Review of development of the Smooth Particle Hydrodynamics (SPH) method

The paper gives an overview of developments of the SPH method. Especial attention is given to the main shortcomings of the original form of the method namely consistency, tensile instability and zero energy modes. An example of derivation of correction necessary to assure first order consistency is given. The origin of the tensile instability and few proposed solutions to this problem are described. Similar consideration is given with respect to the zero energy modes typical for the collocational SPH method.