Numerical Integral Independent of Frequency in the Boundary Element Method for Acoustic Scattering

2013 ◽  
Vol 444-445 ◽  
pp. 650-654
Author(s):  
Zai You Yan ◽  
Chuan Zhen Li
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Acoustic Scattering ◽  
Normal Derivative ◽  
Numerical Results ◽  
New Technique ◽  
Computational Time ◽  
Unknown Variable ◽  
Numerical Integral ◽  
Element Method

Fast algorithm for multi-frequency numerical integration in the simulation of acoustic scattering from rigid object by the boundary element method is presented. Normal derivative of the free-space Greens function is partially approximated with the unknown variable by a set of shape functions. As a result, the numerical integral is independent of frequency and need be calculated only at the first frequency step. Singular integral can be computed using the same procedure as that applied in the conventional boundary element method. Computational efficiency and accuracy of the new technique are demonstrated by an example. Numerical results obtained using the new technique are compared with the corresponding analytical solutions and numerical results obtained using the conventional boundary element method. The new technique works well and saves a lot of computational time in the process of generation of coefficient matrices for multi-frequency analysis.

Fast Calculation of Far-Field Sound Directivity Based on Fast Multipole Boundary Element Method

2020 ◽  
Vol 28 (04) ◽  
pp. 1950024
Author(s):  
Takayuki Masumoto ◽  
Yosuke Yasuda ◽  
Naohisa Inoue ◽  
Tetsuya Sakuma
Keyword(s):  
Boundary Element Method ◽  
High Resolution ◽  
Boundary Element ◽  
Conventional Method ◽  
Numerical Results ◽  
Computational Time ◽  
Fast Method ◽  
Far Field ◽  
Fast Multipole ◽  
Element Method

A fast method for calculating sound radiation/reflection directivities at high resolution in the infinite far field is proposed with the use of the fast multipole boundary element method (FMBEM). This method calculates directivities using direction-dependent coefficients called outgoing coefficients, which are obtained in the calculation process of the matrix-vector products in the FMBEM. Since the outgoing coefficients are generally calculated for a large number of directions high-resolution directivities can be easily obtained with extremely small computational cost and minor modifications in the FMBEM program codes. It is confirmed via comparison with the numerical results using the conventional method that the proposed method can calculate directivities at infinity. Numerical results also show that the computational time for the proposed method is significantly shorter than that for the conventional method with no addition of the required memory.

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.

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.

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

2020 ◽  
pp. 1475472X2097838
Author(s):  
Bassem Barhoumi ◽  
Jamel Bessrour
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Singular Integrals ◽  
Acoustic Radiation ◽  
Normal Derivative ◽  
Boundary Integral ◽  
Meridian Plane ◽  
Mean Flow ◽  
Transform Method ◽  
Element Method

This paper presents a new numerical analysis approach based on an improved Modal Boundary Element Method (MBEM) formulation for axisymmetric acoustic radiation and propagation problems in a uniform mean flow of arbitrary direction. It is based on the homogeneous Modal Convected Helmholtz Equation (MCHE) and its convected Green’s kernel using a Fourier transform method. In order to simplify the flow terms, a general modal boundary integral solution is formulated explicitly according to two new operators such as the particular and convected kernels. Through the use of modified operators, the improved MBEM approach with flow takes a convective form of the general MBEM approach and has a similar form of the nonflow MBEM formulation. The reference and reduced Helmholtz Integral Equations (HIEs) are implicitly taken into account a new nonreflecting Sommerfeld condition to solve far field axisymmetric regions in a uniform mean flow. For isolating the singular integrations, the modal convected Green’s kernel and its modified normal derivative are performed partly analytically in terms of Laplace coefficients and partly numerically in terms of Fourier coefficients. These coefficients are computed by recursion schemes and Gauss-Legendre quadrature standard formulae. Specifically, standard forms of the free term and its convected angle resulting from the singular integrals can be expressed only in terms of real angles in meridian plane. To demonstrate the application of the improved MBEM formulation, three exterior acoustic case studies are considered. These verification cases are based on new analytic formulations for axisymmetric acoustic sources, such as axisymmetric monopole, axial and radial dipole sources in the presence of an arbitrary uniform mean flow. Directivity plots obtained using the proposed technique are compared with the analytical results.

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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