This work presents three-dimensional simulations of core convection in a 15 solar mass star halfway through its main sequence lifetime. We examine the effects of two common modeling choices on the resulting convective flow: using a reduced domain size and using a monatomic, or single species, approximation. We compare a multi-species simulation on a full sphere (360 degree) domain with a multi-species simulation on an octant domain and also with a single species simulation on a full sphere domain.
To perform the long-time calculations, we use the new low Mach number code MAESTRO. The first part of this work deals with numerical aspects of using MAESTRO for the core convection system, a new application for MAESTRO. We extend MAESTRO to include two new models, a single species model and a simplified two-dimensional planar model, to aid in the exploration of using MAESTRO for core convection in massive stars. We discuss using MAESTRO with a novel spherical geometry domain configuration, namely, with the outer boundary located in the interior of the star, and show how this can create spurious velocities that must be numerically damped using a sponging layer. We describe the preparation of the initial model for the simulation. We find that assuring neutral stratification in the convective core and reasonable resolution of the gravity waves in the stable layer are key factors in generating suitable initial conditions for the simulation. Further, we examine a numerical aspect of the velocity constraint that is part of the low Mach number formulation of the Euler equations. In particular, we investigate the numerical procedure for computing β0, the density-like variable that captures background stratification in the velocity constraint, and find that the original method of computation remains a good choice.
The three-dimensional simulation results show that using a single species model actually increases the computational cost of the simulation because the single species system takes longer to reach quasi-steady state convection. This is due to the fact that a single species model cannot effectively model mixing at the convection zone boundary, where fluid of a differing composition is pulled into the convective region.
Simulations in an octant yields flow with statistical properties that are within a factor of two (or less) of the full sphere simulation values. Both the octant and full sphere simulations show similar mixing across the convection zone boundary that is consistent with the turbulent entrainment model. However, the global character of the flow is distinctly different in the octant simulation, showing more rapid changes in the large scale structure of the flow, leading to a more isotropic flow on average. Thus, for studies of more rapid dynamics that could depend sensitively on anisotropy in the flow, such as simulations of the helium flash or oxygen shell burning, performing simulations on a reduced domain is questionable.