Burton–Miller-type singular boundary method for acoustic radiation and scattering

Fu, Zhuojia; Chen, Wen; Gu, Yan

doi:10.1016/j.jsv.2014.04.025

Cited by 113 publications

(51 citation statements)

References 38 publications

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“…This section will introduce a semi-analytical technique [8,9] to calculate the source intensity factors. …”

Section: Semi-analytical Technique With Boundary Iit (Sat1)mentioning

confidence: 99%

“…And then it uses the inverse interpolation technique with boundary source points to determine the source intensity factors of Laplace fundamental solution on a Dirichlet boundary. Then Fu et al [9][10][11] used the relationships between Laplace and Helmholtz fundamental solutions to extend the ISBM to solve Helmholtz equations. Recently, another semianalytical technique (SAT2) has been proposed [12].…”

Section: Introductionmentioning

confidence: 99%

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Numerical investigation on three treatments for eliminating the singularities of acoustic fundamental solutions in the singular boundary method

Fu¹,

Chen²,

Qu³

2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

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This study considers the numerical comparison on three treatments for eliminating the singularities of acoustic fundamental solutions in singular boundary method (SBM). The singular boundary method is a recent meshless boundary collocation method, which introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. Recently, three treatments, the inverse interpolation technique (IIT), the semi-analytical technique with boundary IIT (SAT1) and the semi-analytical technique with integral mean value (SAT2), have been proposed to determine the source intensity factors for removing the singularities of acoustic fundamental solutions at origin. This study compares numerical efficiency and stability of these three approaches on two benchmark examples under two-dimensional exterior acoustic problems.

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“…This section will introduce a semi-analytical technique [8,9] to calculate the source intensity factors. …”

Section: Semi-analytical Technique With Boundary Iit (Sat1)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical investigation on three treatments for eliminating the singularities of acoustic fundamental solutions in the singular boundary method

Fu¹,

Chen²,

Qu³

2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular, meshfree methods are widely applied to solve acoustics problems, because field points used in this method are arbitrarily distributed and the approximation smoothness order is chosen flexibility. The method of fundamental solutions (MFS) [6], the multiple-scale reproducing kernel particle method (RKPM) [7], the element-free Galerkin method (EFGM) [8], and other meshfree methods [9][10][11][12] are used to address certain acoustic problems.…”

Section: Introductionmentioning

confidence: 99%

Modeling Sound Propagation Using the Corrective Smoothed Particle Method with an Acoustic Boundary Treatment Technique

Zhang

2017

Preprint

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Abstract:The development of computational acoustics allows simulation of sound generation and propagation in complex environment. In particular, meshfree methods are widely used to solve acoustics problems through arbitrarily distributed field points and approximation smoothness flexibility. As a Lagrangian meshfree method, smoothed particle hydrodynamics (SPH) method reduce the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase medium. The traditional SPH method has been applied in acoustic simulation. This study presents the corrective smoothed particle method (CSPM), which is a combination of SPH kernel estimate and Taylor series expansion. The CSPM is introduced as a Lagrangian approach to improve accuracy in solving acoustic wave equations in the time domain. Moreover, a boundary treatment technique based on the hybrid meshfree and finite difference time domain (FDTD) method is proposed to represent different acoustic boundaries with particles. To model sound propagation in pipes with different boundaries, soft, rigid, and absorbing boundary conditions are built with this technique. Numerical results show that the CSPM algorithm is consistent and demonstrates convergence with exact solutions. Main computational parameters are discussed, and different boundary conditions are validated to be effective for benchmark problems in computational acoustics.

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“…Meshfree methods has been used to solve the acoustic wave equation in quiescent media in the time domain or the Helmholtz equation in the frequency domain, as in the multiplescale reproducing kernel particle method (RKPM) [29], the element-free Galerkin method (EFGM) [30], the method of fundamental solutions (MFS) [31], etc… [32,33]. When using a meshfree method, the Lagrangian approach proposed in this paper not only has the advantages of the Lagrangian property mentioned before, but also has the benefits of the meshfree method itself, such as avoiding mesh generation.…”

Section: Introductionmentioning

confidence: 99%

A Lagrangian Approach for Computational Acoustics with Meshfree Method

Zhang

Smith

Zhang

et al. 2017

Preprint

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Abstract:Although Eulerian approaches are standard in computational acoustics, they are less effective for certain classes of problems like bubble acoustics and combustion noise. A different approach for solving acoustic problems is to compute with individual particles following particle motion. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically, using three meshfree methods to solve the Lagrangian acoustic perturbation equations (LAPE) in the time domain. The LAPE split the fluid dynamic equations into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, three meshfree methods, the smoothed particle hydrodynamics (SPH) method, the corrective smoothed particle (CSP) method, and the generalized finite difference (GFD) method, are introduced to solve the LAPE and the linearized LAPE (LLAPE). The SPH and CSP methods are widely used meshfree methods, while the GFD method based on the Taylor series expansion can be easily extended to higher orders. Applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. A comparison of the LAPE and the LLAPE using the three meshfree methods is also presented. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP and GFD method exhibit convergence in cases with different background flow. The GFD method is more accurate, while the CSP method can handle higher Courant numbers.

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Burton–Miller-type singular boundary method for acoustic radiation and scattering

Cited by 113 publications

References 38 publications

Numerical investigation on three treatments for eliminating the singularities of acoustic fundamental solutions in the singular boundary method

Numerical investigation on three treatments for eliminating the singularities of acoustic fundamental solutions in the singular boundary method

Modeling Sound Propagation Using the Corrective Smoothed Particle Method with an Acoustic Boundary Treatment Technique

A Lagrangian Approach for Computational Acoustics with Meshfree Method

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