Didier Dragna

Time-domain solver in curvilinear coordinates for outdoor sound propagation over complex terrain

The current work aims at developing a linearized Euler equations solver in curvilinear coordinates to account for the effects of topography on sound propagation. In applications for transportation noise, the propagation environment as well as the description of acoustic sources is complex, and time-domain methods have proved their capability to deal with both atmospheric and ground effects. First, equations in curvilinear coordinates are examined. Then time-domain boundary conditions initially proposed for a Cartesian coordinate system are implemented in the curvilinear solver. Two test cases dealing with acoustic scattering by an impedance cylinder in a two-dimensional geometry and by an impedance sphere in a three-dimensional geometry are considered to validate the boundary conditions. Accurate solutions are obtained for both rigid and impedance surfaces. Finally, the solver is used to examine a typical outdoor sound propagation problem. It is shown that it is well-suited to study coupled effects of topography, mixed impedance ground and meteorological conditions.

Time-domain simulations of outdoor sound propagation with suitable impedance boundary conditions

Finite difference time-domain methods are attractive for the study of broadband outdoor noise propagation, because they can accurately take into account both atmospheric and ground effects. Moreover, these methods allow moving sound sources to be modeled, which can be interesting in the context of transportation noise. A recently proposed method to obtain an impedance boundary condition is implemented in a linearized Euler equations solver. A long-range propagation configuration in a two-dimensional geometry is studied in homogeneous conditions and in downward-refracting conditions with an impedance ground over a distance of 500 m. Two impedance models corresponding to a grassy ground and to a snow-covered ground are considered. Numerical results are compared in the time domain to an analytical solution in homogeneous conditions and to results from a ray-tracing code in downward-refracting conditions. Near the ground, surface waves are detected in the two cases and are the dominant arrivals in the homogeneous case.

Physically Admissible Impedance Models for Time-Domain Computations of Outdoor Sound Propagation

Conditions for an impedance model to be physically admissible are checked for some popular models in the outdoor sound propagation community. They require that the definition of the impedance model is extended in the whole complex plane and that its inverse Fourier transform is real, causal and passive. For the many impedance models that are written as the square-root of a rational function, such as the Zwikker and Kosten model, the fourparameter Attenborough model and the Hamet and Bérengier model, these conditions are shown to be satisfied for a semi-infinite ground and for a rigidly backed layer. The case of polynomial type models is then investigated. The Delany and Bazley model is not physically admissible as it is real or causal depending on its extension in the complex plane, but it can not simultaneously fulfill both conditions. The Miki model for a rigidly backed layer does not satisfy also the passivity condition as its real part is negative for low frequencies. A new polynomial model is thus proposed and is shown to be physically admissible.

On the inadvisability of using single parameter impedance models for representing the acoustical properties of ground surfaces

Although semi-empirical one parameter models are used widely for representing outdoor ground impedance, they are not physically admissible. Even when corrected to satisfy a passivity condition in respect of surface impedance they do not satisfy the condition that the real part of complex density must be greater than zero. Comparison of predictions with frequency-domain data for short range propagation have indicated that physically admissible models provide superior overall agreement. A two parameter variable porosity model yields better agreement for many grassland surfaces and a two parameter version of the slit pore microstructural impedance model yields better agreement with data obtained over low flow resistivity surfaces such as forest floors and gravel. Impedance models and conditions for physical admissibility are summarised. In addition to those examined previously, the slit pore model is shown to be physically admissible. After providing further examples of the better agreement with short range data that can be achieved using two parameter models, it is shown that differences between frequency domain predictions at longer ranges using physically admissible models rather than one parameter models are significantly greater than those resulting from short range spatial variability and comparable with seasonal variability over grassland.

Impulse propagation over a complex site: A comparison of experimental results and numerical predictions

Results from outdoor acoustic measurements performed in a railway site near Reims in France in May 2010 are compared to those obtained from a finite-difference time-domain solver of the linearized Euler equations. During the experiments, the ground profile and the different ground surface impedances were determined. Meteorological measurements were also performed to deduce mean vertical profiles of wind and temperature. An alarm pistol was used as a source of impulse signals and three microphones were located along a propagation path. The various measured parameters are introduced as input data into the numerical solver. In the frequency domain, the numerical results are in good accordance with the measurements up to a frequency of 2 kHz. In the time domain, except a time shift, the predicted waveforms match the measured waveforms with a close agreement.

Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces

The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.

A generalized recursive convolution method for time-domain propagation in porous media

An efficient numerical method, referred to as the auxiliary differential equation (ADE) method, is proposed to compute convolutions between relaxation functions and acoustic variables arising in sound propagation equations in porous media. For this purpose, the relaxation functions are approximated in the frequency domain by rational functions. The time variation of the convolution is thus governed by first-order differential equations which can be straightforwardly solved. The accuracy of the method is first investigated and compared to that of recursive convolution methods. It is shown that, while recursive convolution methods are first or second-order accurate in time, the ADE method does not introduce any additional error. The ADE method is then applied for outdoor sound propagation using the equations proposed by Wilson et al. in the ground [(2007). Appl. Acoust. 68, 173-200]. A first one-dimensional case is performed showing that only five poles are necessary to accurately approximate the relaxation functions for typical applications. Finally, the ADE method is used to compute sound propagation in a three-dimensional geometry over an absorbing ground. Results obtained with Wilsons equations are compared to those obtained with Zwikker and Kostens equations and with an impedance surface for different flow resistivities.

Towards realistic simulations of sound radiation by moving sources in outdoor environments

PACS numbers:43.28.Js, 43.28.En, 43.20.El A time-domain solver of the linearized Euler equations is used to study outdoor propagation of acoustic waves generated by broadband moving sources. For that, high-order schemes, developed initially in the computational aeroacoustics community, are employed. A time-domain impedance boundary condition recently proposed in the literature is implemented to deal with reflexion of acoustic waves over the ground. In addition, curvilinear coordinates are used to account for topographic effects. First, test cases show that long range sound propagation and diffraction by obstacles in three-dimensional geometries are accurately determined. Simulation of the acoustic radiation by a broadband monopole source moving above a perfectly reflecting plane is then considered. Numerical results are satisfactorily compared to those obtained from an analytical solution. At last, the case of a broadband source moving above a non-flat terrain, with an inhomogeneous impedance ground, is investigated. The effects of a topography defect on the acoustic field are examined.

Modeling of broadband moving sources for time-domain simulations of outdoor sound propagation

Although time-domain solutions of the linearized Euler equations are well adapted to study the acoustic propagation in an outdoor environment, the modeling of sources in motion in time-domain solvers has not been investigated in the literature yet. This is done here by considering distributed volume sources. First, the influence of the spatial distribution of the source on the acoustic field is analyzed. Results obtained for a nonmoving source are summarized, and the example of a Gaussian spatial distribution is presented. The case of a harmonic volume source moving at a constant speed is then investigated in the geometrical far field. The directivity of a noncompact source is shown to be dramatically different from that of a point source. Numerical simulations are performed in a three-dimensional geometry in free-field configurations, and waveforms of the acoustic pressure exhibit Doppler shift and convective amplification. Finally, simulations of a broadband moving source above an impedance ground surfa...

Toward Hybrid CAA with Ground Effects

CAA based on the Linearised Euler Equations (LEE) is applied to propagate aerodynamic sound over an extended distance including ground effects. The LEE are coupled to data from an LES via an acoustic analogy to follow-up the sound from the source to the extended far field: the complete chain is illustrated on the sound generated by a cylinder in a M ∼ 0.2 and Re ∼ 48000 flow. A very good agreement is found in free field between the approach based on the Ffowcs-Williams & Hawkings (FWH) analogy only and the combined FWH-LEE approach. The ability of the combined approach to handle complex boundary conditions is illustrated on the same data set with a rigid and a grassy ground.