Author(s): Ghostine Rabih; Kesserwani Georges; Vazquez Jose; Mose Robert; Ghenaim; Abdellah
Linked Author(s): Georges Kesserwani
Keywords: Saint Venant equations; Combining models; Subcritical; Steady; Transient
Abstract: In this study, a comparison between the one and two-dimensional numerical simulation for subcritical flow in open channel networks are presented and completely described allowing for a full comprehension of the modeling of water flow. For the one-dimensional simulation, the mathematical model used is the 1D Saint Venant equations to find the solution in branches. For junction, these equations are not available and the junction is considered as internal boundary conditions, then a special treatment of the junction is necessary. Different junction models exist in the literature based on momentum approach, but they are of empirical nature due to certain parameters given by experimental results and often present a reduced field of validity. These models are: the equality of water stage model, Gurram et al. model (1997), Hsu et al. model (1998) and Shabayek et al. model (2002). Therefore, the whole system is considered as a set of branches in which the 1D Saint Venant equations are applied and linked by different hydraulic models of junction. The first order explicit scheme of Roe is used to solve the Saint Venant equations in branches, while for junction, the four models quoted above coupled with the method of characteristics are solved by using NewtonRaphson algorithm. Oppositely, for the two-dimensional simulation, the whole system (branches and junction) is considered as one system and the domain is discretised into triangular cells forming an unstructured computational mesh. The finite volume method with the Riemann solver of Roe on unstructured triangular grids is considered to solve the 2D Saint Venant equations. In order to study the performance of the two approaches, the 1D and 2D numerical results are compared to the experimental data of Hsu et al. (1998) and to each other in simulating steady and transient flow problems through a combining junction.
Year: 2007