# Resolution Study for Three-dimensional Supernova Simulations with the Prometheus-Vertex Code

## TL;DR

This study systematically examines how angular resolution affects 3D supernova simulations using the Prometheus-Vertex code, revealing that higher resolution improves explosion conditions and discussing the impact of mesh refinement on turbulence and shock dynamics.

## Contribution

It introduces a static mesh refinement technique on the Yin-Yang grid and analyzes its effects on supernova simulation accuracy and turbulence modeling.

## Key findings

- Higher angular resolution leads to more favorable explosion conditions.
- Overall dynamics converge at about 1 degree resolution.
- Mesh refinement can dissipate kinetic energy, affecting turbulence and shock expansion.

## Abstract

We present a carefully designed, systematic study of the angular resolution dependence of simulations with the Prometheus-Vertex neutrino-hydrodynamics code. Employing a simplified neutrino heating-cooling scheme in the Prometheus hydrodynamics module allows us to sample the angular resolution between 4 degrees and 0.5 degrees. With a newly-implemented static mesh refinement (SMR) technique on the Yin-Yang grid, the angular coordinates can be refined in concentric shells, compensating for the diverging structure of the spherical grid. In contrast to previous studies with Prometheus and other codes, we find that higher angular resolution and therefore lower numerical viscosity provides more favorable explosion conditions and faster shock expansion. We discuss the possible reasons for the discrepant results. The overall dynamics seem to converge at a resolution of about 1 degree. Applying the SMR setup to marginally exploding progenitors is disadvantageous for the shock expansion, however, because kinetic energy of downflows is dissipated to internal energy at resolution interfaces, leading to a loss of turbulent pressure support and a steeper temperature gradient. We also present a way to estimate the numerical viscosity on grounds of the measured turbulent kinetic-energy spectrum, leading to smaller values that are better compatible with the flow behavior witnessed in our simulations than results following calculations in previous literature. Interestingly, the numerical Reynolds numbers in the turbulent, neutrino-heated postshock layer (some 10 to several 100) are in the ballpark of expected neutrino-drag effects on the relevant length scales in the turbulent postshock layer. We provide a formal derivation and quantitative assessment of the neutrino drag terms in an appendix.