid and compare against analytical multipole results, achieving sub‑percent errors. They simulate the free‑fall collapse of a pressureless dust sphere and the homologous collapse of an ideal gas sphere, both reproducing known analytic solutions. Multidimensional (2‑D and 3‑D) adiabatic collapse simulations of spherically symmetric pre‑supernova progenitors are then performed. The simulations exhibit prompt, spherically symmetric explosions; the average shock expansion speed and total kinetic energy are found to be inversely correlated with the progenitor’s mass at collapse and with its compactness parameter. These results are proposed as a standard benchmark for code‑to‑code comparisons in the supernova community.

Performance measurements show that the multipole Poisson solver and the fluid solver each benefit substantially from GPU acceleration, while the coarsening operations remain a small fraction of the total wall‑clock time. The paper concludes that the presented framework provides a robust, high‑performance foundation for Newtonian self‑gravity simulations of baryonic matter and sets the stage for future extensions to general‑relativistic gravity and neutrino radiation transport, ultimately aiming at fully realistic core‑collapse supernova modeling.