A comparative study of 1D and 2D approaches for simulating flows at right angled dividing junctions

• Published in: Applied mathematics and computation 2013-01, Vol.219 (10), p.5070-5082
• Main Authors: Ghostine, R., Vazquez, J., Terfous, A., Rivière, N., Ghenaim, A., Mosé, R.
• Format: Article
• Language: English
• Subjects: Engineering Sciences; Open channel junctions; Other; RKDG method; Saint-Venant equations; Subcritical flow; Supercritical flow; Transcritical flow
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2012.11.048

This paper widens insight on the comparison between 1D and 2D approaches when simulating flow division at a 90° open-channel junction. For the 1D simulation, existing models regarding this issue are, on the one hand, of empirical nature and depend on the flow regime, thus not practical in the unsteady case. On the other hand, theoretical dividing models are strongly nonlinear, thus do not guarantee compatibility if combined with the shallow water model. By explicitly inducting the mathematical model of the side weir into the source terms of the conservative form of the 1D shallow water equations, the flow bifurcation is represented by considering a crest-free lateral spillway. For the 2D simulation, the whole system (branches and junction) is considered as one system and discretized into triangular cells forming an unstructured mesh. The numerical approximation of the two approaches is performed by a second order Runge–Kutta Discontinuous Galerkin (RKDG) scheme and tested through a pre-defined flow problem to illustrate the effects of the two approaches. The results are validated by experimental data. Comparisons are carried out for a super-, trans- and subcritical bifurcation, respectively, showing the practicality of the 1D approach and the advantage of the 2D approach.