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

Katz & Zingale (2019) 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 $0.1\,\textrm{km}$, which are beyond the capability of multi-dimensional simulations. This is in a contradiction with the claims of Kushnir et al. (2013), 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 show that the slow convergence obtained by Katz & Zingale (2109) in the case that includes He is due to a boundary numerical artifact that can (and should) be avoided by suppressing the burning in the $1-3$ cells next to the reflecting boundary of the test problem. Correcting the boundary conditions allows convergence with resolution of $\sim10\,\textrm{km}$ in an agreement with the claims of Kushnir et al. (2013). Katz & Zingale (2019) further recommended to avoid the use of the burning limiter introduced by Kushnir et al. (2013). We show that their recommendation is not justified.