Astrophysical Smooth Particle Hydrodynamics

In this review the basic principles of smooth particle hydrodynamics (SPH) are outlined in a pedagogical fashion. To start, a basic set of SPH equations that is used in many codes throughout the astrophysics community is derived explicitly. Much of SPH’s success relies on its excellent conservation properties and therefore the numerical conservation of physical invariants receives much attention throughout this review. The self-consistent derivation of the SPH equations from the Lagrangian of an ideal fluid is the common theme of the remainder of the text. Such a variational approach is applied to derive a modern SPH version of Newtonian hydrodynamics. It accounts for gradients in the local resolution lengths which result in corrective, socalled ”grad-h-terms”. This strategy naturally carries over to the special-relativistic case for which we derive the corresponding grad-h set of equations. This approach is further generalized to the case of a fluid that evolves on a curved, but fixed background space-time.