NUMERICAL TECHNIQUES FOR 3-DIMENSIONAL SMOOTHED PARTICLE HYDRODYNAMICS SIMULATIONS - APPLICATIONS TO ACCRETION DISKS

Numerical techniques are described for three-dimensional fluid systems in the absence of self-gravity using the Lagrangian method of smoothe d particle hydrodynamics (SPH). In particular, we present an efficient method for locating nearest neighbors that uses an ancillary Eulerian grid and conserves memory by partitioning the computational space int o manageable layers. Further savings in both memory and computational time are achieved by using interparticle distances that are discretize d with respect to small integral increments of the smoothing length. W e also present a time integration algorithm using multiple time steps which guarantees that all particles are always synchronous in phase sp ace to a least first-order accuracy with respect to the individual tim e steps. These techniques are used to simulate an accretion disk in a low mass ratio (M(2)/M(1) = 0.08) binary system with the ideal gas law , low adiabatic gamma (gamma = 1.01), and excluding radiation effects and magnetic fields. The results agree qualitatively with the Shukura- Sunyaev alpha-disk model but overestimate the radial temperature profi le by a factor of similar to 10, indicating that radiation effects mus t be included for a complete model.