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Potential-flow models based on linear wave theory have the advantage of short computation times but their fundamental assumptions can limit them in their application such as in the presence of steep or breaking waves. ( 1992) for thin vertical barriers and by Liu and Li ( 2017) for an iterative boundary element model. ( 1974) in combination with shallow water theory, by Bennett et al. A quadratic pressure-drop formulation has for instance been used by Mei et al. Examples for work that use a linear relationship between pressure-drop and flow velocity are studies on a nearly vertical porous wall, done by Chakrabarti and Sahoo ( 1996), or for investigations on the effects of bottom topography, done by Kaligatla and Sahoo ( 2017) and Kaligatla et al.
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Regarding the porosity representation, most potential-flow models apply the porous pressure-drop in a linearised way and only few models use a non-linear formulation. Solitary waves have been used to study interaction with a concentric porous cylinder system, done by Zhong and Wang ( 2006), or with vertical wall porous breakwaters, done by Lynett et al. ( 2016) and with a concentric cylindrical structure with an arc-shaped outer cylinder by Zhai et al. Interaction of cnoidal waves with an array of vertical concentric porous cylinders has been investigated by Weng et al. Relatively little work has been done on higher-order or non-linear potential-flow models for porous structures.
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( 1992), or modelling of a series of vertical porous plates in a flume by Molin and Fourest ( 1992). Some examples of existing work are studies on a simplified representation of a Jarlan-type breakwater, done by Fugazza and Natale ( 1992), work on a vertical porous barrier, done by Mei et al. This assumes that the wave steepness and body motions are small. Potential-flow models for wave interaction with porous structures have mainly been based on linear wave theory. Regarding the wave condition, there is a large volume of work on both linear and fully non-linear potential-flow models for wave interaction with impermeable structures. One concerns the wave condition, the other concerns the implementation of macroscopic porosity representation. In the context of potential-flow modelling for porous structures, two main types of linearisation can be employed.
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The latter, which is commonly referred to as computational fluid dynamics (CFD) accounts for the viscosity of the fluid, can be used with both compressible or incompressible fluid properties and generally offers various levels of turbulence modelling. The first assumes the fluid to be inviscid, incompressible and irrotational. In general, numerical modelling of fluid–structure interaction with thin perforated barriers is often based either on potential-flow theory or on the Navier–Stokes (NS) equations. Examples are fixed or floating breakwaters, cages for aquaculture or tuned liquid dampers with slotted baffles.
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Modelling wave interaction with structures consisting of thin porous or perforated elements is of interest in various contexts. The approach can therefore be an efficient alternative for engineering problems where large-scale effects such as global forces and the overall flow-behaviour are of the main interest. This approach offers greater flexibility in the range of wave conditions that can be modelled compared to approaches based on linear potential-flow theory and requires a smaller computational effort compared to CFD approaches which resolve the flow through the openings. It is demonstrated that an isotropic macroscopic porosity representation used for large volumetric granular material can also be used for thin perforated structures. The applied pressure gradient formulation produces good agreement for all porosity values, wave frequencies and wave steepnesses investigated. The CFD results are verified against results from a linear potential-flow model and validated against experimental results. The horizontal force on the structures and the free-surface elevation at wave gauges around the cylinder model have been analysed for a range of porosities and regular wave conditions. The perforated structures are not resolved explicitly but represented by a volumetric porous zone where a volume-averaged pressure gradient in the form of a drag term is applied to the Navier–Stokes momentum equation. This work presents the use of a porous-media approach for computational fluid dynamics (CFD) modelling of wave interaction with thin perforated sheets and cylinders.