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Delta shock waves and wave front tracking method

dc.contributor.advisorNedeljkov, Marko
dc.contributor.otherPilipović, Stevan
dc.contributor.otherNedeljkov, Marko
dc.contributor.otherKrejić, Nataša
dc.contributor.otherSimić, Srboljub
dc.creatorDedović, Nebojša
dc.date.accessioned2015-12-29T11:17:52Z
dc.date.available2015-12-29T11:17:52Z
dc.date.available2020-07-03T13:44:05Z
dc.date.issued2014-04-24
dc.identifier.urihttp://www.cris.uns.ac.rs/DownloadFileServlet/DisertacijaDisertacija%20-%20Dedovic%20Nebojsa.pdf?controlNumber=(BISIS)84813&fileName=Disertacija%20-%20Dedovic%20Nebojsa.pdf&id=1029&source=NaRDuS&language=srsr
dc.identifier.urihttps://nardus.mpn.gov.rs/handle/123456789/1748
dc.identifier.urihttp://www.cris.uns.ac.rs/record.jsf?recordId=84813&source=NaRDuS&language=srsr
dc.identifier.urihttp://www.cris.uns.ac.rs/DownloadFileServlet/IzvestajKomisijeObrazac_6_NDedovic.pdf?controlNumber=(BISIS)84813&fileName=Obrazac_6_NDedovic.pdf&id=1030&source=NaRDuS&language=srsr
dc.description.abstractU doktorskoj disertaciji posmatrani su Rimanovi problemi kod strogo i slabo hiperboličnih nelinearnih sistema PDJ. U uvodu je predstavljena jednačina zakona održanja u jednoj prostornoj dimenziji i definisani su Košijevi i Rimanovi problemi. U drugoj glavi, date su osnovne osobine nelinearnih hiperboličnih zakona održanja, uvedeni supojmovi stroge hiperboličnosti i slabog rešenja zakona održanja. Definisani su Rankin-Igono i entropijski uslovi kao i opšte rešenje Rimanovog problema (za dovoljno male početne uslove). U trećoj glavi detaljno je objašnjena Glimova diferencna  šema. Metod praćenja talasa predstavljen je u četvrtoj glavi. Pokazano je da se ovom metodom, za dovoljno male početne uslove, dobija stabilno i jedinstveno rešenje koje u svakom vremenu ima ograničenu totalnu varijaciju. U petoj glavi, posmatrana je jednačina protoka izentropnog gasa u Lagranžovim koordinatama. Uz pretpostavku da je početni uslov ograničen i da ima ograničenu totalnu varijaciju, pokazano je da Košijev problem ima jedinstveno slabo rešenje ako je totalna varijacija početnog uslova pomnožena sa  0<ε<< 1 dovoljno mala. Slabo rešenjedobijeno je metodom praćenja talasa. U glavi šest ispitana je interakcija dva delta talasa koji su posmatrani kao specijalna vrsta shadowtalasa. U glavi sedam, pokazano je da za proizvoljno velike početne uslove, rešenje Rimanovog problema jednodimenzionalnog Ojlerovog zakona održanja gasne dinamikepostoji, daje jedinstveno i entropijski dopustivo, uz drugačiju ocenu snaga elementarnih talasa. Data je numerička verifikacija interakcije dva delta talasa korišćenjem metode praćenja talasa.sr
dc.description.abstractIn this doctoral thesis, Riemann problems for strictly and weakly nonlinear hyperbolic PDE systems were observed. In the introduction, conservation laws in one spatial dimension were presented and the Cauchy and Riemann problems were defined. In the second chapter, the basic properties of nonlinear hyperbolic conservation laws were intorduced, as well as the terms such as strictly hyperbolic system and weak solution of conservation law. Also, Rankine -Hugoniot and entropy conditions were introduced and the general solution to the Riemann problem (for sufficiently small initial conditions) were defined. Glimm’s difference scheme was explained in the third chapter. The wave front tracking method was introduced in the fourth chapter. It was shown that, using this method, for sufficiently small initial conditions, it could be obtained a unique solution with bounded total variation for t ≥0. In the fifth chapter, the Euler equations for isentropic fluid inLagrangian coordinates were observed. Under the assumption that the initial condition was bounded and had bounded total variation, it was shown that the Cauchy problem had a weak unique solution, provided that the total variation of initial condition multiplied by 0<ε<<1 was sufficiently  small. Weak solution was obtained by applying the wave front tracking method. In the sixth chapter, the interaction of two delta shock waves were examined. Delta shock waves were regarded as special kind of shadowwaves. In the chapter seven, it was shown that for arbitrarily large initial conditions, solution to the Riemann problem of one-dimensional Euler conservation laws of gas dynamics existed, it was unique and admissible. New bounds on the strength of elementary waves in the wave front tracking algorithm were given. The numerical verification of two delta shock waves interaction via wave front tracking method was given at the end of the thesis.en
dc.languagesr (latin script)
dc.publisherУниверзитет у Новом Саду, Природно-математички факултетsr
dc.relationinfo:eu-repo/grantAgreement/MESTD/Technological Development (TD or TR)/31046/RS//
dc.rightsopenAccessen
dc.rights.urihttps://creativecommons.org/share-your-work/public-domain/cc0/
dc.sourceУниверзитет у Новом Садуsr
dc.subjectzakoni održanjasr
dc.subjectconservation lawsen
dc.subjectRimanov problemsr
dc.subjectdelta udarni talasisr
dc.subjectmetod praćenja talasasr
dc.subjectinterakcijesr
dc.subjecttežinski talasisr
dc.subjectRiemann problemen
dc.subjectdelta shock wavesen
dc.subjectwave front trackingen
dc.subjectinteractionsen
dc.subjectweighted shadow wavesen
dc.titleDelta udarni talasi i metod praćenja talasasr
dc.titleDelta shock waves and wave front tracking methoden
dc.typedoctoralThesisen
dc.rights.licenseCC0
dcterms.abstractНедељков Марко; Симић Србољуб; Пилиповић Стеван; Крејић Наташа; Недељков Марко; Дедовић Небојша; Делта ударни таласи и метод праћења таласа; Делта ударни таласи и метод праћења таласа;
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/38375/Disertacija.pdf
dc.identifier.fulltexthttp://nardus.mpn.gov.rs/bitstream/id/38376/IzvestajKomisije.pdf
dc.identifier.fulltexthttps://nardus.mpn.gov.rs/bitstream/id/38375/Disertacija.pdf
dc.identifier.fulltexthttps://nardus.mpn.gov.rs/bitstream/id/38376/IzvestajKomisije.pdf
dc.identifier.rcubhttps://hdl.handle.net/21.15107/rcub_nardus_1748


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