Acoustic Scattering in the Time Domain Using an Equivalent Source Method

Lee, Seongkyu; Brentner, Kenneth S.; Morris, Philip J.

doi:10.2514/1.45132

Cited by 59 publications

(57 citation statements)

References 22 publications

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“…This time-domain ESM did not receive much attention and was not been used for practical engineering problems until Lee et al [77][78][79] presented significant improvements of the method and revived it. Lee et al [77][78][79] used analytical formulations of the pressure gradient 80 for the boundary condition to derive a new formulation to include the effect of a uniform motion of the surface and equivalent sources and to consider the incident field generated by arbitrary moving sources such as rotor blades. They introduced a first-order shape function to discretize the source strength in time and used the SVD to improve the numerical instability issue.…”

Section: Equivalent Source Methodsmentioning

confidence: 99%

“…They introduced a first-order shape function to discretize the source strength in time and used the SVD to improve the numerical instability issue. 77 They also introduced a time-averaging algorithm to further remove the numerical instability. 78 In the time-domain ESM, the strength of equivalent sources is given as a function of time, q e (t).…”

Section: Equivalent Source Methodsmentioning

confidence: 99%

“…A linear global shape function was used in the literatures. [77][78][79] For rectilinear motion of a slender body or a stationary body with an arbitrary shape, the boundary condition for an acoustically rigid surface can be written as…”

Section: Equivalent Source Methodsmentioning

confidence: 99%

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Review: The Use of Equivalent Source Method in Computational Acoustics

Lee

2017

J. Comp. Acous.

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This paper reviews the equivalent source method (ESM), an attractive alternative to the standard boundary element method (BEM). The ESM has been developed under different names: method of fundamental solutions, wave superposition method, equivalent source method, etc. However, regardless of the method name, the basic concept is very similar; that is to use auxiliary points called equivalent sources to reconstruct the acoustic pressure for radiation or scattering problems. The strength of the equivalent sources are then determined via various approaches such that the boundary conditions on the boundary surface are satisfied. This paper reviews several frequencydomain and time-domain ESMs. There are several distinct advantages in these types of methods: (1) the method is a meshless approach so that it is easy and simple to implement; (2) it does not have a numerical singularity problem that occurs in the BEM; (3) the number of equivalent sources can be fewer than the number of surface collocation points so that the matrix size is reduced and a fast computation is achieved for large problems. The main issue of the ESM is that there is no rule to find out the optimal number and position of equivalent sources. In addition, the ESM suffers from the numerical instability that is associated with the ill-conditioned matrix. Some guidelines have been suggested in terms of finding the number and position of the sources, and several numerical techniques have been developed to resolve the numerical instability. This paper reviews the common theories, numerical issues and challenges of the ESM, and it summarizes recent developments and applications of the ESM to aircraft noise.

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Section: Equivalent Source Methodsmentioning

confidence: 99%

Section: Equivalent Source Methodsmentioning

confidence: 99%

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Review: The Use of Equivalent Source Method in Computational Acoustics

Lee

2017

J. Comp. Acous.

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“…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 with 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 meshfree methods [9][10][11][12] are used to address certain acoustic problems, mainly in the frequency domain, and other methods like the equivalent source method (ESM) [13][14][15] solve problems in the time domain. Moreover, there is also a kind of method The present paper is organized as follows: In Section 2, the CSPM formulations are provided to solve the acoustic wave equations.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

2017

MCA

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Abstract:The development of computational acoustics allows the simulation of sound generation and propagation in a 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, the smoothed particle hydrodynamics (SPH) method reduces 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 the SPH kernel estimate and Taylor series expansion. The CSPM is introduced as a Lagrangian approach to improve the accuracy when 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. The main computational parameters are discussed, and different boundary conditions are validated as being effective for benchmark problems in computational acoustics.

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“…The first point is that pressure gradient formulations were developed to solve acoustic scattering problems [4,5,6,7,8] that require the pressure gradient as the boundary condition in acoustic scattering problems rather than an indirect step in computing the acoustic velocity. Thus pressure gradient formulations are required in their own right.…”

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confidence: 99%