# Numerical Stability of Detonations in White Dwarf Simulations

## TL;DR

This paper investigates the numerical resolution needed to accurately simulate thermonuclear detonations in white dwarf collisions, revealing that current computational limits hinder convergence and may affect the reliability of supernova models.

## Contribution

It identifies the resolution threshold for converged detonations in white dwarf simulations and highlights the challenges posed by current computational constraints.

## Key findings

- Converged detonations require spatial resolution finer than 1 km.
- Current simulations likely do not achieve true convergence.
- Results suggest caution in interpreting existing supernova models.

## Abstract

Some simulations of Type Ia supernovae feature self-consistent thermonuclear detonations. However, these detonations are not meaningful if the simulations are not resolved, so it is important to establish the requirements for achieving a numerically converged detonation. In this study we examine a test detonation problem inspired by collisions of white dwarfs. This test problem demonstrates that achieving a converged thermonuclear ignition requires spatial resolution much finer than 1 km in the burning region. Current computational resource constraints place this stringent resolution requirement out of reach for multi-dimensional supernova simulations. Consequently, contemporary simulations that self-consistently demonstrate detonations are possibly not converged and should be treated with caution.