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master's thesis
Shema usrednjenja prijenosa za zakone sačuvanja
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:187592
Budiša, Ana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Budiša, A. (2016). Shema usrednjenja prijenosa za zakone sačuvanja (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:187592

Budiša, Ana. "Shema usrednjenja prijenosa za zakone sačuvanja." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:187592

Budiša, Ana. "Shema usrednjenja prijenosa za zakone sačuvanja." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:187592

Budiša, A. (2016). 'Shema usrednjenja prijenosa za zakone sačuvanja', Master's thesis, University of Zagreb, Faculty of Science, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:187592

Budiša A. Shema usrednjenja prijenosa za zakone sačuvanja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:217:187592

A. Budiša, "Shema usrednjenja prijenosa za zakone sačuvanja", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:187592

Metadata
TitleShema usrednjenja prijenosa za zakone sačuvanja
AuthorAna Budiša
MentorBoris Muha (mentor)
Committee memberBoris Muha (predsjednik povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
Committee memberFilip Najman (član povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-07-18, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Zakoni sačuvanja opisuju brojne prirodne pojave, između ostalog tok u poroznoj sredini (Buckley-Leverettove jednadžbe). U ovom diplomskom radu opisat ćemo nedavno uvedenu numeričku metodu za zakone sačuvanja te dokazati konvergenciju metode prema entropijskom rješenju. Metoda povezuje suvremene s poznatim tehnikama iz tog područja, poput kinetičke formulacije i entropijskih uvjeta. Opisno govoreći, osnova metode je pretvaranje nelinearne jednadžbe skalarnog zakona sačuvanja u linearnu (kinetičku) jednadžbu. Usrednjavanjem rješenja linearne jednadžbe dobiva se dopustivo entropijsko rješenje inicijalnog problema. Na kraju dajemo numeričku implementaciju metode na poznatim problemima Burgersove i Buckley-Leverettove jednadžbe.
Abstract (english)
Scalar conservation laws are key in modelling different natural phenomena, for example two-phase flow in porous media (Buckley-Leverett equations). In this thesis a new numerical method for conservation laws is described and it is proven that the solution given by this method converges to the entropy solution. This method includes both modern and classic methods for solving conservation laws, such as entropy conditions in method of characteristics and kinetic formulation. Basic idea is to make a linear (kinetic) equation from a nonlinear homogeneous conservation law and then average out the solution to get the entropy admissible solution of the initial problem. We also provide numerical examples of implementing the described method on Burgers’ equation and Buckley-Leverett equation.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:187592
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 on2017-06-09 11:40:24