Development and Astrophysical Applications of a Parallel Smoothed Particle Hydrodynamics Code with Mpi 1.1 Basic Principles

Smoothed Particle Hydrodynamics (SPH) is a particle method to simulate compressible uids. First we present a brief introduction to SPH, where we focus on an approach to treat the physical viscosity. Then we describe in detail the basic principles of our parallel implementation of the SPH method. The eeciency of the code on Cray T3E and IBM SP2 is discussed. In the last part we present a short introduction to accretion disks in interacting binary stars and report on some new results in that eld achieved with our code. Smoothed Particle Hydrodynamics (SPH) is a grid-free Lagrangian method for solving the hydrodynamic equations numerically. It was introduced in 1977 by Gingold & Monaghan 2] and by Lucy 3]. The method is especially suited for compressible ows involving free boundaries, a commonplace situation in astrophysics. In SPH the matter distribution is divided into small overlapping mass packets, so-called particles, which do not exchange matter. The particles move in space following the motion of the uid while interacting with their neighbor particles. The system of hydrodynamic equations, i. e., the Navier-Stokes equation, the equation of continuity, and the energy equation together with an equation of state, form a system of coupled partial diierential equations. Applying the SPH formalism, these are transformed into a set of ordinary diierential equations (ODEs) in two steps. These ODEs are subsequently integrated numerically using standard methods. First the eld quantities f(r) are smoothed, i. e., they are replaced by the convolution