Martsafei A. Numerical modeling of hydrodynamic processes using multiprocessor systems

Thesis is focused on the development of new effective numerical modeling methods on multiprocessor systems of various kinds of processes of transport of physical of substances and of processes of dynamics of a viscous incompressible fluids, which are described the Navier-Stokes equations. In work proposed new computational methods. It offered new computational approaches based upon the idea of double-step symmetrized algorithm and the principles of efficient numerical algorithms suitable for use on multiprocessor complexes. These approaches are proved and implemented for solving problems convection-diffusion and systems Navier-Stokes equations. Constructed and proved generalized double-step symmetrized algorithm for iterative modeling of stationary of transfer processes. It was developed and investigated splitting algorithm for systems of equations of convection-diffusion based on the double-step symmetrized algorithm. It was proved that splitting double-step symmetrized algorithm are stability, dissipative and dispersive. It was constructed double-step symmetrized algorithms for solving systems of Navier-Stokes equations written in divergent form. It was proved that constructed double-step symmetrized algorithms are conservative, dissipative and dispersive. It was developed and proved a new scheme of implementing for Navier-Stokes equations on multiprocessor systems. Have been analyzed its effectiveness.