An effective boundary element model to calculate the interaction between waves and flexible membrane

Flexible membranes are widely used in marine engineering, but how to calculate their hydrodynamic performance under wave action remains a challenging problem. In this paper, a new model based on the eigenfunction expansion boundary element method (EEBEM) is proposed to calculate the wave-membrane interaction under two-dimensional conditions. A general dynamic boundary condition suitable for linear and arcuate membranes is established based on the membrane’s constitutive equations under cylindrical coordinates. This condition considers the dynamic tension and curvature of the membrane, and an integral expression for the dynamic tension is also derived. Subsequently, the dynamic boundary condition is transformed into a function of the velocity potential and applied to the EEBEM, overcoming the difficulty of the coupled solutions for the arcuate membrane’s motion and the flow field. Moreover, a generalized solution framework for wave-structure interaction is established by constructing a fully closed form of the water wave equations, which effectively shortens the modeling time and expands the application scope. After verifying the accuracy and effectiveness of the model, the hydrodynamic performance (wave force, membrane tension and wave transmission coefficient) and motion response of a submerged flexible membrane breakwater (SFMB) are investigated. The results demonstrate that the model exhibits high accuracy, which is beneficial for elucidating the mechanism of wave-membrane interaction and providing robust support for related research fields.