Many astrophysical phenomena are highly subsonic, requiring specialized
numerical methods suitable for long-time integration. In a series of earlier
papers we described the development of MAESTRO, a low Mach number stellar
hydrodynamics code that can be used to simulate long-time, low-speed flows that
would be prohibitively expensive to model using traditional compressible codes.
MAESTRO is based on an equation set derived using low Mach number asymptotics;
this equation set does not explicitly track acoustic waves and thus allows a
significant increase in the time step. MAESTRO is suitable for two- and
three-dimensional local atmospheric flows as well as three-dimensional
full-star flows. Here, we continue the development of MAESTRO by incorporating
adaptive mesh refinement (AMR). The primary difference between MAESTRO and
other structured grid AMR approaches for incompressible and low Mach number
flows is the presence of the time-dependent base state, whose evolution is
coupled to the evolution of the full solution. We also describe how to
incorporate the expansion of the base state for full-star flows, which involves
a novel mapping technique between the one-dimensional base state and the
Cartesian grid, as well as a number of overall improvements to the algorithm.
We examine the efficiency and accuracy of our adaptive code, and demonstrate
that it is suitable for further study of our initial scientific application,
the convective phase of Type Ia supernovae.Comment: Accepted to Astrophysical Journal Suppliment (http://iop.org). 56
pages, 15 figures
