Smoothed Particle Hydrodynamics

The major hydrodynamical problems in astrophysics, for example, galaxy formation and evolution, the collapse of interstellar clouds in star formation, and the evolution of disks, have been attacked numerically through two major approaches. The first is the grid-based method, which was introduced in Chapter 2 and will be elaborated upon in Chapter 6. In one space dimension, grids can be either Lagrangian or Eulerian in nature, but in two or three space dimensions, a fixed Eulerian grid is generally used, with the option of subdividing the grid as the calculation proceeds. However, particularly in two or three space dimensions, it has also been found productive to use a Lagrangian method that is more closely related to N -body methods, known as smoothed particle hydrodynamics (SPH). This chapter provides an introduction to that method. Section 4.1 considers the very basic equations, in their simplest form, that must be put together to perform hydrodynamical calculations in three space dimensions using the SPH technique. Section 4.2 shows the results of a simple test calculation. Section 4.3 then discusses improvements needed in various aspects of an SPH code to bring it up to research grade. The techniques have been expertly reviewed by Benz (1990), Monaghan (1992), and Price (2004). At the end of the chapter appears a summary of the advantages and disadvantages of SPH as compared with grid-based codes.