Shema usrednjenja prijenosa za zakone sačuvanja

master's thesis

• Author: Ana Budiša
• Mentor: Boris Muha (mentor)
• Committee member: Boris Muha (predsjednik povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-07-18, 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: zakoni sačuvanja; Buckley-Leverettove jednadžbe; Burgersova jednadžba
• Keywords (english): scalar conservation laws; Buckley-Leverett equations; Burgers’ equation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:187592
• 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: 2017-06-09 11:40:24