The derivation of the Smoothed Particle Hydrodynamics (SPH) method is reviewed. Some comments about the proper determination of the density are made. In particular, the problem of second-order derivative terms is investigated. This scheme is applied to construct a physical viscosity, based on the representation of the viscous force as a divergence of a symmetric tensor. Requiring the conservation of both linear and angular momentum even in the particle formulation, the SPH structure of the viscous stress tensor is determined. Concerning the energy balance, the particle and continuum representations are compared. The code was tested on an analytically solvable problem, namely the spreading of a ring of gas moving with Keplerian speed around a point mass. The results of the particle simulation are in very good agreement with the theory. With the help of our SPH code the formation of an accretion disk in a close binary system up to the stationary state is investigated. Characteristics of its structure are discussed.
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Flebbe et al. (1994) studied this question.