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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.
The FLASH code, currently in its 4th version, is a publicly available high performance application code which has evolved into a modular, extensible software system from a collection of unconnected legacy codes. FLASH consists of inter-operable modules that can be combined to generate different applications. The FLASH architecture allows arbitrarily many alternative implementations of its components to co-exist and interchange with each other. A simple and elegant mechanism exists for customization of code functionality without the need to modify the core implementation of the source. A built-in unit test framework combined with regression tests that run nightly on multiple platforms verify the code.
CASTRO is a multi-dimensional Eulerian AMR radiation-hydrodynamics code that includes stellar equations of state, nuclear reaction networks, and self-gravity. Initial target applications for CASTRO include Type Ia and Type II supernovae. CASTRO supports calculations in 1-d, 2-d and 3-d Cartesian coordinates, as well as 1-d spherical and 2-d cylindrical (r-z) coordinate systems. Time integration of the hydrodynamics equations is based on an unsplit version of the the piecewise parabolic method (PPM) with new limiters that avoid reducing the accuracy of the scheme at smooth extrema. CASTRO can follow an arbitrary number of isotopes or elements. The atomic weights and amounts of these elements are used to calculate the mean molecular weight of the gas required by the equation of state. CASTRO supports several different approaches to solving for self-gravity. The most general is a full Poisson solve for the gravitational potential. CASTRO also supports a monopole approximation for gravity, and a constant gravity option is also available. The CASTRO software is written in C++ and Fortran, and is based on the BoxLib software framework developed by CCSE.
pyro is a simple python-based tutorial on computational methods for hydrodynamics. It includes 2-d solvers for advection, compressible, incompressible, and low Mach number hydrodynamics, diffusion, and multigrid. It is written with ease of understanding in mind. An extensive set of notes that is part of the Open Astrophysics Bookshelf project provides details of the algorithms.