Numerical methods for viscous fluid flows in sectors, cones, and domains with corners

Abstract

This thesis deals with three fluid dynamics problems: the problems of the viscous fluid flows in infinite sectors, cones, and finite 2D domains with corners. The focus of the research was on the flow regimes near the corner, far from the corner (in case of sectors and cones), and in the transition zones. Efficient computational methods were developed for these problems. Examples of flows were computed and respective fluid dynamics phenomena were studied. Particularly, the flows in cones with large opening angles were consistently described for the first time. High accuracy of computational methods was confirmed on the basis of numerical experiments. Particularly, for the flows in domains with corners, the comparison of the present results with the literature shows that the developed method computes the main flow with a comparable accuracy and the flow near the corners with higher accuracy than the best of existing methods.