In the dissertation work, the actual scientific and applied problem of increasing the
efficiency of mathematical and computer modeling in forecasting systems and providing real-time control of fast-flowing processes is solved. Increasing the efficiency of modeling is achieved through the methodology of constructing models based on singular integrals, which take into account only the main dominant factors of phenomena and processes, through the use of improved discretized models, new methods, computational algorithms and computational technologies suitable for use in predictive systems and in decision support systems in real time. The use of the method of singular integral equations for constructing models of dynamic processes, constructing discretized models of mass transfer, based on Lagrangian principles of observation and adapted for use with computational algorithms, makes it possible to create effective computational technologies intended for use in computer systems for forecasting and controlling fast-flowing processes in real time. A laboratory stand and a methodology for laboratory studies of unsteady circulation flows in a plane curved channel with obstacles in the range of Reynolds numbers have been developed 0 Re 1.5 104 . Laboratory verification of models makes it possible to extend the applicability of the discrete singularity method to new classes of applied problems. A new method and algorithms for transforming a system of discrete singularities have been developed for the correct calculation of values of discretized integral representations with singular integrand functions. New computational technologies have been created, in which methods and algorithms for transforming a system of discrete features are applicable, a method and algorithms for calculating local and distributed dynamic characteristics and actions, at arbitrary points of the flow region, in which the deformation and motion of the boundaries of the region are taken into account, together with separation phenomena, as well as discretized models of mass transfer and advection based on Lagrangian observation principles. Computing technologies are intended for use in modeling computer systems of engineering and technological specialization (design, information and analytical systems for decision support and control of fast-flowing processes): – to carry out pre-design studies in high-rise construction, to determine aerodynamic effects on structures and structures, to identify manifestations of aerodynamic interference, to zonate territories according to the level of comfort; – to carry out pre-design studies in hydraulic engineering, to determine the hydrodynamic effects on hydraulic structures and structures in sea areas, to identify areas with increased intensity of hydrological processes; – for systems for predicting hazardous hydroecological consequences of possible accidents and disasters in sea water areas and water areas of straits, in order to ensure realtime control of emergency response and threat prevention means; – when conducting research to identify modes of effective functioning of new designs of rotors in wind / hydropower. A new mathematical model of a three-dimensional vortex structure has been developed, which has its own topological characteristics – nodes and links that affect its stability. The model is suitable for investigating meteorological phenomena such as tornado / tornado. Using the method of computer simulation, the emergence of the effect of the inversion of the jet, which flows from the confuser with a given shape of the hole, is revealed. The conditions for the occurrence of inversion in jets are determined. A catalog of jet inversion for confusers has been created, with a set of holes of arbitrary shape.
