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