Primjeri egzaktnih rješenja Navier-Stokesovih jednadžbi

master's thesis

• Author: Lana Reščec
• Mentor: Eduard Marušić-Paloka (mentor)
• Committee member: Eduard Marušić-Paloka (predsjednik povjerenstva)
• Committee member: Zlatko Drmač (član povjerenstva)
• Committee member: Miljenko Marušić (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-11-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad daje pregled nekih egzaktnih rješenja Navier-Stokesovih jednadžbi, dakle jednažbi koje opisuju kretanje viskoznog fluida. Promatrani su isključivo stacionarni tokovi omeđeni ravninskim granicama, koje bilo miruju ili se gibaju. Tokovi su podijeljeni u pet kategorija prema tipu (Couette-Poiseuilleovi tokovi, Beltramijevi tokovi, tokovi s točkom stagnacije, tokovi u kanalu i trodimenzionalne verzije tokova)i u svakoj je dan jedan ili više primjera. Primjeri su birani tako da daju neki uvid u dinamiku fluida. Iako egzaktna rješenja više nisu fokus istraživanja matematičara koji se bave ovim područjem, čine bitan segment razvoja teorije mehanike fluida.

Abstract (english)

This paper gives an overview of some of the exact solutions to Navier-Stokes equations, i.e. equations describing the movement of viscous fluid. Only stationary flows bounded by plane boundaries are observed, which could be fixed or moving. The flows are divided into five categories by type (Couette-Poiseuille flows, Beltrami flows, stagnation-point flows, channel flows and three-dimensional flows) and for each is given one or more examples. Examples are chosen to give some insight into fluid dynamics. Although exact solutions are no longer the focus of mathematicians involved in this area, they form an essential segment of the theory of fluid mechanics.

• Keywords: Navier-Stokesove jednadžbe; viskozni fluid; Couette-Poiseuilleovi tokovi; Beltramijevi tokovi; tokovi s točkom stagnacije; tokovi u kanalu; trodimenzionalne verzije tokova
• Keywords (english): Navier-Stokes equations; viscous fluid; Couette-Poiseuille flows; Beltrami flows; stagnation-point flows; channel flows; three-dimensional flows
• Language: croatian
• URN:NBN: urn:nbn:hr:217:654247
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-06-14 11:30:15