Network flows and specifically water flow in open canals can be modeled bysystems of balance laws defined ongraphs.The shallow water or Saint-Venant system of balance laws is one of the most used modeland present two phases: fluvial or sub-critical and torrential or super-critical.Phase transitions may occur within the same canal but transitions relatedto networks are less investigated.In this paper we provide a complete characterization of possible phase transitionsfor a case study of a simple scenariowith two canals and one junction.However, our analysis allows the study of more complicate networks.Moreover, we provide some numerical simulations to show the theory at work.
Citation: Maya Briani, Benedetto Piccoli. Fluvial to torrential phase transition in open canals[J]. Networks and Heterogeneous Media, 2018, 13(4): 663-690. doi: 10.3934/nhm.2018030
Network flows and specifically water flow in open canals can be modeled bysystems of balance laws defined ongraphs.The shallow water or Saint-Venant system of balance laws is one of the most used modeland present two phases: fluvial or sub-critical and torrential or super-critical.Phase transitions may occur within the same canal but transitions relatedto networks are less investigated.In this paper we provide a complete characterization of possible phase transitionsfor a case study of a simple scenariowith two canals and one junction.However, our analysis allows the study of more complicate networks.Moreover, we provide some numerical simulations to show the theory at work.
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Maya Briani, Benedetto Piccoli. Fluvial to torrential phase transition in open canals[J]. Networks and Heterogeneous Media, 2018, 13(4): 663-690. doi: 10.3934/nhm.2018030
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