Development of smoothed particle hydrodynamics method and its application in the hydrodynamics of condensed matter

An improved smoothed particle hydrodynamics (SPH) method is described; in this method, the solution to the Riemann problem in strength media is described. Generalization of this approach to solving heat conduction problems is performed. The improved SPH method is used to solve a wide range of problems. Problems of heat conduction and volume energy release accompanied by spallation effects, simulation of high speed perforation, and propagation of failure waves in brittle materials are considered. Shock wave compression of porous materials and diffraction of detonation waves in heterogeneous explosives are simulated on the mesostructure scale.