Einladung zum Vortrag (Zoom) von Frau Dr. Maya Briani am 05.05.2021 - 14:30 Uhr im Rahmen des Forschungsseminars Analysis[05.05.2021]
Im Rahmen des Forschungsseminars Analysis hält am Mittwoch, den 5. Mai 2021, um 14:30 Uhr,
Frau Dr. Maya Briani (IAC -- CNR, Rom) einen Vortrag zum Thema:
Shallow water equations in channel networks
Abstract: Shallow water equations are a model for describing free surface water flows such as those in artificial canals and water canals with applications to environmental problems, for example. They are a non-linear hyperbolic system of PDEs consisting of a mass and momentum balance. In water management problems, these equations are often used as a fundamental tool to describe the dynamics of networks of canals or of the branching of rivers.
In the present talk, we consider a network as a set of one dimensional canals coupled through junctions. The main mathematical difficulty is the definition of the coupling conditions at the junction between the adjoining channels. The coupling condition can be seen as a Riemann problem involving a constant state for each of the adjoining canals. Then, one completes the Riemann problem by adding physical conservation properties across the junction. Riemann problems at a junction are widely discussed in literature. Here, we examine the problem in the subcritical regime and we discuss the supercritical regime providing a characterization of possible phase transitions for a simple network with two canals and one junction.
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