Review: The Use of Equivalent Source Method in Computational Acoustics

Abstract

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.

Fundamental solutions for water wave animation

“…It is used in acoustics as an alternative to the Boundary Element Method, as it does not rely on a mesh and does not suffer from singularity problems at the boundaries. Lee [2017] reviews recent uses of ESM in computational acoustics.…”

On the use of the equivalent source method for free-field calibration of an acoustic radiator in a reverberant tank

“…If the collocation points densely cover the measurement surface S M and µ ≪ 1, then outside the area bounded by this surface, the equivalent sources well reproduce the field of the radiator. A weak point of the equivalent source method is the lack of general rules for choosing the necessary number of equivalent sources and their positions [6,10]. In practice, the problem of selecting the points r n and ρ ρ ρ m is usually solved empirically, that is, through trial-and-error.…”

“…In the present paper, we discuss an alternative approach that can be used for a free-field calibration of an acoustic radiator in a finite-sized tank without isolating the direct signal. To solve the problem, it is proposed to apply the well-known equivalent source method [5][6][7][8][9][10]. The sound field excited by the radiator is represented as a weighted superposition of fields excited by a set of acoustic monopoles called the equivalent sources.…”

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

“…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.…”