ABSTRACT
: In this paper, the Riemann solution of an extended Riemann problem in channelnetworks is presented. The Riemann problem at a junction network is well defined in theliterature. However, it is limited to symmetric networks. Here, we extend the Riemann problemto non-symmetric networks such that neither the channel width equality nor the dischargeequality are assumed. The Riemann solution is given under subcritical flow conditions to ensurethe existence and uniqueness of the solution at the junction. Taking into account the massand energy conservation laws, the necessary conditions for the Riemann solution are drawn.The results are summarized in a theorem. The theorem is illustrated with a set of numericalexamples.In order to perform a one-dimensional simulation in channel networks, the inner boundaryconditions at the junction (i.e., the channel intersection point) are required. It has turned outthat the classical models (i.e., the Equality, Gurram, Hsu models) that have been used to supplysuch a boundary suffer from many drawbacks.Thus, here we propose to use the Riemann solution at the junction networks to provideproper boundary conditions. Then, we compare all the junction models together. The junctionmodels are validated against experimental results found in the literature for steady state flows.Generally, the Riemann model shows good results in matching the experimental data. Inparticular, the Riemann model shows the best results when the bottom discontinues at thejunction. For the unsteady state flows, we perform prototype case studies to test the junctionmodels in the channel networks, and the numerical solutions are compared with the analyticalsolutions. The Riemann model continues to show the best results that agree with the analyticalsolutions. However, the validation of the junction models in the unsteady state flows remainsfor future work due to the limited amount of real data. |
