Natural Frequencies of Submerged Structures Using an Efficient Calculation of the Added Mass Matrix in the Boundary Element Method

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Luis E. Monterrubio ◽  
Petr Krysl
Keyword(s):  
Boundary Element Method ◽  
Eigenvalue Problem ◽  
Boundary Element ◽  
Numerical Integration ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Computational Cost ◽  
Added Mass ◽  
Computational Time ◽  
Element Method

This work presents an efficient way to calculate the added mass matrix, which allows solving for natural frequencies and modes of solids vibrating in an inviscid and infinite fluid. The finite element method (FEM) is used to compute the vibration spectrum of a dry structure, then the boundary element method (BEM) is applied to compute the pressure modes needed to determine the added mass matrix that represents the fluid. The BEM requires numerical integration which results in a large computational cost. In this work, a reduction of the computational cost was achieved by computing the values of the pressure modes with the required numerical integration using a coarse BEM mesh, and then, interpolation was used to compute the pressure modes at the nodes of a fine FEM mesh. The added mass matrix was then computed and added to the original mass matrix of the generalized eigenvalue problem to determine the wetted natural frequencies. Computational cost was minimized using a reduced eigenvalue problem of size equal to the requested number of natural frequencies. The results show that the error of the natural frequencies using the procedure in this work is between 2% and 5% with 87% reduction of the computational time. The motivation of this work is to study the vibration of marine mammals' ear bones.

scholarly journals The Added Mass Coefficient computation of sphere, ellipsoid and marine propellers using Boundary Element Method

2011 ◽  
Vol 18 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Hassan Ghassemi ◽  
Ehsan Yari
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Boundary Element ◽  
Mass Matrix ◽  
Added Mass ◽  
Experimental Results ◽  
Marine Propellers ◽  
Mass Coefficient ◽  
Added Mass Coefficient ◽  
Element Method

The Added Mass Coefficient computation of sphere, ellipsoid and marine propellers using Boundary Element Method Added mass is an important and effective dynamic coefficient in accelerating, non uniform motion as a result of fluid accelerating around a body. It plays an important role, especially in vessel roll motion, control parameters as well as in analyzing the local and global vibration of a vessel and its parts like propellers and rudders. In this article, calculating the Added Mass Coefficient has been examined for a sphere, ellipsoid, marine propeller and hydrofoil; using numerical Boundary Element Method. Since an Ellipsoid and a sphere have simple geometric shapes and the Analytical values of their added mass coefficients are available, so that the results of added mass matrix are obtained and evaluated, using the boundary element method. Then the added mass matrix is computed in a given geometrical and flow specifications for a specific propeller and its results are studied versus experimental results, which it's current numerical data In comparison with other numerical methods has a good conformity with experimental results. The most important advantage of the method in determining the added mass matrix coefficients for the surface and underwater vessels and the marine propellers is extracting all the added mass coefficients with very good Accuracy, while in other numerical methods it is impossible to extract all the coefficients with the Desired Accuracy.

Anti-Sloshing Effects of Longitudinal Partial Baffles in a Partly-Filled Container Under Lateral Excitation

2014 ◽  
Author(s):  
Amir Kolaei ◽  
Subhash Rakheja ◽  
Marc J. Richard
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Eigenvalue Problem ◽  
Boundary Element ◽  
Lateral Force ◽  
Computational Time ◽  
Generalized Coordinates ◽  
Liquid Slosh ◽  
Lateral Excitation ◽  
Element Method

This study is aimed at analysis of transient lateral slosh in a partially-filled cylindrical tank with different designs of longitudinal partial baffles using a coupled multimodal and boundary-element method. A boundary element method is initially formulated to solve the eigenvalue problem of free liquid slosh, assuming inviscid, incompressible and irrotational flows. Significant improvement in computational time is achieved by reducing the generalized eigenvalue problem to a standard one involving only the velocity potentials on the half free-surface length using the zoning method. The generalized coordinates of the free-surface oscillations under a lateral excitation are then obtained from superposition of the natural slosh modes. The lateral slosh force is also formulated in terms of the generalized coordinates and hydrodynamic coefficients. The validity of the model is illustrated through comparisons with available analytical solutions. Two different designs of longitudinal baffles are considered: bottom- and top-mounted baffles. The effect of different baffle designs on the normalized slosh frequencies, modes and lateral force are investigated. It is shown that the multimodal method yields computationally efficient solutions of liquid slosh within moving baffled containers. The results suggest that the effectiveness of baffles in suppressing the liquid oscillations is strongly affected by the baffle length relative to the free-surface height. The top-mounted baffle yields the greatest effectiveness, when it pierces the free-surface. The bottom-mounted baffle, however, may not be considered as an efficient mean for controlling the liquid slosh in tank vehicles where the liquid fill height is above 50%.

Weighted Finite Difference and Boundary Element Methods Applied to Groundwater Pollution Problems

1991 ◽  
Vol 23 (1-3) ◽  
pp. 517-524
Author(s):  
M. Kanoh ◽  
T. Kuroki ◽  
K. Fujino ◽  
T. Ueda
Keyword(s):  
Boundary Element Method ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Element ◽  
Difference Method ◽  
Groundwater Pollution ◽  
Small Region ◽  
Boundary Element Methods ◽  
Computational Time ◽  
Element Method

The purpose of the paper is to apply two methods to groundwater pollution in porous media. The methods are the weighted finite difference method and the boundary element method, which were proposed or developed by Kanoh et al. (1986,1988) for advective diffusion problems. Numerical modeling of groundwater pollution is also investigated in this paper. By subdividing the domain into subdomains, the nonlinearity is localized to a small region. Computational time for groundwater pollution problems can be saved by the boundary element method; accurate numerical results can be obtained by the weighted finite difference method. The computational solutions to the problem of seawater intrusion into coastal aquifers are compared with experimental results.

scholarly journals Hydrodynamic Interactions in Multiple Body Array: A Simple and Fast Approach Coupling Boundary Element Method and Plane Wave Approximation

2013 ◽  
Author(s):  
Jitendra Singh ◽  
Aurélien Babarit
Keyword(s):  
Boundary Element Method ◽  
Plane Wave ◽  
Boundary Element ◽  
Hydrodynamic Interaction ◽  
Computational Time ◽  
Linear Potential ◽  
Wave Approximation ◽  
Interaction Problem ◽  
Plane Wave Approximation ◽  
Element Method

The hydrodynamic forces acting on an isolated body could be considerably different than those when it is considered in an array of multiple bodies, due to wave interactions among them. In this context, we present in this paper a numerical approach based on the linear potential flow theory to solve full hydrodynamic interaction problem in a multiple body array. In contrast to the previous approaches that considered all bodies in an array as a single unit, the present approach relies on solving for an isolated body. The interactions among the bodies are then taken into account via plane wave approximation in an iterative manner. The boundary value problem corresponding to a isolated body is solved by the Boundary Element Method (BEM). The approach is useful when the bodies are sufficiently distant from each other, at-least greater than five times the characteristic dimensions of the body. This is a valid assumption for wave energy converter devices array of point absorber type, which is our target application at a later stage. The main advantage of the proposed approach is that the computational time requirement is significantly less than the commonly used direct BEM. The time savings can be realized for even small arrays consisting of four bodies. Another advantage is that the computer memory requirements are also significantly smaller compared to the direct BEM, allowing us to consider large arrays. The numerical results for hydrodynamic interaction problem in two arrays consisting of 25 cylinders and same number of rectangular flaps are presented to validate the proposed approach.

An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Sofia Sarraf ◽  
Ezequiel López ◽  
Laura Battaglia ◽  
Gustavo Ríos Rodríguez ◽  
Jorge D'Elía
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Computational Time ◽  
Creeping Flows ◽  
Order Of Magnitude ◽  
Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

A Novel Boundary Element Method for Linear Elasticity With No Numerical Integration for Two-Dimensional and Line Integrals for Three-Dimensional Problems

1994 ◽  
Vol 61 (2) ◽  
pp. 264-269 ◽  
Author(s):  
A. Nagarajan ◽  
E. Lutz ◽  
S. Mukherjee
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Numerical Integration ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Contour Method ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Boundary Contour Method ◽  
Element Method

This paper presents a novel application of the boundary element method to solve problems in linear elasticity. The new method is called the Boundary Contour Method. This approach requires no numerical integration at all for two-dimensional problems and numerical evaluation of line integrals only for three-dimensional problems; even for curved line or surface boundary elements of arbitrary shape! Numerical results are presented for some two-dimensional problems.

Validation Study of Smoothed Particle Hydrodynamics in Fluid and Structure Interaction and the Comparison to Boundary Element Method

2017 ◽  
Author(s):  
Nhu Nguyen ◽  
Krish P. Thiagarajan ◽  
Matthew Cameron
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Smoothed Particle Hydrodynamics ◽  
Computational Time ◽  
Floating Structure ◽  
Structure Interaction ◽  
Advantages And Disadvantages ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Element Method

The purpose of this research is to validate the usage of Smoothed Particle Hydrodynamics (SPH) method in solving fluid-structure interaction problems as well as study its advantages and disadvantages compared to another well-known technique Boundary Element Method (BEM). The goal is achieved by 1) evaluating the Response Amplitude Operator (RAO) and 2) analyzing the drifting motion of a 1:10 scaled 3m-discus oceanographic buoy developed by the National Oceanographic and Atmospheric Administration (NOAA), using both experimental and numerical approaches. For the experimental study, the testing was carried out in an 8-m long wave tank and the buoy motions were measured using non-intrusive techniques. For numerical analysis, the project used DualSPHysics — open source code — and ANSYS AQWA — one of the leading software widely used in the marine applications — to simulate all the experimental scenarios via SPH and BEM techniques respectively. It is observed that while BEM has clear advantages in computational time and the ability to study applicable range of frequencies, SPH, in addition to its capability to simulate drifting motion of the floating structure, has shown to outperform the RAO predictions from BEM (especially in low frequency region). In higher frequency regions, the lack of experimental data hinders the conclusion on which method might be more suitable, as both have their own limitations.

Simulation of Acoustical Response Using Rayleigh Method

2006 ◽  
Author(s):  
Ahlem Alia ◽  
Mhamed Souli
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Computational Time ◽  
Complex Character ◽  
Surface Integration ◽  
Rayleigh Method ◽  
Element Method

The Boundary Element Method is one of the most used techniques for the simulation of acoustic problems especially for external ones. However, it leads to large computational time because of the complex character of the resulting linear system and the calculation of its different terms by surface integration. In this paper, the Rayleigh method is used to calculate the acoustical pressure at any point in the space. This method is very fast since it does not need to construct and to solve a linear system.

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