Title
Proračun podzemnog toka metodom konačnih zapremina
Creator
Dotlić, Milan D. 1984-
Copyright date
2015
Object Links
Select license
Autorstvo 3.0 Srbija (CC BY 3.0)
License description
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Language
Serbian
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 09.06.2015.
Other responsibilities
mentor
Jovanović, Boško. 1946-
član komisije
Vidović, Dragan.
član komisije
Jovanović, Boško, 1946-
član komisije
Radunović, Desanka, 1950-
Academic Expertise
Prirodno-matematičke nauke
Academic Title
-
University
Univerzitet u Beogradu
Faculty
Matematički fakultet
Alternative title
Computation of subsurface flow using finite volume method.
Publisher
[M. Dotlić]
Format
XI, 124 lista
description
numerička matematika-numeričke metode rešavanja parcijalnih diferencijalnih
jednačina / numerical mathematics-numerical methods for solving partial differential equations
Abstract (sr)
U disertaciji su razmatrane numerićke metode za rešavanje problema podzemnog
strujanja, transporta mase i energije u anizotropnoj i deo po deo neprekidnoj sredini.
Ovakvi problemi sreću se u hidrologiji, naftnoj industriji, ekologiji i drugim
oblastima.
Podzemno strujanje u zasićenoj sredini opisano je linearnom parcijalnom diferencijalnom
jednačinom, dok je u nezasićenoj sredini opisano Ričardsovom nelinearnom
parcijalnom diferencijalnom jednačinom. Transport mase i energije opisan je
advektivno-difuznim jednačinama...
Abstract (en)
The thesis considers numerical methods for the computation of subsurface flow and
transport of mass and energy in an anisotropic piecewise continuous medium. This
kind of problems arises in hidrology, petroleum engineering, ecology and other fields.
Subsurface flow in a saturated medium is described by a linear partial differential
equation, while in an unsaturated medium it is described by the Richards nonlinear
partial differential equation. Transport of mass and energy is described by advectiondiffusion
equations.
The thesis considers several finite volume methods for the discretization of diffusive
and advective terms. An interpolation method for discretization of diffusion
through discontinuous media is presented. This method is applicable to several
nonlinear finite volume schemes.
The presence of a well in the reservoir determines the subsurface flow to a large
extent. Standard numerical methods produce a completely wrong flux and an inaccurate
hydraulic head distribution in the well viscinity. Two methods for the well
flux correction are introduced in this thesis. One of these methods gives second-order
accuracy for the hydraulic head and first-order accuracy for the flux.
Explicit and implicit time discretizations are presented. Preservation of the
maximum and minimum principles in all considered schemes is analyzed.
All considered schemes are tested using numerical examples that confirm teoretical
results.
Authors Key words
metoda konačnih zapremina, parcijalne diferencijalne jednačine,
Ričardsova jednačina, transport mase, transport energije, princip minimuma i maksimuma,
nestrukturna mreža
Authors Key words
finite volume methods, partial differential equations, Richards equation,
mass transport, energy transport, maximum and minimum principle, unstructured
mesh.
Classification
519.63:556.3(043.3)
Type
Tekst
Abstract (sr)
U disertaciji su razmatrane numerićke metode za rešavanje problema podzemnog
strujanja, transporta mase i energije u anizotropnoj i deo po deo neprekidnoj sredini.
Ovakvi problemi sreću se u hidrologiji, naftnoj industriji, ekologiji i drugim
oblastima.
Podzemno strujanje u zasićenoj sredini opisano je linearnom parcijalnom diferencijalnom
jednačinom, dok je u nezasićenoj sredini opisano Ričardsovom nelinearnom
parcijalnom diferencijalnom jednačinom. Transport mase i energije opisan je
advektivno-difuznim jednačinama...
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