Journal of Computational Acoustics

Acoustic radiation from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity distribution, while immersed near a thermoviscous fluid sphere suspended in an unbounded viscous thermally conducting fluid medium is computed. The formulation utilizes the appropriate wave field expansions and boundary conditions along with the translational addition theorem for spherical wave functions to develop a closed-form solution in form of infinite series. The prime objective is to investigate the thermoviscous loss effects on acoustic radiation and its associated field quantities. The analytical results are illustrated with a numerical example in which the spherical source, that may vibrate either in a monopole-like or a dipole-like mode, is suspended in a thermoviscous fluid medium near an equal-sized viscous thermally conducting fluid sphere. To avoid numerical difficulties normally arising in process of solving thermoviscous radiation/scattering problems in the frequency range of interest, a basic multiple precision FORTRAN computation package was utilized in developing specialized codes for computing special mathematical functions including spherical Bessel functions of complex argument and performing large complex matrix manipulations on floating point numbers of arbitrarily high precision. The essential acoustic field quantities such as the modal acoustic radiation impedance load on the source, the radiated far-field pressure directivity pattern and the radiated on-axis pressure are evaluated and discussed for representative values of the parameters characterizing the system. Limiting cases are examined and excellent agreements with well known solutions are attained.

A plane acoustic wave is scattered by either a soft or a hard small torus. The incident wave has a wavelength which is much larger than the characteristic dimension of the scatterer and thus the low-frequency approximation method is applicable to the scattering problem. It is shown that there exists exactly one toroidal coordinate system that fits the given geometry. The R-separation of variables is utilized to obtain the series expansion of the fields in terms of toroidal harmonics (half-integer Legendre functions of first and second kind). The scattering problem for the soft torus is solved analytically for the near field, governing the leading two low-frequency coefficients, as well as for the far field, where both the amplitude and the cross-section are evaluated. The scattering problem for the hard torus appears to be much more complicated in calculations. The Neumann boundary condition on the surface of the torus leads to a three-term recurrence relation for the series coefficients corresponding to the scattered fields. Thus, the potential boundary-value problem for the leading low-frequency approximations is reduced to infinite systems of linear algebraic equations with three-diagonal matrices. An analytical technique for solving systems of diagonal form is developed.

In a precursor to this article the Biot model was used to model poroelastic media. The question this article addresses is whether the sort of experiments described by McKelvie and Palmer, Williams, and Hosokawa and Otani can be used to determine the parameters of the Biot model. A method of computing acoustic pressure in the low 100 kHz range was developed in Buchanan and Gilbert, "Determination of the parameters of cancellous bone using high frequency acoustic measurements," which appeared in Math. Comput. Modelling. In the present work a parameter recovery algorithm which uses parallel processing is developed and tested. It is found that when it is assumed that the agreement between calculated and measured data is about two digits, porosity can be determined to within about 1–2% and permeability, pore size and the bulk moduli to within about 40%, but in most cases less than 20%.

The azimuthal limitation of the Parabolic Equation (PE) approximation in solving the three-dimensional (3D) wave equation in cylindrical coordinate has been studied in this paper. Typically, 3D problems are dealt with an N × 2D approximation, which treats a 3D field as a fan-like composition of many 2D vertical slices (r - z plane in cylindrical coordinate) ignoring the θ-coupling terms. To deal with problems possessing 3D effects, the θ-coupling terms have to be considered in PE approximation. Nevertheless, the azimuthal limitation in the 3D PE approximation is not defined as well as the vertical angle limitation. Hence, the theoretical derivation estimating the azimuthal limitation is put forth in this work. Numerical results of a modified benchmark problem are also presented to validate the arguments and the wide angle version of the 3D PE model, FOR3D.

Finite difference approximations for the convection equation are developed, which exhibit enhanced stability limits for explicit Runge–Kutta integration. Stability limits are increased by adding artificial dissipation terms, which are optimized to yield greatest stable time steps. For the artificial dissipation terms, symmetric finite difference approximations of even-order derivatives are used with differencing stencils equal to the convective stencils. The spatial discretization inclusive of the added dissipation term is shown to be consistent with a first derivative. The formal order of accuracy in space is decreased by one order, while the order of time integration is not affected. As a result, the time step limits of originally stable Runge–Kutta integration is increased, for some combinations of spatial discretization and time integration by a factor of two. Algorithms, which are unstable without damping are stabilized. The dispersion properties of the algorithms are not influenced by the proposed damping terms. Spectral analysis of the algorithms show very low dissipation error for dimensionless wave numbers k Δ x < 0.5. Stability conditions based on von Neumann stability analysis are given for the proposed schemes for explicit Runge–Kutta time integration of orders up to ten.

Finite-difference time-domain (FDTD) method has been successfully developed to model electromagnetic systems in recent years. Since acoustics and electromagnetism share certain undulatory properties, a natural adaptation of this technique has been developed too. Several acoustics problems, such as room acoustics, require the use of fibrous tangles to attenuate the propagation speed of sound waves. Notwithstanding, although free air acoustic propagation is known, FDTD technique is not developed yet to model fibrous materials. To characterize this behavior, only a few and measurable set of parameters must be considered. In this paper, a new approach for modeling fibrous materials analysis using FDTD is presented and validated. A set of simulations covering various packing densities of a real fibrous material is performed. Loudspeaker cabinets, virtual acoustics and room acoustics are situations in which this method can be applied.