ABSTRACT: In this paper, the Riemann solution of an extended Riemann problem in channel
networks is presented. The Riemann problem at a junction network is well defined in the
literature. However, it is limited to symmetric networks. Here, we extend the Riemann problem
to non-symmetric networks such that neither the channel width equality nor the discharge
equality are assumed. The Riemann solution is given under subcritical flow conditions to ensure
the existence and uniqueness of the solution at the junction. Taking into account the mass
and 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 numerical
examples.
In order to perform a one-dimensional simulation in channel networks, the inner boundary
conditions at the junction (i.e., the channel intersection point) are required. It has turned out
that the classical models (i.e., the Equality, Gurram, Hsu models) that have been used to supply
such a boundary suffer from many drawbacks.
Thus, here we propose to use the Riemann solution at the junction networks to provide
proper boundary conditions. Then, we compare all the junction models together. The junction
models 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. In
particular, the Riemann model shows the best results when the bottom discontinues at the
junction. For the unsteady state flows, we perform prototype case studies to test the junction
models in the channel networks, and the numerical solutions are compared with the analytical
solutions. The Riemann model continues to show the best results that agree with the analytical
solutions. However, the validation of the junction models in the unsteady state flows remains
for future work due to the limited amount of real data.
