Abstract: This paper describes a new and pure Lagrangian method——called "Smoothed Particle Hy drodynamics" (SPH) method. The method is to actually evaluate spatial gradients without the use of any grid. Thus it does not suffer form the severe problems always associated with mesh tangling and distortion. Therefore it can be applied to multidimensional hydrodynamics which could effectively model three-dimensional systems which lack symmetry and possess large voids. At first, the paper gives an introduction to theoretical basis to SPH. Emphasis is given to a proper derivation of the SPH equations from the hydrodynamical conservation equations. Discussion covers some relative problems such as artifical viscosity, thermal conduction, self-gravity and sink and magnetic fields, choosing the smoothing kernels, and implementation of SPH code, etc.

Key words: SPH, Smoothing Kernel, Integral Interpolant