A thorough description of one-dimensional steady open channel flows using the notion of viscosity solution

Sovanna Mean, Koichi Unami, Hisashi Okamoto and Masayuki Fujihara

Applied Mathematics and Computation, 2022, vol. 415, issue C

Abstract: Determining water surface profiles of steady open channel flows in a one-dimensional bounded domain is one of the well-trodden topics in conventional hydraulic engineering. However, it involves Dirichlet problems of scalar first-order quasilinear ordinary differential equations, which are of mathematical interest. We show that the notion of viscosity solution is useful in thoroughly describing the characteristics of possibly non-smooth and discontinuous solutions to such problems, achieving the conservation of momentum and the entropy condition. Those viscosity solutions are the generalized solutions in the space of bounded measurable functions. Generalized solutions to some Dirichlet problems are not always unique, and a necessary condition for the non-uniqueness is derived. A concrete example illustrates the non-uniqueness of discontinuous viscosity solutions in a channel of a particular cross-sectional shape.

Keywords: Open channel flow; Viscosity solution; Generalized solution; Hydraulic jump; Gradually varied flow (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:415:y:2022:i:c:s0096300321008122

DOI: 10.1016/j.amc.2021.126730

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