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F. Toth, M. Kaltenbacher:
"Fully Coupled Linear Modelling of Incompressible Free-Surface Flow, Compressible Air and Flexible Structures";
International Journal for Numerical Methods in Engineering, 107 (2016), 947 - 969.

Incompressible free-surface flow is a common assumption for the modelling of water waves. Connected with the aim to develop very large floating platforms, air chamber supported floating structures have attracted considerable research interest in the past. Such structures are carried by air entrapped in chambers formed by stiff, vertical walls. In order to model these types of structures, the interactions between surface gravity waves and compressible air must be taken into account. If the payload requirements for air chamber supported structures are low enough, the air chambers may be formed by flexible membrane cylinders. In such systems, pressure variations can lead to considerable changes in chamber volume. Therefore, the flexibility of the bounding structures must be taken into account. We present a modelling strategy to tackle the fully coupled problem of compressible gas in a flexible chamber and incompressible free-surface flow in an unbounded domain. The governing equations and boundary conditions are described and solved by the finite element method. A perfectly matched layer is used to obtain a solution for an unbounded domain. Finally, the numerical implementation is validated by various test cases.

http://dx.doi.org/10.1002/nme.5194