prikaz prve stranice dokumenta Mathematical models of flows in porous and mixed media
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doctoral thesis
Mathematical models of flows in porous and mixed media
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:872665
Novak, Andrej
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Novak, A. (2017). Mathematical models of flows in porous and mixed media (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:872665

Novak, Andrej. "Mathematical models of flows in porous and mixed media." Doctoral thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:872665

Novak, Andrej. "Mathematical models of flows in porous and mixed media." Doctoral thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:872665

Novak, A. (2017). 'Mathematical models of flows in porous and mixed media', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 28 March 2025, https://urn.nsk.hr/urn:nbn:hr:217:872665

Novak A. Mathematical models of flows in porous and mixed media [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2025 March 28] Available at: https://urn.nsk.hr/urn:nbn:hr:217:872665

A. Novak, "Mathematical models of flows in porous and mixed media", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:872665

Metadata
TitleMathematical models of flows in porous and mixed media
Title (croatian)Matematički modeli tokova u poroznim i miješanim sredinama
AuthorAndrej Novak
MentorDarko Mitrović (mentor)
MentorMladen Jurak (komentor)
Committee memberNenad Antonić (predsjednik povjerenstva)
Committee memberHenrik Kalisch (član povjerenstva)
strani drzavljanin: Nije dostupno
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-01-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
This thesis consists of two parts. In the first part, nontrivial generalizations of the transport-collapse scheme are presented. The initial value problem for heterogeneous scalar conservation laws is considered and as a consequence of the analysis of the scheme a new solution concept of the initial-boundary value problem for scalar conservation laws arose. This is the most important contribution of this part of the thesis. In the both situations under the consideration the rigorous proofs of... More the convergence of the numerical scheme are given. In the last two chapters two models of fluid flows in different environments are presented. The first one models slow flows of two immiscible fluids with the source term put in the context of water pollution. Using the second model, the analysis of the evolution of the interface between immiscible fluids of different densities in porous media, is performed. The fluids can be compressible (CO2 or natural gases) or incompressible (oil, water). It is proven that, if the heavier fluid is on top and there is no sink or source term, a tip of the interface will move in the direction of the gravity or the buoyancy. In both situations, the appropriate numerical simulations are given. Less
Abstract (croatian)
Ovaj rad se sastoji od dva dijela. U prvom dijelu predstavljamo netrivijalnu generalizaciju sheme brzinskog usrednjenja. Promatramo početni problem za heterogeni zakon sačuvanja, a analiza spomenute sheme poslužit će nam kao motivacija za uvođenje novog koncepta rješenja za početno-rubnu zadaću za skalarne zakone sačuvanja. To je i jedan od najznačajnijih znanstvenih doprinosa ove radnje. U obje situacije sve tvrdnje su popraćene rigoroznim dokazima, a radi zornije ilustracije poglavlje... More završavamo s numeričkim simulacijama. U posljednja dva poglavlja razmatramo dva modela za dinamiku fluida. Prvi opisuje spori protok dva skoro nepomiješiva fluida s izvorom stavljen u kontekst onečišćenja vode. Koristeći drugi model, analiziramo granicu između dva nepomješiva fluida različitih gustoća u poroznoj sredini. Fluidi mogu biti stlačivi (kao prirodni plinovi) ili nestlačivi (kao ulje ili voda). Dokazat ćemo da ako je teži fluid na vrhu i ako nema izvora ili ponora da se granica počinje kretati u smjeru gravitacije ili uzgona. U obje situacije dajemo i numeričke simulacije složenijih situacija. Less
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:217:872665
Study programmeTitle: Mathematics
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
Type of resourceText
Extentvi, 106 str.
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2019-03-20 10:44:38
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