Simulations of planet-disc interactions using Smoothed Particle Hydrodynamics

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 proto- planet 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, es- pecially 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 penetra- tion, 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.