Level-set methods applied to the kinematic wave equation governing surface water flows

Mean, Sovanna; Unami, Koichi; Fujihara, Masayuki

doi:10.1016/j.jenvman.2020.110784

Cited by 5 publications

(2 citation statements)

References 44 publications

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“…Two numerical examples, referred to as Case 1 and Case 2, are presented. Case 1 deals with the practical problem of abrupt water release from Chan Thnal Reservoir located in Cambodia into an initially dry bed of its irrigation canal (Mean et al, 2020). Case 2 deals with a hypothetical problem under the smoothness of all input.…”

Section: Numerical Examples and Discussionmentioning

confidence: 99%

“…Such a phenomenon is intrinsic to first-order quasilinear partial differential equations (FOQLPDEs), including the kinematic wave model, the Kynch's sedimentation model (Bürger and Wendland, 2001), the compressible Euler equations (Chen et al, 2017), and traffic flow models (Corli and Malaguti, 2021). Conversely, treatment of the kinematic wave model not as a FOQLPDE but a Hamilton-Jacobi type leads to inconsistency as in Mean et al (2020). Those properties are well-known among mathematicians since Oleĭnik (1957) established the theory of FOQLPDEs in 1D domains, considering generalized solutions in the space of measurable and bounded functions.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Examples of Non-Dissipative Discontinuous Kinematic Waves in Open Channels

Mean

Unami

Fujihara

2022

Journal of Rainwater Catchment Systems

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The kinematic wave model under the assumption of balanced gravity and friction forces has been applied in open channel hydraulics and surface hydrology. There persists a severe misunderstanding that a discontinuity of a kinematic wave occurs due to a discontinuity of input and then dissipates. This study clarifies that a discontinuity can develop without dissipation under the smoothness of all input. The theory of first-order quasilinear partial differential equations shows that Cauchy problems for the kinematic wave model have unique measurable and bounded solutions, which are possibly discontinuous. Numerical examples are presented to visualize the fundamental properties of discontinuous kinematic waves.

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Section: Numerical Examples and Discussionmentioning

confidence: 99%