The wave superposition method as a robust technique for computing acoustic fields

Abstract

The wave superposition method has recently been advocated [Koopmann et al., ‘‘A method for computing acoustic fields based on the principle of wave superposition,’’ J. Acoust. Soc. Am. 86, 2433–2438 (1989)], as a reliable and accurate technique for computing the acoustic fields generated by arbitrary-shaped radiators; this study examines in depth the robustness and numerical stability of the method. The implementation of the method requires the placement of a finite number of point sources on a surface interior to the body of the radiator. The magnitude of these point sources can be evaluated in terms of the prescribed velocity distribution on the surface of the radiator. Once calculated, the magnitude of these point sources allow the pressure distribution exterior to the radiator to be evaluated. The first improvement made to the robustness of the method is the use of a hybrid combination of monopole and dipole sources; this modification allows the inherent problem of nonuniqueness of the method at certain frequencies to be overcome. Both discrete point and continuous source distributions are used to evaluate the method on a variety of test cases involving both spherical and prolate spheroid geometries. The prime motivation for using such a method is the avoidance of the singular integration inherent is the application of the normal boundary element methods, however, for the method to be successful, the resulting matrix approximations need to be well-conditioned. This numerical conditioning was found to be dependent not only on the position of the boundary and the source nodal points but also on the interpolation or the location of these sources on the retracted surface.

Near field acoustic holography based on the equivalent source method and pressure-velocity transducers

“…In addition to the classical NAH technique based on spatial discrete Fourier transforms, 1-3 many alternative methods have been developed in the past years, e.g., the inverse boundary element method, [4][5][6] the statistically optimized method, 7,8 the Helmholtz equation least-squares method, 9,10 and the equivalent source method ͑ESM͒ ͑also known as the wave superposition method͒. [11][12][13][14][15][16] Usually the measured quantity is the sound pressure rather than the particle velocity, simply because pressure microphones are readily available and easy to calibrate whereas the particle velocity has been difficult to measure. However, in recent years, a particle velocity transducer called Microflown has appeared.…”

Time-Domain Simulation of Directive Sources in 3-D Digital Waveguide Mesh-Based Acoustical Models

“…The following selection is made for convenience: In octant I, ; in octant II, ; in octant III, ; in octant IV, ; in octant V, ; in octant VI, ; in octant VII, ; and finally in octant VIII, . The outgoing wave variables are then initialized accordingly by using the velocity values obtained by weighting the gradient of the selected velocity potential function defined as in (20) and (21). After the initialization stage, the iteration is started at the propagation step instead of the scattering pass.…”

“…The initial omnidirectional velocity, , at the given position can then be calculated using (11) with a change of coordinates from spherical to Cartesian as (20) The directional velocity vectors with which the DWM is initialized can then be obtained as (21) where is the frequency-independent directivity function with arbitrary rotation angles in azimuth and in elevation. Here, and .…”

“…These include spherical harmonic decomposition [20], wave superposition [21], [22], and multipole synthesis [20], [23]. These methods are based on the harmonic solution of the wave equation and they operate in the frequency domain.…”

Numerical Analysis of Structure Acoustic Radiation Based on Wave Superposition Method

“…The numerical method is implemented by using the acoustic field from a series of virtual sources which are collected near the boundary surface to replace the actual acoustic field of radiator, called the principle of equivalent. Jeans, Mathews [2] and Xiang Yu [3] successively presented the Burton-Miller's superposition integral and the wave superposition method with complex radius vector. Chen Xinzhao, Yu Fei [4,5] and Li Jiaqing [6] et al developed the mechanism of near field acoustic holography based on wave superposition method and related experiment, but the acoustic field prediction and how to collocate these equivalent sources are not researched.…”