Kosianov D. An implicit high-order method with splitting for numerical integration of the fluid dynamics equations on unstructured grids

The object of the research are the fluid flow processes in the elements of power plants and aircrafts with complex shape. The purpose of research is the development of an implicit high-order finite volume method with splitting for the numerical integration of fluid flow equations on unstructured grids. The methods of mathematical modeling, theoretical and computational fluid dynamics, the elements of the difference schemes theory, a computational experiment were used. The results are the basis for the development of high-order methods and applied software for the numerical simulation and study of three-dimensional unsteady fluid and gas flows in the regions with complex shape. The novelty consists in the development approaches for identifying and minimizing the piecewise-polynomial reconstruction coefficients and in the development of an implicit high-order finite-volume scheme with splitting for unstructured grids and its generalization to the solution of the Euler equations for modeling the non-viscous compressible gas and incompressible fluid flows. Results are used at the Public Corporation "TURBOATOM" and in the educational process at the Department of Physics and Energy of V.N. Karazin Kharkiv National University. The scope of use of the results is Power Engineering.