| Title |
Numerical Simulation of Convection-dominated Flow Using SU/PG Scheme |
| Authors |
송창근(Song, Chang Geun) ; 서일원(Seo, Il Won) |
| DOI |
https://doi.org/10.12652/Ksce.2012.32.3B.175 |
| Keywords |
사류;천이류;천수방정식;사각도수 Galerkin;SU/PG;supercritical flow;transcritical flow;shallow water equations;oblique hydraulic jump |
| Abstract |
In this study, Galerkin scheme and SU/PG scheme of Petrov-Galerkin family were applied to the shallow water equations and a finite element model for shallow water flow was developed. Numerical simulations were conducted in several flumes with convection-dominated flow condition. Flow simulation of channel with slender structure in the water course revealed that Galerkin and SU/PG schemes showed similar results under very low Fr number and Re number condition. However, when the Fr number increased up to 1.58, Galerkin scheme did not converge while SU/PG scheme produced stable solutions after 5 iterations by Newton-Raphson method. For the transcritical flow simulation in diverging channel, the present model predicted the hydraulic jump accurately in terms of the jump location, the depth slope, and the flow depth after jump, and the numerical results showed good agreements with the hydraulic experiments carried out by Khalifa(1980). In the oblique hydraulic jump simulation, in which convection-dominated supercritical flow (Fr=2.74) evolves, Galerkin scheme blew up just after the first iteration of the initial time step. However, SU/PG scheme captured the boundary of oblique hydraulic jump accurately without numerical oscillation. The maximum errors quantified with exact solutions were less than 0.2% in water depth and velocity calculations, and thereby SU/PG scheme predicted the oblique hydraulic jump phenomena more accurately compared with the previous studies (Levin et al., 2006; Ricchiuto et al., 2007). |