Well-Posedness of a Nonlinear Shallow Water Model for an Oscillating Water Column with Time-Dependent Air Pressure

被引：0

作者：

Edoardo Bocchi

Jiao He

Gastón Vergara-Hermosilla

机构：

[1] Universidad de Sevilla,Departamento de Análisis Matemático, Instituto de Matemáticas de la Universidad de Sevilla

[2] Université Paris-Saclay,CNRS, Laboratoire de mathématiques d’Orsay

[3] Université de Bordeaux,Institut de Mathématiques de Bordeaux

来源：

Journal of Nonlinear Science | 2023年 / 33卷

关键词：

Oscillating water column; Fluid–structure interaction; Initial boundary value problems for hyperbolic PDEs; Time-dependent air pressure; Local well-posedness; 35Q35; 76B15; 35L04; 74F10;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We propose in this paper a new nonlinear mathematical model of an oscillating water column (OWC). The one-dimensional shallow water equations in the presence of this device are reformulated as a transmission problem related to the interaction between waves and a fixed partially immersed structure. By imposing the conservation of the total fluid-OWC energy in the non-damped scenario, we are able to derive a transmission condition that involves a time-dependent air pressure inside the chamber of the device, instead of a constant atmospheric pressure as in Bocchi et al. (ESAIM Proc Surv 70:68–83, 2021). We then show that the transmission problem can be reduced to a quasilinear hyperbolic initial boundary value problem with a semi-linear boundary condition determined by an ODE depending on the trace of the solution to the PDE at the boundary. Local well-posedness for general problems of this type is established via an iterative scheme by using linear estimates for the PDE and nonlinear estimates for the ODE.

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