  We study the coupling of hydrodynamics and reactions in simulations of the
double detonation model for Type Ia supernovae. When assessing the convergence
of simulations, the focus is usually on spatial resolution; however, the method
of coupling the physics together as well as the tolerances used in integrating
a reaction network also play an important role. In this paper, we explore how
the choices made in both coupling and integrating the reaction portion of a
simulation (operator / Strang splitting vs.\ the simplified spectral deferred
corrections method we introduced previously) influences the accuracy,
efficiency, and the nucleosynthesis of simulations of double detonations. We
find no need to limit reaction rates or reduce the simulation timestep to the
reaction timescale. The entire simulation methodology used here is
GPU-accelerated and made freely available as part of the Castro simulation
code.
