# Comments on "Numerical Stability of Detonations in White Dwarf Simulations"

## TL;DR

This paper challenges previous claims about the numerical stability of white dwarf detonation simulations, demonstrating that convergence can be achieved at km-scale resolutions without artificial modifications, and clarifying the role of boundary conditions.

## Contribution

The authors show that proper boundary conditions enable convergence in white dwarf detonation simulations at km-scale resolutions, countering prior claims of instability and invalidating the need for certain numerical fixes.

## Key findings

- Converged ignition is achievable without He or temperature increase.
- Boundary artifacts can hinder convergence and should be corrected.
- The burning limiter recommended by KZ19 is unnecessary.

## Abstract

Katz & Zingale (2019, KZ19) recently studied a one-dimensional test problem, intended to mimic the process of detonation ignition in head-on collisions of two carbon--oxygen (CO) white dwarfs. They do not obtain ignition of a detonation in pure CO compositions unless the temperature is artificially increased or 5% He is included. In both of these cases they obtain converged ignition only for spatial resolutions better than 0.1 km, which are beyond the capability of multidimensional simulations. This is in a contradiction with the claims of Kushnir et al. (2013, K13), that a convergence to $\sim10\%$ is achieved for a resolution of a few km. Using Eulerian and Lagrangian codes we show that a converged and resolved ignition is obtained for pure CO in this test problem without the need for He or increasing the temperature. The two codes agree to within 1% and convergence is obtained at resolutions of several km. We calculate the case that includes He and obtain a similar slow convergence, but find that it is due to a boundary numerical artifact that can (and should) be avoided. Correcting the boundary conditions allows convergence with resolution of $\sim10\,\textrm{km}$ in an agreement with the claims of K13. It is likely that the slow convergence obtained by KZ19 in this case is because of a similar boundary numerical artifact, but we are unable to verify this. KZ19 further recommended to avoid the use of the burning limiter introduced by K13. We show that their recommendation is not justified.