ABSTRACT
Abstract In this paper we derive a new model for the junctions in a network of canals individually modeled by Saint-Venant equations.
14.1 Introduction Jack Lagnese, Guenter Leugering, and the author have been collaborating for over a decade
on the modeling and analysis of a variety of linked structures in which distinct components are joined together. In particular, this collaboration, spurred on by the focused energy of Jack Lagnese, led to a monograph [4]. More recently in Reference 3, stimulated by the earlier paper of Coron et al. [1], Leugering and Schmidt considered networks of canals. Our approach, partially in the framework of Reference 4, drew heavily on results from the literature on conservation laws to obtain results on stabilization of flows in a simple star configuration of canals. The model used derived the Saint-Venant equations, first introduced in Reference 5, from a variational principle that also yielded conditions governing the dynamics of the flow through the junctions at which canals meet. Capturing the character of the junctions at which various components of a linked structure meet has repeatedly presented a challenge. In the case of the canal networks, the conditions at junctions that were used in Reference 3 did not take into account the angles at which the canals meet nor any other features of the geometry of the junction.
