Министерство высшего и средного специального образования республики узбекистан

Область применения: Разработанный метод можно рекомендовать как надежный аппарат при численном решении проблемы гидродинамической устойчивости. Выводы по устойчивости могут быть использованы при анализе различных атмосферных потоков (запыленный воздух) и процессов добычи нефти и газа.
R e s u m e
Thesis of Normurodov Chori Begalievich on the scientific degree competition of the doctor of Physics - Mathematical Sciences specialty 05.13.18 - theoretical basis of mathematical simulation “Spectral-grid method and its application of the hydrodynamic stability problems”
Key words: mathematical simulation, spectral-grid method, convergence, high accuracy, efficiency, distorting and surface neutral stability, condition of orthogonolity.
Subjects of the inquiry: mathematical models of one and two - phased flows, spectral-grid method for solution of the hydrodynamic stability problems.
Aim of the inquiry: theoretical and experimental (numerical calculation) ground of spectral-grid method and research by this method, the problems of hydrodynamic stability of one and two - phased Poiseuille flows and boundary layer.
Methods of inquiry: There used methods of calculus mathematics, theory of hydrodynamic stability, functional analysis in the work.
The results achieved and their novelty: there was suggested new numerical method - spectral-grid method for problem solution of eigenvalue for differential equation m - order. Proved convergence method and convergence of approximate eigenvalue to exact reception of estimation of velocity convergence. Spectral-grid method was applied to the solution problem of stability of one - phased Poiseuille flow and boundary layer. Researched hydrodynamic stability problems of two - phased flows. There shown high accuracy and efficiency of spectral-grid method. For two - phased flows built space dependence typical parameters.
Practical value: Proved theorem is remarkable grows and generalized spectral - grid method to new class of tasks of multi - phased hydromechanics and allow to give theoretical ground of convergence of approximate method and set its velocity.