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New Approximate Solution with Resonance Modes of Saint-Venant Equations by WKB-Type Method

Abstract : Exact analytical solutions of linearized Saint-Venant equations remain unknown except for uniform regimebut this later configuration is not often encountered in realopen-channel hydraulic system. In this paper, an approximatesolution of linearized Saint-Venant equations in their generalnon-uniform shape is proposed. This solution is based ona mathematical method developed in quantum mechanics tohandle differential equations with space-varying coefficients. Itresults in irrational transfer functions between levels or flowsand boundary flows at any point of the channel and it capturesall resonance modes. The accuracy of the method is illustratedon a case study.
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https://hal.archives-ouvertes.fr/hal-01906237
Contributor : Gildas Besancon Connect in order to contact the contributor
Submitted on : Friday, October 26, 2018 - 3:31:30 PM
Last modification on : Wednesday, November 3, 2021 - 7:50:32 AM

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  • HAL Id : hal-01906237, version 1

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Violaine Dalmas, Gérard Robert, Gildas Besancon, Didier Georges. New Approximate Solution with Resonance Modes of Saint-Venant Equations by WKB-Type Method. ECC 2018 - 16th European Control Conference, Jun 2018, Limassol, Cyprus. ⟨hal-01906237⟩

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