Journal of Computational Acoustics

The need to analyze aircraft noise over ground with general properties occurs in various applications, most notably in environmental engineering, where the analysis of the sound pressure level (SPL) distribution near the ground due to aircraft noise is desired. Since the human hearing range is very wide, the determination of the SPL distribution for a given source spectrum is not trivial and may be regarded as a multiscale problem. One has to solve repeatedly, for many different wave numbers, the Helmholtz equation in the upper half space while imposing the given impedance boundary condition on the possibly non-flat ground. An efficient Helmholtz solver must therefore be incorporated in the scheme that finds the SPL distribution. Three totally different computational methods that may be used to solve this problem are considered here: A fictitious sources method, a parabolic approximation method and a wave-enriched finite element method (with two versions: PUM and GFEM). The three methods are compared in terms of their computational properties, and numerical examples are presented to demonstrate their performance.

Optimized local radiation boundary conditions to truncate the computational domain by a rectangular boundary have been constructed for acoustic waves propagating into a homogeneous, isotropic far field. Here we try to achieve comparable efficiencies in stratified media and cylindrical coordinates. We find that conditions constructed for homogeneous media are highly effective in the stratified case. On the circle we derive boundary conditions by optimizing a semidiscretized perfectly matched layer. Though we are unsuccessful in matching the accuracies of the Cartesian case, our experiments show that older sequences based on the progressive wave expansion are surprisingly efficient.

Through finite difference time domain (FDTD) numerical simulation, we have studied the possible observation settings to improve the cost effectiveness in time-reversal (TR) source relocation in a two-dimensional (2D) urban setting under a number of typical scenarios. All scenario studies were based on the FDTD computation of the acoustic wave field resulted from an impulse source, propagated through an artificial village composed of 15 buildings and a set of sources and receivers, a typical urban setting has been extensively analyzed in previous studies. The FDTD numerical modeling code can be executed on an off-the-shelf graphic processor unit (GPU) that increases the speed of the time-reversal calculations by a factor of 200. With this approach the computational results lead to some significant conclusions. In general, using only one non-line-of-sight (NLOS) single receiver is not enough to do a quality work to re-locate the source via time-reversal. This is particularly true when there are more than one path between the source and this receiver with similar wave energy travel time. However, when the single sensor is located in an acoustic channel, reverberation inside the waveguide may increase the effective aperture of the single receiver enough to give a good location. It is equivalent to say that the waveguide and the single receiver form a "virtual array". It appears that a sensor array with a minimum number of three receivers might be the most cost-effective way to carry out TR source relocation in an urban environment. The most optimal geometry of a sensor array with a minimum number of three receivers could be an equal side-length triangle. Simple analysis showed that by this setup it is possible to catch sound sources from almost all possible azimuths. Effective source relocation essentially depends on the geometry, relativity to the scatters, etc. of the sensing array. Generally, adding another single sensor relatively far away from the main array will not improve the results. It is practically useful and achievable to have a sensor array mounted on the outside of a single building, and in these cases successful source relocations were obtained. As stated by the fundamental TR theory, increasing the number of scatters, here, increasing the number of buildings will definitely be helpful to increase the effectiveness of TR source relocation.

A wide range of applications requires the modeling of wave propagation phenomena in media with variable physical properties in the domain of interest, while highly accurate algorithms are needed to avoid unphysical effects. Spectral element methods (SEM), based on either a Chebyshev or a Legendre polynomial basis, have excellent properties of accuracy and flexibility in describing complex models, outperforming other techniques. In the standard SEM approach the computational domain is discretized by using very coarse meshes and constant-property elements, but in some cases the accuracy and the computational efficiency may be seriously reduced. For instance, a finely heterogeneous medium requires grid resolution down to the finest scales, leading to an extremely large problem dimension. In such problems the wavelength scale of interest is much larger but cannot be exploited in order to reduce the problem size. A poly-grid Chebyshev spectral element method (PG-CSEM) can overcome this limitation. In order to accurately deal with continuous variation in the properties, or even with small scale fluctuations, temporary auxiliary grids are introduced which avoid the need of using any finer global grid, and at the macroscopic level the wave field propagation is solved maintaining the SEM accuracy and computational efficiency.

This paper addresses the application of the spectral finite element (FE) method to problems in the field of computational aeroacoustics (CAA). We apply a mixed finite element approximation to the acoustic perturbation equations, in which the flow induced sound is modeled by assessing the impact of a mean flow field on the acoustic wave propagation. We show the properties of the approximation by numerical benchmarks and an application to the CAA problem of sound generated by an airfoil.

This work deals with the extension of the partition of unity finite element method (PUFEM) "(Comput. Meth. Appl. Mech. Eng.139 (1996) pp. 289–314; Int. J. Numer. Math. Eng.40 (1997) 727–758)" to solve wave problems involving propagation, transmission and reflection in layered elastic media. The proposed method consists of applying the plane wave basis decomposition to the elastic wave equation in each layer of the elastic medium and then enforce necessary continuity conditions at the interfaces through the use of Lagrange multipliers. The accuracy and effectiveness of the proposed technique is determined by comparing results for selected problems with known analytical solutions. Complementary results dealing with the modeling of pure Rayleigh waves are also presented where the PUFEM model incorporates information about the pressure and shear waves rather than the Rayleigh wave itself.

The scattering from roughly meter-sized targets, such as pipes, cylinders and unexploded ordnance shells in the 1–30 kHz frequency band is studied by numerical simulations and compared to experimental results. The numerical tool used to compute the frequency and aspect-dependent target strength is a hybrid model, consisting of a local finite-element model for the vicinity of the target, based on the decomposition of the three-dimensional scattering problem for axially symmetric objects into a series of independent two-dimensional problems, and a propagation model based on the wavenumber spectral integral representation of the Green's functions for layered media.

A laser-ultrasonic experimental setup was used to study, at a reduced scale, the wave propagation inside and around fluid-filled wells. Simulations tools were also developed and calibrated from comparisons with experimental signals. These tools serve as a connection to realistic scale. A semi-analytical approach, the discrete wave number method was first used to compute signals in a simplified geometrical configuration. This method is fast enough to be used in the identification of the main parameters that describe at best the experimental signals. Then a finite difference scheme was implemented in order to describe accurately the actual well. The two methods describe the attenuation mechanisms by using the Kelvin–Voigt model for the solid and the Maxwell model for the fluid. Comparisons between numerical and experimental waveforms, obtained in the two fundamental elastic configurations: the fast and the slow formations, show very good agreement in arrival times, waveforms and relative amplitudes. This satisfactory result provides insights useful for the recognition and interpretation of wave propagation in complex media. Such is the case of modern sonic-logging technology.

A finite-difference algorithm is developed in the 3D cylindrical coordinate system. Synthetic waveforms excited by monopole and dipole acoustic sources are calculated for acoustic logging in a tilted layered formation composed of two poroelastic media. It is revealed that the existence of a tilted layer drives more acoustic energy out and therefore reduces the reflection back to the wellbore. Numerical results show that the amplitudes and the arrival times of the shear waves and flexural modes are influenced by the borehole inclination. The Stoneley modes, however, show little sensitivity to the orientation of the layer interface.