The hierarchical SPH-method for mathematical simulation in gravitational gas dynamics

This work has been directed to a creation of new modern computer technologies and methods of programming for the rise of efficacy of solving of fundamental scientific and applied problems in gravitational gas dynamics connected with great volume of the calculations. The main attention has been given to theoretical questions and their practical application for the improvement of Smoothed Particles Hydrodynamics (SPH) method and algorithm of solving of complicated integro-differential systems of equations. The various aspects of method are considered. The degree of efficacy has been analyzed for determination of an optimal way of problem solving. The careful verification of theoretical method, calculating algorithm and computer program complex for detailed analysis of properties (exactitude of calculation and performance of computing process) is carried out. The executed theoretical investigations are used for creation of computer program complex of new generation for solving of space gas dynamics problems. The cycle of computer calculations of problems (in wide range of determinating parameters and starting data) of self-gravitational sphere collapse and protoplanet gas cloud evolution is executed and the analysis of received results is carried out.