The solution of the Riemann problem in rectangular channels with constrictions and obstructions

The exact solution to the Shallow water Equations Riemann problem at width jumps in rectangular channels

“…Remark 3. Note that these solution classes differ from those discussed in Pepe et al (2019) because in the present case the internal structure of the geometric discontinuity is monotonic.…”

“…Remark 1. Note that these flow configurations do not correspond to those discussed in Pepe et al (2019) because the rapid width variation considered in the present work is monotonic. This implies that a critical state can be exhibited only at one of the geometric discontinuity ends.…”

“…in the literature (Castro et al 2007, Cozzolino et al 2018b, Pepe et al 2019 as good candidates to supply a relationship between u1 and u2, and they will be used in the present work. These stationary solutions are characterized by the invariance of the discharge Q = Bhu, implying that this condition must be always assumed for the definition of the SW.…”

“…Usually, this Riemann problem is studied considering the one-dimensional Shallow water Equations, which are the restriction of the Saint Venant Equations to the case of rectangular cross section. In this context, many different types of geometric discontinuities have been considered in the literature, such as sluice gates (De Marchi 1945, Montuori and Greco 1973, Cozzolino et al 2015, bed steps (Alcrudo and Benkhaldoun 2001, LeFloch and Than 2011, and Han and Warnecke 2014, free or submerged weirs (Guerra et al 2008), and obstructions or constrictions (Cozzolino et al 2017, Pepe et al 2019).…”