Journal of Computational Acoustics

One of the most popular radiation boundary conditions for the Helmholtz equation in exterior 3-D regions has been the sequence of operators developed by Bayliss et al.¹ for computational domains with spherical exterior boundaries. The present paper extends those spherical operators to triaxial ellipsoidal boundaries by utilizing two mathematical constructs originally developed for ellipsoidal acoustic infinite elements.² The two constructs are: (i) a radial/angular coordinate system for ellipsoidal geometry, and (ii) a convergent ellipsoidal radial expansion for exterior fields, analogous to the classical spherical multipole expansion. The ellipsoidal radial and angular coordinates are smooth generalizations of the traditional radial and angular coordinates used in spherical, prolate spheroidal and oblate spheroidal systems. As a result, all four coordinate systems and their corresponding radiation boundary conditions are included within this single ellipsoidal system, varying smoothly from one to the other. The geometric flexibility of this system enables the exterior boundary of the computational domain to closely circumscribe objects with a wide range of aspect ratios, thereby reducing the size and cost of 3-D computational models.

Ocean acoustic wave propagation can be predicted by applying numerical methods to solve representative wave equations computationally. For this purpose, numerical methods have been introduced; a latest introduction was the Predictor-Corrector Method. An important question arises: Whether or not these numerical methods can produce satisfactory required accurate results? This may cause an accuracy concerned by the users. This paper introduces a new Predict-Correct Procedure to examine whether or not the result meets the accuracy requirement. If not, the procedure can improve the result until it becomes satisfactorily accurate. Discussions will be given on the mathematical and computational developments of the Predictor-Corrector Method as well as the Predict-Correct Procedure. Following that is a discussion on how the Predict-Correct Procedure works. An important part of this paper is devoted to show how this new procedure can achieve the goal of obtaining the required accurate prediction results.

An efficient and accurate numerical frequency domain formulation is proposed to investigate the 2D acoustic wave propagation within a shallow water region with a rigid bottom and a free surface. The proposed configuration combines different regions that have either a sloping or a flat rigid bottom.

The numerical approach used here is based on the method of fundamental solutions (MFS). In this model only the vertical interface between different regions is discretized, as the model incorporates Green's functions that take into account the free water surface and the presence of either a horizontal or sloping rigid bottom.

Dispersive properties of elastic waves in a periodic composite with an array of fluid-filled holes are studied in this paper. A finite element method taking into account of the fluid–solid interaction is developed to calculate the dispersion curves. The finite element formulation is presented for one unit cell by taking advantage of the periodicity of the structures and the Bloch theorem. After dividing the equations in the real and imaginary parts, the numerical computation is performed by using the standard finite element code ABAQUS. As numerical examples, some typical two- and three-dimensional systems with circular or spherical holes filled with air, water or mercury are considered in detail. The method can yield precise results with fast convergence for all cases from very low-density fluids to very high-density fluids.

Traditionally, high-accuracy full-sphere polar measurements require dense sampling of the sound field at very-fine angular increments, particularly at high frequencies. The proposed HELS (Helmholtz equation least squares) method allows this restriction to be relaxed significantly. Using this method, far fewer sampling points are needed for full and accurate reconstruction of the radiated sound field. Depending on the required accuracy, sound fields can be reconstructed using only 10% to 20% of the number of sampling points required by conventional techniques. The HELS method allows accurate reconstruction even when the Nyquist spatial sampling rate is violated in certain directions. This paper examines the convergence of HELS solutions via theory and simulation for reconstruction of the acoustic radiation patterns generated by a rectangular plate mounted on an infinite rigid flat baffle. In particular, the impact of the number of expansion terms and that of measurement points as well as errors imbedded in the input data on the resultant accuracy of reconstruction is analyzed.

The concept of acoustic contrast control divides a sound field into bright zone and dark zone. A source array is used to increase acoustic potential energy density in the bright zone and to decrease acoustic potential energy density in the dark zone by controlling amplitude and phase of each source. In the present study, a personal audio system which is based on acoustic contrast control is designed. The purpose is to focus the acoustic potential energy around the region of listener. The optimal configuration for sound field is controlled by using a loudspeaker array. Parameters analysis is considered in simulation. Parameters, such as: the quantity of loudspeakers, the spacing of loudspeakers, the length of array, and the emission frequency are discussed. Finally, two experiments are conducted in a semi-anechoic room and a reverberation room, respectively. The results are shown to verify this approach in the present study.

This paper proposes an extension of the variational theory of complex rays (VTCR) to three-dimensional linear acoustics, The VTCR is a Trefftz-type approach designed for mid-frequency range problems and has been previously investigated for structural dynamics and 2D acoustics. The proposed 3D formulation is based on a discretization of the amplitude portrait using spherical harmonics expansions. This choice of discretization allows to substantially reduce the numerical integration work by taking advantage of well-known analytical properties of the spherical harmonics. It also permits (like with the previous 2D Fourier version) an effective a priori selection method for the discretization parameter in each sub-region, and allows to estimate the directivity of the pressure field by means of a natural definition of rescaled amplitude portraits. The accuracy and performance of the proposed formulation are demonstrated on a set of numerical examples that include results on an actual case study from the automotive industry.

A novel adaptive strategy, dubbed m-adaptation, is developed for solving the acoustic wave equation (in the time domain) on square meshes. The finite element, the finite difference and a few other more recent methods are shown to be particular members of the mimetic family. Analysis of the parametric family of mimetic discretization methods is performed to find the optimal member that eliminates the numerical dispersion at the fourth-order (as in Ref. 1) and the numerical anisotropy at the sixth-order (higher than in Ref. 1). The stability condition for the optimal method is derived that turns out to be comparable to the classical Courant condition. The numerical experiments show that the new approach is consistently better than the classical methods for reducing a long-time integration error.