An efficient coupled-mode/FEM numerical method for linear wave propagation over 3D variable bathymetry domains

© Copyright 2016 by the International Society of Offshore and Polar Engineers (ISOPE).A robust numerical algorithm for the simulation of linear water wave propagation over uneven bottom topography is developed. The solution strategy is based on a highly efficient reduction of the 3D problem to a system of partial differential equations by means of a consistent coupled mode series expansion for water wave propagation over variable seabed. The main feature of the proposed series representation is the incorporation of special terms in the vertical expansion basis, accounting for the bottom boundary condition of the varying seabed. The formulation of the 2D system follows from the variations, with respect to the expansion coefficients (functions of the horizontal plane spatial coordinates), of a suitably chosen energy functional. The resulting model is a variable coefficient system of second order, with respect to the spatial coordinates, Partial Differential Equations (PDEs). Linear triangular finite elements are employed for the solution of this PDE system offering flexibility in the discretization of complex 2D domains. The numerical method developed has been applied to several test cases yielding accurate representations of the wave field at relatively low computational cost and small execution times

Resonances of enclosed shallow water basins with slender floating elastic bodies

A model for the hydroelastic response of enclosed shallow water basins with floating slender plates of large span, in variable bathymetry is presented. The eigenproblem for the system's resonant behaviour is formulated in the strong and variational form. Based on the variational form, and special hydroelastic finite elements, a quadratic eigenvalue problem is derived for the eigenfrequencies and eigenmodes of the basin-floating body system. Benchmark examples, for simplified configurations, are used to study the effects of parameters like the plate's span, position, draft, mass, stiffness and depth of the basin. It is observed that the presence of the plate can alter significantly the eigenstates of the pond if the depth of the basin is relatively small, compared to the plate draft. In such cases the plate span and position play a crucial role. The hydroelastic analysis can be important even in cases where the depth increases and the upper surface elevation differences, in the presence or absence of the floating plate, appear to be less significant. This is due to the importance in accurately calculating the curvature and hence bending moments inside the plate. The proposed model could be relevant to the seiche formation analysis in reservoirs with floating photovoltaic platforms or ice-covered lakes

Time-domain, shallow-water hydroelastic analysis of VLFS elastically connected to the seabed

In order to ensure the safe operation of a VLFS, a combination of mooring, breakwater and other motion reducing systems is employed. In the present work, the transient hydroelastic response of a floating, thin elastic plate, elastically connected to the seabed, is examined. The plate is modelled as an Euler-Bernoulli strip, while the linearized shallow water equations are used for the hydrodynamic modelling. Elastic connectors are approximated by a series of simple spring-dashpot systems positioned along the strip. A higher order finite element scheme is employed for the calculation of the hydroelastic response of the strip-connector configuration, over the shallow bathymetry. After the definition of the initial-boundary value problem, its variational form is derived and discussed. Next, on the basis of the aforementioned formulation, an energy balance expression is obtained. The effect of variable bathymetry on the response of a two connector-strip system, is examined by means of three seabed profiles, featuring a flat bottom, an upslope and a downslope environment. For the flat bottom case, the strip response mitigating effect exerted by the employment of two and three elastic connectors is considered. Finally, by means of the derived energy balance equation, the energy exchange is monitored, providing a valuable insight into the transient phenomena that take place in the studied configurations.The present work has been supported by the project HYDELFS funded by the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF 2007-2013) -Research Funding Program ARHIMEDES-III: Investing in knowledge society through the European Social Fund. In particular, author Theodosios K. Papathanasiou acknowledges support from the aforementioned program for the period from 6/9/2012 to 30/09/2014