Axisymmetric smoothed particle hydrodynamics with self-gravity

TL;DR

This paper introduces an axisymmetric SPH formulation with improved handling of singularities, artificial viscosity, heat conduction, and self-gravity, validated through astrophysical, gas dynamics, and fusion scenarios.

Contribution

It presents a novel axisymmetric SPH method with enhanced numerical techniques and a gridless self-gravity implementation, expanding SPH applicability.

Findings

Validated with astrophysical collapse and pulsation scenarios

Accurate handling of particles near the symmetry axis

Effective incorporation of self-gravity without grid reliance

Abstract

The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation of a sun-like star), gas dynamics (wall heating problem, collision of two streams of gas) and inertial confinement fusion (ICF, -ablative implosion of a small capsule-). New material concerning the standard SPH formalism is given. That includes the numerical handling of those mass points which move close to the singularity axis, more accurate expressions for the artificial viscosity and the heat conduction term and an easy way to incorporate self-gravity in the simulations. The algorithm developed to compute gravity does not rely in any sort of grid, leading to a numerical scheme totally compatible with the lagrangian nature of the SPH equations.