Simulations of planet-disc interactions using Smoothed Particle Hydrodynamics

¹ Computational Physics, Auf der Morgenstelle 10C, 72076 Tübingen, Germany
² Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK
³ Wilhelm-Schickard-Institut für Informatik, Sand 13, 72076 Tübingen, Germany

Corresponding author: C. Schäfer, schaefer@tat.physik.uni-tuebingen.de

Received: 2 July 2003
Accepted: 5 January 2004

Abstract

We have performed Smoothed Particle Hydrodynamics (SPH) simulations to study the time evolution of one and two protoplanets embedded in a protoplanetary accretion disc. We investigate accretion and migration rates of a single protoplanet depending on several parameters of the protoplanetary disc, mainly viscosity and scale height. Additionally, we consider the influence of a second protoplanet in a long time simulation and examine the migration of the two planets in the disc, especially the growth of eccentricity and chaotic behaviour. One aim of this work is to establish the feasibility of SPH for such calculations considering that usually only grid-based methods are adopted. To resolve shocks and to prevent particle penetration, we introduce a new approach for an artificial viscosity, which consists of an additional artificial bulk viscosity term in the SPH-representation of the Navier-Stokes equation. This allows accurate treatment of the physical kinematic viscosity to describe the shear, without the use of artificial shear viscosity.