Semi-Analytical Boundary Collocation Technique for Wave Propagation Applications

2015 ◽  
Author(s):  
Zhuo-Jia Fu
Keyword(s):  
Wave Propagation ◽  
Wave Structure ◽  
Fundamental Solutions ◽  
Singular Boundary ◽  
Sh Wave ◽  
Propagation Analysis ◽  
Collocation Technique ◽  
Singular Boundary Method ◽  
Wave Structure Interaction

This study presents on a recent semi-analytical boundary collocation technique, the singular boundary method (SBM), for exterior wave propagation analysis. The SBM is mathematically simple, easy-to-program, meshless and applies the concept of source intensity factors to eliminating the singularity of the fundamental solutions and avoiding singular numerical integrals in the boundary element method. The Burton and Miller’s method is introduced to the present SBM to enhance the quality of the solution, particularly in the vicinity of irregular frequencies. Then the present SBM is applied to water wave-structure interaction with four-cylinder structure and SH wave scattering in 2D hill.

scholarly journals Wake Effect Assessment in Long- and Short-Crested Seas of Heaving-Point Absorber and Oscillating Wave Surge WEC Arrays

Water ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1126 ◽  
Author(s):  
Gael Verao Fernandez ◽  
Vasiliki Stratigaki ◽  
Panagiotis Vasarmidis ◽  
Philip Balitsky ◽  
Peter Troch
Keyword(s):  
Wave Propagation ◽  
Wave Structure ◽  
Irregular Waves ◽  
Wake Effect ◽  
Coupled Models ◽  
Propagation Models ◽  
Power Absorption ◽  
Structure Interaction ◽  
Wake Effects ◽  
Wave Structure Interaction

In the recent years, the potential impact of wave energy converter (WEC) arrays on the surrounding wave field has been studied using both phase-averaging and phase-resolving wave propagation models. Obtaining understanding of this impact is important because it may affect other users in the sea or on the coastline. However, in these models a parametrization of the WEC power absorption is often adopted. This may lead to an overestimation or underestimation of the overall WEC array power absorption, and thus to an unrealistic estimation of the potential WEC array impact. WEC array power absorption is a result of energy extraction from the incoming waves, and thus wave height decrease is generally observed downwave at large distances (the so-called “wake” or “far-field” effects). Moreover, the power absorption depends on the mutual interactions between the WECs of an array (the so-called “near field” effects). To deal with the limitations posed by wave propagation models, coupled models of recent years, which are nesting wave-structure interaction solvers into wave propagation models, have been used. Wave-structure interaction solvers can generally provide detailed hydrodynamic information around the WECs and a more realistic representation of wave power absorption. Coupled models have shown a lower WEC array impact in terms of wake effects compared to wave propagation models. However, all studies to date in which coupled models are employed have been performed using idealized long-crested waves. Ocean waves propagate with a certain directional spreading that affects the redistribution of wave energy in the lee of WEC arrays, and thus gaining insight wake effect for irregular short-crested sea states is crucial. In our research, a new methodology is introduced for the assessment of WEC array wake effects for realistic sea states. A coupled model is developed between the wave-structure interaction solver NEMOH and the wave propagation model MILDwave. A parametric study is performed showing a comparison between WEC array wake effects for regular, long-crested irregular, and short-crested irregular waves. For this investigation, a nine heaving-point absorber array is used for which the wave height reduction is found to be up to 8% lower at 1.0 km downwave the WEC array when changing from long-crested to short-crested irregular waves. Also, an oscillating wave surge WEC array is simulated and the overestimation of the wake effects in this case is up to 5%. These differences in wake effects between different wave types indicates the need to consider short-crested irregular waves to avoid overestimating the WEC array potential impacts. The MILDwave-NEMOH coupled model has proven to be a reliable numerical tool, with an efficient computational effort for simulating the wake effects of two different WEC arrays under the action of a range of different sea states.

scholarly journals Numerical Investigation on Convergence Rate of Singular Boundary Method

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Junpu Li ◽  
Wen Chen ◽  
Zhuojia Fu
Keyword(s):  
Short Communication ◽  
Convergence Rates ◽  
Fundamental Solutions ◽  
Benchmark Problems ◽  
Singular Boundary ◽  
Intensity Factors ◽  
Collocation Points ◽  
Boundary Method ◽  
Collocation Scheme ◽  
Singular Boundary Method

The singular boundary method (SBM) is a recent boundary-type collocation scheme with the merits of being free of mesh and integration, mathematically simple, and easy-to-program. Its essential technique is to introduce the concept of the source intensity factors to eliminate the singularities of fundamental solutions upon the coincidence of source and collocation points in a strong-form formulation. In recent years, several numerical and semianalytical techniques have been proposed to determine source intensity factors. With the help of these latest techniques, this short communication makes an extensive investigation on numerical efficiency and convergence rates of the SBM to an extensive variety of benchmark problems in comparison with the BEM. We find that in most cases the SBM and BEM have similar convergence rates, while the SBM has slightly better accuracy than the direct BEM. And the condition number of SBM is lower than BEM. Without mesh and numerical integration, the SBM is computationally more efficient than the BEM.

An Improved Formulation of Singular Boundary Method

2012 ◽  
Vol 4 (5) ◽  
pp. 543-558 ◽  
Author(s):  
Wen Chen ◽  
Yan Gu
Keyword(s):  
Intensity Factor ◽  
Neumann Boundary ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Benchmark Problems ◽  
Singular Boundary ◽  
Boundary Method ◽  
New Formulation ◽  
Physical Boundary ◽  
Singular Boundary Method

AbstractThis study proposes a new formulation of singular boundary method (SBM) to solve the 2D potential problems, while retaining its original merits being free of integration and mesh, easy-to-program, accurate and mathematically simple without the requirement of a fictitious boundary as in the method of fundamental solutions (MFS). The key idea of the SBM is to introduce the concept of the origin intensity factor to isolate the singularity of fundamental solution so that the source points can be placed directly on the physical boundary. This paper presents a new approach to derive the analytical solution of the origin intensity factor based on the proposed subtracting and adding-back techniques. And the troublesome sample nodes in the ordinary SBM are avoided and the sample solution is also not necessary for the Neumann boundary condition. Three benchmark problems are tested to demonstrate the feasibility and accuracy of the new formulation through detailed comparisons with the boundary element method (BEM), MFS, regularized meshless method (RMM) and boundary distributed source (BDS) method.

scholarly journals Influence of Power Take-Off Modelling on the Far-Field Effects of Wave Energy Converter Farms

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 429
Author(s):  
Gael Verao Fernandez ◽  
Vasiliki Stratigaki ◽  
Nicolas Quartier ◽  
Peter Troch
Keyword(s):  
Wave Propagation ◽  
Coupled Model ◽  
Wave Structure ◽  
Propagation Model ◽  
Far Field ◽  
Energy Converter ◽  
Coupled Models ◽  
Structure Interaction ◽  
Field Effects ◽  
Wave Structure Interaction

The study of the potential impact of wave energy converter (WEC) farms on the surrounding wave field at long distances from the WEC farm location (also know as “far field” effects) has been a topic of great interest in the past decade. Typically, “far-field” effects have been studied using phase average or phase resolving numerical models using a parametrization of the WEC power absorption using wave transmission coefficients. Most recent studies have focused on using coupled models between a wave-structure interaction solver and a wave-propagation model, which offer a more complex and accurate representation of the WEC hydrodynamics and PTO behaviour. The difference in the results between the two aforementioned approaches has not been studied yet, nor how different ways of modelling the PTO system can affect wave propagation in the lee of the WEC farm. The Coastal Engineering Research Group of Ghent University has developed both a parameterized model using the sponge layer technique in the mild slope wave propagation model MILDwave and a coupled model MILDwave-NEMOH (NEMOH is a boundary element method-based wave-structure interaction solver), for studying the “far-field” effects of WEC farms. The objective of the present study is to perform a comparison between both numerical approaches in terms of performance for obtaining the “far-field” effects of two WEC farms. Results are given for a series of regular wave conditions, demonstrating a better accuracy of the MILDwave-NEMOH coupled model in obtaining the wave disturbance coefficient (Kd) values around the considered WEC farms. Subsequently, the analysis is extended to study the influence of the PTO system modelling technique on the “far-field” effects by considering: (i) a linear optimal, (ii) a linear sub-optimal and (iii) a non-linear hydraulic PTO system. It is shown that modelling a linear optimal PTO system can lead to an unrealistic overestimation of the WEC motions than can heavily affect the wave height at a large distance in the lee of the WEC farm. On the contrary, modelling of a sub-optimal PTO system and of a hydraulic PTO system leads to a similar, yet reduced impact on the “far-field” effects on wave height. The comparison of the PTO systems’ modelling technique shows that when using coupled models, it is necessary to carefully model the WEC hydrodynamics and PTO behaviour as they can introduce substantial inaccuracies into the WECs’ motions and the WEC farm “far-field” effects.

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