Numeričko modeliranje tokova koje karakteriše nagla lokalna promena dubine i protoka
Numerical modelling of discontinuous flows
Master/Magistarski rad (Objavljena verzija)
,
Dejana Đorđević
Metapodaci
Prikaz svih podataka o dokumentuApstrakt
Discontinuous flows are the flows in which large gradients arise in both the flow
depth and the discharge due to specific external and/or internal boundary conditions. With
reference to the discontinuity and through the discontinuity itself, the basic hypotheses, upon
which the Saint-Venant shallow water equations are based, are violated. The problems in
mathematical and numerical modelling of discontinuous flows arising from this violation, and
the specific structure of the appropriate numerical schemes used in solving such problems are
discussed in this Thesis.
Three approaches to mathematical modelling of discontinuous flows: shock-fitting,
through method and pseudoviscosity method, are presented first. They are followed by a
review of numerical methods used in numerical modelling of free-surface flows with
discontinuities: the Method of characteristics, the Godunov method, the Finite Difference
Methods based on the flux-splitting technique, and the Finite Element Method.... Close
attention is paid to the approach and the scheme that allows for weak solutions, i.e. to the
through method and the Finite Difference Method based on the explicit MacCormack scheme.
The proposed scheme is verified using:
1° the analytical solutions,
2° the author's measurement performed on a laboratory rig and
3° the available measurements of the other authors.
Since the quality of the computational results highly depends on:
1° the form under which the governing equations are written (conservation or non-
conservation form),
2° the conservative property of the numerical scheme used, and
3° the diffusive/dispersive character of the scheme,
great attention is paid to the analysis of the conservation property of the MacCormack
scheme and the problems regarding the quasi-physical effects of the scheme, such as spurious
oscillations in the vicinity of the discontinuity.
Finally, a case study is included to indicate the performance of the proposed model
in the engineering practice.
Ključne reči:
naglo promenljivi tokovi / discontinuous flows / direktan pristup / through method / "slabo" rešenje / weak solution / konzervativni oblik / conservation form / svojstvo konzervativnosti / conservation property / numerička disipacija / numerical dissipation / numerička disperzija / numerical dispersionIzvor:
Građevinski fakultet Univerziteta u Beogradu, 1998Finansiranje / projekti:
- Развој метода управљања у водопривреди, Министарство за науку и технологије републике Србије