Proračun podzemnog toka metodom konačnih zapremina
Computation of subsurface flow using finite volume method
Doktorand
Dotlić, Milan D.Mentor
Jovanović, BoškoČlanovi komisije
Vidović, DraganJovanović, Boško
Radunović, Desanka
Metapodaci
Prikaz svih podataka o disertacijiSažetak
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...
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.
Fakultet:
Универзитет у Београду, Математички факултетDatum odbrane:
09-06-2015Projekti:
- Metodologija ocene, projektovanja i održavanja izvorišta podzemnih voda u aluvijalnim sredinama u zavisnosti od stepena aerobnosti (RS-MESTD-Technological Development (TD or TR)-37014)