Brazaluk I. Mathematical models of hydrodynamical interaction of bodies in the flow.

An object is the hydrodynamic fields and forces which arise up at potential or vortical flows of ideal fluids in the complex shape domains. An aim is development of mathematical and numeral models of hydrodynamic problems on the basis of computational potential theory and application of them to the calculation of hydrodynamic interaction. Methods are a numeral calculation of the hydrodynamic fields on the basis of application of computational potential theory. Theoretical results - three new high-efficiency algorithms of boundary element method are proposed; the new approach is created for determination of interaction of fluid flow with small-scale objects; a new concept of dipole-vortex sheet is introduced; an existence of new type of stability of discrete vortex structures "in sense of cloud" is found out; a new phenomenon of instability of the element system in the superfluidic flow with respect to transversal perturbations is found out. A practical value is creation of new program complexes for the calculation of hydrodynamic interactions which can be useful for organizations of technological and environment protection direction, at the calculations of hydrodynamic processes with kinematics or geometrical singularities. An application field is an educational process, design of space-rocket technique, ore mining and processing production.