A BEM-ISOGEOMETRIC method for the ship wave-resistance problem

In the present work IsoGeometric Analysis is applied to the solution of the Boundary Integral Equation associated with the Neumann-Kelvin problem and the calculation of the wave resistance of ships. As opposed to low-order panel methods, where the body is represented by a large number of quadrilateral panels and the velocity potential is assumed to be piecewise constant (or approximated by low degree polynomials) on each panel, the isogeometric concept is based on exploiting the same NURBS basis, used for representing exactly the body geometry, for approximating the singularity distribution (and, in general, the dependent physical quantities). In order to examine the accuracy of the present method, numerical results obtained in the case of submerged and surface piercing bodies are * Corresponding author. Tel: (+30) 2107721138, Fax: (+30) 2107721397, e-mail: [email protected] 2 compared against analytical solutions, experimental data and predictions provided by the low-order panel or other similar methods appeared in the pertinent literature, illustrating the superior efficiency of the isogeometric approach. The present approach by applying Isogeometric Analysis and Boundary Element Method to the linear NK problem has the novelty of combining modern CAD systems for ship-hull design with computational hydrodynamics tools

Isogeometric Boundary-Element Analysis for the Wave-Resistance Problem using T-splines

In this paper we couple collocated Boundary Element Methods (BEM) with unstructured analysis suitable T-spline surfaces for solving a linear Boundary Integral Equation (BIE) arising in the context of a ship-hydrodynamic problem, namely the so-called Neumann-Kelvin problem, following the formulation by Brard (1972) [1] and Baar & Price (1988) [2]. The local-refinement capabilities of the adopted T-spline bases, which are used for representing both the geometry of the hull and approximating the solution of the associated BIE, in accordance with the Isogeometric concept proposed by Hughes et al. (2005) [3], lead to a solver that achieves the same error level for many fewer degrees of freedom as compared with the corresponding NURBS-based Isogeometric-BEM solver recently developed in Belibassakis et al. (2013) [4]. In this connection, this paper makes a step towards integrating modern CAD representations for ship-hulls with hydrodynamic solvers of improved accuracy and efficiency, which is a prerequisite for building efficient ship-hull optimizers

A cost-effective method for estimating long-term effects of waves on beach erosion with application to Sitia Bay, Crete

Summary: Considering the significant role of beaches for the sea environment and welfare of coastal communities, a variety of process-based models are applied in order to examine and understand the interaction of hydrodynamic processes with seabed material at different time scales. However, a long-term view of this interaction requires a great amount of computational time. In this work a cost-effective methodology is proposed to surpass this shortcoming and estimate bed level evolution. The technique is relied on an objective criterion to assess spectral wave time series of wave height, period and direction and identify the wave conditions that contribute to the initiation of sediment movement. After implementing the so-called Shields criterion, the full wave climate is reduced to two classes of representative wave conditions: the over-critical ones, mainly responsible for long-term erosion, and the sub-critical wave conditions. By applying a well-known process-based model, the representative wave conditions are used as input for the wave-current-sediment transport simulation and rates of bed level changes are obtained, on the basis of which the long-term effects of waves on beach erosion are estimated. Taking into account that erosion is a threatening phenomenon along the sandy beaches of Mediterranean Sea, the present method is demonstrated at a sandy coast of Sitia Bay, Crete. The bed levels derived from the proposed methodology and the full time series are compared. The results indicate reasonable agreement at the selected locations with deviations under 7%, and conformity of the tendency of seabed evolution, rendering the new methodology a useful tool. Keywords: Beach erosion, Bed level evolution, Wave/current modelling, Shields criterion, Sitia-Crete coas

Modelling nearshore hydrodynamics and circulation under the impact of high waves at the coast of Varkiza in Saronic-Athens Gulf

A plethora of physical parameters, such as hydro-, litho- and morpho-dynamic char- acteristics, are essential for understanding the response of coastal systems to intense sea states in terms of sediment transport and shoreline evolution. Nowadays, numerical models are extensively applied to meet the above needs and support coastal planning and management. In the present work, a 2DH dynamic modelling system is used for simulating the hydrodynamic and meteorological/ oceanographic characteristics of the Saronic Gulf, in order to examine circulation patterns and predict sediment transport phenomena under high wave conditions at the coast of Varkiza, a sandy beach in the southern Attica, Greece. Time series of wind and wave data were used as input at the open boundaries of the model domain while the model was calibrated and validated through (linear and directional) statistical measures with respect to in situ wave measurements, since there was lack of hydrodynamic data at the site of interest.The simulation period of the model was between January 3 and February 19, 2013, with consecutive high waves in-between. The good agreement of the numerical results from the wave and hydrodynamic model with in situ measurements confirmed the suitability of the model for the support of sediment transport rates at Varkiza coastal segment. Model results reveal that there is a counter-clockwise water circulation during high waves that contribute to the erosion of the examined beach, which is also confirmed by independent field measurements

A novel coupled-mode model for waves propagating in variable bathymetry in the presence of sheared currents

International audienc

A coupled-mode model for water wave scattering by vertically sheared currents in variable bathymetry regions

International audienc

Propagation and scattering of waves by dense arrays of impenetrable cylinders in a waveguide

International audienceA coupled numerical scheme, based on modal expansions and boundary integral representations , is developed for treating propagation and scattering by dense arrays of impenetrable cylinders inside a waveguide. Numerical results are presented and discussed concerning reflection and transmission, as well as the wave details both inside and outside the array. The method is applied to water waves propagating over an array of vertical cylinders in constant depth extended all over the water column, operating as a porous breakwater unit in a periodic arrangement (segmented breakwater). Focusing on the reflection and transmission properties, a simplified model is also derived, based on Foldy-Lax theory. The latter provides an equivalent index of refraction of the medium representing the porous structure, modeled as an inclusion in the waveguide. Results obtained by the present fully coupled and approximate models are compared against experimental measurements, collected in wave tank, showing good agreement. The present analysis permits an efficient calculation of the properties of the examined structure, reducing the computational cost and supporting design and optimization studies

A coupled mode – hp FEM for the hydroelastic analysis of shear-deformable floating bodies of general thickness in variable bathymetry

An efficient computational procedure is presented for the solution of coupled hydroelastic problems involving bodies of general thickness, floating over variable bathymetry regions. The problem is treated by the coupled mode system of horizontal equations derived by Athanassoulis and Belibassakis (2009), for the analysis of floating, shear deformable plates or beams. The proposed beam (or plate) model is based on the addition of extra vertical elastic deformation modes, at each horizontal position along the floating body, permitting shear strain and stress to vanish on both the upper and lower boundaries and extending third-order plate theories. The final coupled mode system is derived from a variational principle combining the one – field functional of the elastodynamics in the plate region with the pressure functional in the water region. The wave potential in the water column is represented by means of a local – mode series containing an extra mode, accounting for not mildly sloped bottom variations. The addition of the additional modes results to increased convergence rate, enabling high accuracy with the use of a relatively small number of vertical modes. In the present work the hp-version of the Finite Element Method is applied to the solution of a simplified version of the resulting system of coupled horizontal differential equations with respect to the modal amplitudes, providing good convergence rates and adaptivity capabilities, and increasing the overall efficiency of the solution strategy. Numerical results are presented demonstrating the applicability of present method

An isogeometric BEM for exterior potential-flow problems around lifting bodies

In this paper, the Isogeometric Analysis (IGA) concept is combined with the Boundary Element Method (BEM) for solving the exterior Neumann problem associated with the steady lifting flow around a hydrofoil. The formulation of the problem is based on a Boundary Integral Equation for the associated velocity potential combined with the null-pressure jump Kutta condition at the trailing edge. The developed Isogeometric-BEM is based on a parametric NURBS representation of the hydrofoil and employs the very same basis for representing the velocity potential. The Boundary Integral Equation is numerically solved by collocating at the Greville abscissas of the knot vector of the hydrofoil's parametric representation. Numerical error analysis of the Isogeometric-BEM using h-renement is performed and compared with classical low-order panel methods

Isogeometric boundary-element analysis for the wave-resistance problem using T-splines

In this paper we couple collocated Boundary Element Methods (BEM) with unstructured analysis-suitable T-spline surfaces for solving a linear Boundary Integral Equation (BIE) arising in the context of a ship-hydrodynamic problem, namely the so-called Neumann–Kelvin problem, following the formulation by Brard (1972) and Baar and Price (1988). The local-refinement capabilities of the adopted T-spline bases, which are used for representing both the geometry of the hull and approximating the solution of the associated BIE, in accordance with the Isogeometric concept proposed by Hughes et al. (2005), lead to a solver that achieves the same error level for many fewer degrees of freedom as compared with the corresponding NURBS-based Isogeometric-BEM solver recently developed in Belibassakis et al. (2013). In this connection, this paper makes a step towards integrating modern CAD representations for ship-hulls with hydrodynamic solvers of improved accuracy and efficiency, which is a prerequisite for building efficient ship-hull optimizers