Chernij D. Numerical modeling of flows of ideal incompressible fluid in domains with polytypic impenetrable moving boundaries

In the thesis, a non-linear mathematical model is generalized, which permits to consider creation of new elements of non-stationary flow of ideal incompressible fluid in a deformable domain with polytypical impenetrable moving boundaries. For numerical solution of a system of integro-differential equations describing fluid flows in domains with free boundaries of media, the method of discrete singularities (MDS) is generalized and updated. A formula is obtained for determination of flow characteristics depending on velocity of creation of new elements. A local vortex "discretion radius" value is determined for the case of arbitrary partition of the boundary. Restrictions for the MDS application are defined, both on the flow domain geometry and on solution existence in the MDS representation. It allowed to reduce the error of determination of the flow characteristics within the domain, to continue the process of modelling to the moment of domain connectedness change. Vortex structure dynamics, effects o f jet spray flows creation, of the boundary interaction and deformation apparent in the processes of penetration through the free boundary and of the free boundary field are investigated. The phenomenon of reconstruction of wave structures after collapse of the cavity on the free boundary is studied.