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

摘要

Numerical techniques are described for three-dimensional fluid systems in the absence of self-gravity using the Lagrangian method of smoothed 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 into manageable layers. Further savings in both memory and computational time are achieved by using interparticle distances that are discretized with respect to small integral increments of the smoothing length. We also present a time integration algorithm using multiple time steps which guarantees that all particles are always synchronous in phase space to a least first-order accuracy with respect to the individual time 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 (γ = 1.01), and excluding radiation effects and magnetic fields. The results agree qualitatively with the Shukura-Sunyaev α-disk model but overestimate the radial temperature profile by a factor of ～ 10, indicating that radiation effects must be included for a complete model.