Astrophysical Smooth Particle Hydrodynamics

TL;DR

This paper reviews the astrophysical applications of the smooth particle hydrodynamics (SPH) method, emphasizing its derivation, conservation properties, and extensions to relativistic regimes, providing a comprehensive guide for implementing SPH in various astrophysical contexts.

Contribution

It provides a modern, Lagrangian-based derivation of SPH equations, including relativistic extensions and correction terms, enhancing the theoretical foundation and practical implementation of SPH in astrophysics.

Findings

Derivation of a Newtonian SPH formulation with grad-h corrections.

Extension of SPH to special and general relativity.

Emphasis on conservation properties and practical implementation details.

Abstract

The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that are necessary for a practical implementation of the method in a working SPH code. 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. We derive a modern, Newtonian SPH formulation from the Lagrangian of an ideal fluid. It accounts for changes of the local resolution lengths which result in corrective, so-called "grad-h-terms". We extend this strategy to special relativity for which we derive the corresponding grad-h equation set. The variational approach is further applied to a general-relativistic fluid evolving in a fixed, curved background space-time. Particular care is taken to explicitely derive all relevant equations in a coherent way.