Konformne preslikave in tok tekočin

delo diplomskega seminarja

Žan Šifrer (Author), Uroš Kuzman (Mentor)

Abstract

V svoji diplomski nalogi sem se ukvarjal z mehaniko tekočin. V prvem delu sem svojo analizo omejil na idealne tekočine, fluide, katerih tokovnice lahko ponazorimo z dvodimenzionalnimi vektorskimi polji brez izvorov in vrtincev. Dokazal sem, da lahko le-te povežemo s teorijo holomorfnih funkcij, ter nato s pomočjo Riemannovega upodobitvenega izreka tokove okoli zapletenih objektov reduciramo na nekatere elementarne primere. V zadnjem delu naloge sem nato dodatno predstavil tudi Blasiousov izrek in nekaj primerov ne-idealnih tokov, ki pa generirajo vzgon.

Keywords

matematika;holomorfizem;biholomorfizem;meromorfizem;harmonične funkcije;konformne preslikave;idealni tok tekočin;kompleksni potencial;tokovnice;ekvipotenciali;Joukowskijeva preslikava;Riemannov upodobitveni izrek;Blasiusov izrek;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[Ž. Šifrer]
UDC:	517.5
COBISS:	18440025
Views:	692
Downloads:	232
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Conformal mappings and fluid flows
Secondary abstract:	In my thesis I dealt with fluid mechanics. In first part of my analysis I focused on ideal fluids. These are fluids, whose streamlines can be represented with twodimenzional vector fields without sources and vortices. I proved that such vector fields can be connected to theory of holomorphic functions. Using Riemann mapping theorem, flows around complicated objects can be reduced to elementary examples. In last part I also additionally presented Blasius theorem and some non-ideal flow examples, which do produce lift.
Secondary keywords:	mathematics;holomophism;biholomorphism;meromorphism;harmonic functions;conformal maps;ideal fluid flow;complex potential;streamlines;equipotentials;Joukowsky map;Riemann mapping theorem;Blasius theorem;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	25 str.
ID:	10960824