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Astron. Astrophys. 325, 857-865 (1997)

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1. Introduction

Smooth particle hydrodynamics (SPH) has become an increasingly popular method in simulations of different astrophysical phenomena. Its Lagrangian formulation allows the study of large density differences. The particle formulation makes grids unnecessary and allows for easy implementation in three dimensions. A recent review of the method can be found in Monaghan (1992), and a technical description in for example Hernquist & Katz (1989).

Two forms of artificial viscosity are needed in SPH, the bulk and the von Neumann-Richtmeyer artificial viscosity respecticely. They prevents interparticle penetration, allow shocks to form and damp the post shock oscillations. They do, however, induce transfer of kinetic energy in fluid motions to thermal energy. Many simulations using SPH involve the compression of a gas, often in a gravitational collapse of an initially cool gas cloud. The velocities in these simulations can be highly supersonic, which implies that the unphysically large artificial viscosity may dominate the heating. This heating and deceleration of the gas prevent further collapse.

Martel et. al. (1995) have introduced a new formalism which they call Adaptive SPH. They use an ellipsoid kernel that adapts itself to the surrounding medium, and therefore avoid unnecessary use of artificial viscosity. The authors claim good results in cosmological collapse simulations.

In the present study a different approach is suggested. The von Neumann-Richtmeyer artificial viscosity is restricted to supersonic velocities. It is therefore used only to form shocks and to prevent interparticle penetration for supersonic particles. Its adverse effect at subsonic velocities is avoided. A region under compression is described by a limited number of particles. The relative velocities among neighbouring particles in a region under compression can be supersonic due to the limited resolution, but despite that the gas is not expected to form shocks. Therefore the von Neumann-Richtmeyer viscosity is restricted to regions that are not under compression. To avoid spurious heating in the subsonic regions, but prevent interparticle penetration and maintain the damping of post shock oscillations, the bulk artificial viscosity is modified. Instead of integrating the effect from the neighbouring particles individually, their collective effect at one point is considered.

The SPH method is briefly described, and the suggested changes in artificial viscosity are presented. These modifications of artificial viscosity have been tested in the simulation of a shock tube, the homologous compression of a gas sphere and the gravitational collapse of an initially cool gas sphere at rest. The results are compared with results from a standard formulation of artificial viscosity.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998