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A perturbation analysis and finite element approximate model for free surface flow over curved beds
Author(s) -
Berger R. C.,
Carey G. F.
Publication year - 1991
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620310306
Subject(s) - hydraulic jump , curvature , finite element method , perturbation (astronomy) , free surface , dissipation , mathematics , jump , mechanics , shallow water equations , numerical analysis , mathematical analysis , flow (mathematics) , geometry , physics , engineering , structural engineering , quantum mechanics , thermodynamics
Abstract A perturbation analysis is developed for 1‐D shallow water flow over a curved bed for applications such as spillways. The perturbation approach leads to a new formulation of the problem with associated weak integral statement and approximation using finite elements. The flow may exhibit a hydraulic jump in the downstream regime. An artificial dissipation technique is introduced to stabilize the non‐linear problem and suppress numerical oscillations. Numerical results demonstrate the performance of the model and compare it with the steep‐slope shallow water formulation corresponding to the model with zero curvature.