All areas of astronomy and astrophysics rely on computation to look at, manipulate, and understand data. The field of Computational Astrophysics is distinct in that its goal is to address problems in astronomy and astrophysics where observational data is inaccessible to instruments. This can happen, for example, when the physical processes of interest occur deep inside the observed object, or when the object is too far away. Computational astrophysics also allows us to address questions where extreme heat and density, or extreme length and time scales are involved, so that complete observations of the phenomenon are unavailable and laboratory experiments on earth are limited.

Researchers working in the field of computational astrophysics formulate a theoretical model of the physical process. Theoretical models are typically mathematically complex, so that testing the model, or using the model to make predictions requires solving nonlinear partial differential equations using massively parallel simulations.

Many astrophysical phenomena can be approximated using a fluid approach. In this case hydrodynamic or magnetohydrodynamic (MHD) equations consisting of conservation laws for mass, momentum, and energy, along with the evolution of the magnetic field, are solved. These equations may be solved on a fixed Eulerian grid using pseudospectral methods, finite-element methods (FEM), or finite-volume methods. They may also be solved using Lagrangian methods which do not use a grid, or where the grid moves; For example these codes may be called arbitrary Lagrangian-Eulerian (ALE) codes, or smoothed particle hydrodynamics (SPH) codes.

Other astrophysical phenomena require an approach that includes specifics of the particle dynamics or gas dynamics. These approaches involve solution of a kinetic equation for the distribution of particles in position, velocity, and time. Variations on this type of equations are called the Boltzmann equation, the Vlasov-Poisson equations, or the Vlasov-Maxwell equations. Computational astrophysicists tend to use numerical methods such as Monte Carlo or particle-in-cell (PIC) methods to solve these types of equations.

Because of the complexity of equations for astrophysical modeling, the use of a computer designed for parallel computation is needed. Typical simulations use thousands of compute nodes, with each node multi-threaded, and are performed at national and international super-computing facilities. Both message passing interface (MPI) and programs for multi-threading (OpenMP) are used, while more efficient programming solutions are constantly being developed. Researchers in the field of Computational Astrophysics are deeply invested in extending existing numerical techniques and developing innovative, new approaches to capture ever more complex physics in computer simulations.

In the field of Computational Astrophysics, the majority of the data we examine is simulation data, produced from theoretical models based on the laws of physics. It is important that this data be carefully processed so that comparison with observational data -- which is usually much more limited -- can be made. This comparison allows us to make predictions for the future, and to improve theoretical models. Theoretical models provide a framework for understanding the broader meaning of observational data.