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master's thesis
Numeričko rješavanje Navier-Stokeosve jednadžbe 'operator splitting' metodom
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:745939
Galić, Marija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Galić, M. (2014). Numeričko rješavanje Navier-Stokeosve jednadžbe 'operator splitting' metodom (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:745939

Galić, Marija. "Numeričko rješavanje Navier-Stokeosve jednadžbe 'operator splitting' metodom." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:745939

Galić, Marija. "Numeričko rješavanje Navier-Stokeosve jednadžbe 'operator splitting' metodom." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:745939

Galić, M. (2014). 'Numeričko rješavanje Navier-Stokeosve jednadžbe 'operator splitting' metodom', Master's thesis, University of Zagreb, Faculty of Science, accessed 29 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:745939

Galić M. Numeričko rješavanje Navier-Stokeosve jednadžbe 'operator splitting' metodom [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 December 29] Available at: https://urn.nsk.hr/urn:nbn:hr:217:745939

M. Galić, "Numeričko rješavanje Navier-Stokeosve jednadžbe 'operator splitting' metodom", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:745939

Metadata
TitleNumeričko rješavanje Navier-Stokeosve jednadžbe 'operator splitting' metodom
AuthorMarija Galić
MentorJosip Tambača (mentor)
Committee memberJosip Tambača (predsjednik povjerenstva)
Committee memberEduard Marušić-Paloka (član povjerenstva)
Committee memberMladen Jurak (član povjerenstva)
Committee memberVedran Krčadinac (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-09-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu izveli smo Navier-Stokesove jednadžbe kojima smo opisali tok inkompresibilnog viskoznog Newtonovog fluida i naveli neke rezultate o egzistenciji rješenja tih jednadžbi. Njihovo rješavanje je netrivijalan zadatak jer se mora riješiti sustav nelinearnih parcijalnih diferencijalnih jednadžbi uvažavajući dodatni uvjet inkompresibilnosti. Primjenom jedne operator-splitting metode uspjeli smo razdvojiti nelinearnost i inkompresibilnost. Numerički eksperimenti su pokazali da se potproblem vezan uz nelinearnost može linearizirati bez većeg gubitka točnosti. Zatim smo implementirali tu metodu u FreeFEM-u koji je softver za numeričko rješavanje parcijalnih diferencijalnih jednadžbi baziran na metodi konačnih elemenata i primijenili je za rješavanje Navier-Stokesovih jednadžbi u različitim dvodimenzionalnim domenama.
Abstract (english)
In this diploma thesis we derived Navier-Stokes equations for incompressible Newtonian viscous fluid and provided some results on the existence of solutions to these equations. Solving Navier-Stokes equations is a nontrivial task because one has to solve a system of partial differential equations taking into account the additional incompressibility condition. Applying one operator-splitting method to time discretization, we managed to decouple the difficulties associated to the nonlinearity with those associated to the incompressibility condition. Numerical experiments have shown that subproblem related to nonlinearity can be linearized without significant loss of accuracy. Then we implemented this method in FreeFEM, the software specialized for solving PDEs based on finite element method and apllied it to solve Navier-Stokes equations in different two-dimensional domains.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:745939
Study programmeTitle: Applied Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-01-23 12:04:49