Journal of Computational Acoustics

A multidomain pseudospectral time-domain (PSTD) method is developed for acoustic wave equations in lossy media. The method is based on the spectral derivative operator approximated by Chebyshev Lagrange polynomials. In this multidomain scheme, the computational domain is decomposed into a set of subdomains conformal to the problem geometry. Each curved subdomain is then mapped onto a cube in the curvilinear coordinates so that a tensor-product Chebyshev grid can be utilized without the staircasing error. An unsplit-field, well-posed PML is developed as the absorbing boundary condition. The algorithm is validated by analytical solutions. The numerical solutions show that this algorithm is efficient for simulating acoustic wave phenomena in the presence of complex objects in inhomogeneous media. To our knowledge, the multidomain PSTD method for acoustics is a new development in three dimensions, although in two dimensions the method can be made equivalent to the two-dimensional method in electromagnetics.

The inverse problem of determining the size, shape and orientation of a submerged object using the scattered field data is studied. Based on the physical optics approximate, the profile function of the object is found directly proportional to its ramp response that is the second integral of the impulse response. Through analyzing the feature of the ramp response in different computed frequency ranges, it is found that the low-frequency data are essential to the shape of the underwater object while the high-frequency data are very important to the size of the object. Therefore, when employing the high-frequency data to compute the ramp response, the edge of the object can only be highlighted in the illuminated region at certain aspect. Based on this finding, a new method is developed to estimate the size of underwater objects. The present method uses different frequency ranges to determine different parameters of the underwater objects so as to achieve the best accuracy. A number of examples are presented to demonstrate the effectiveness of the present method in using the ramp response technique to identify the size of both rigid and elastic bodies.

The numerical scheme for the analysis of the acoustic wave transformation in materials with nonlinearity hysteresis and end-point memory is developed. Both numerical and analytical predictions are obtained concerning mixing of a wave at fundamental frequency (ω-wave) and a wave at doubled frequency (2ω-wave) in the materials with hysteretic quadratic nonlinearity. The observed wave spectrum broadening is found to be in qualitative agreement with the selection rules for the multi-phonon processes in this type of materials. The predicted transformation of an initially complex wave (with four extrema over a period) into a simplex wave (with two extrema over a period) in nonlinear propagation is found to be one of the manifestations of the nonlinear hysteretic absorption. It is demonstrated that at short propagation distances the interaction of the ω- and 2ω-waves is mainly through the mechanism of the nonlinear hysteretic absorption and is not strongly influenced by the process of higher harmonics generation and their inverse influence on the input waves. The regimes of the induced and self-induced transparency are predicted. The influence of the transition from the simplex wave to complex wave emission (or vice versa) on the processes of the induced absorption and transparency is identified.

The observed time-of-arrival patterns from a number of long-range ocean acoustic propagation experiments show early geometrical-like arrivals followed by a crescendo of energy that propagates along the sound channel axis and is not resolved into individual arrivals. To describe in a simple model case the interference of near-axial waves which results in forming the so-called axial wave and propose formulas for the axial wave in more general cases, the two-dimensional reference point source problem for the parabolic index of refraction squared is investigated. Using the method proposed by V. Buldyrev, the integral representation for the exact solution is transformed in such a way to extract ray summands corresponding to rays radiated from the source at angles less than a certain angle, the axial wave, and a term corresponding to the sum of all the rays having launch angles greater than the indicated angle. Numerical results for the axial wave and the last term are obtained for parameters corresponding to long-range ocean acoustic propagation experiments.

The paper derives the finite element equation for acoustic wave in time domain and presents a transparent-plus-attenuation boundary condition. Forward modeling demonstrates that the boundary condition absorbs boundary reflection wave very well. On these bases, we derive the equation satisfied by elements of Jacobi matrix used in the inversion of the physical property parameters of acoustic media. In fact, the equation is the same as that of forward modeling in form. Only the right force item is different. So with the same method of forward modeling, we can get the elements of Jacobi matrix. Because the elements are variable with time and the present inversion does not permit too many unknowns. We integrate the finite elements with the same physical property as one unknown structure unit (for example, a horizontal layer or an oblique layer, etc.) and inverse the physical property parameters of these unknown structure units instead all element's unknown parameters. The method greatly reduces calculation time and saves computer memory. Also, it improves the accuracy of the inversion results and improves the stability of the solving process. The inversion equations are solved with QR decomposition method. Model results prove that the full wave equation inversion method in time domain is effective.

Cubic serendipity elements have been implemented into a nonuniform duct model of acoustic propagation in a moving medium. This model uses a convective potential formulation derived from the inviscid linearized mass and momentum equations. The model requires post-processing to calculate acoustic pressure. These elements outperform the quadratic serendipity elements in terms of computational efficiency based on visual observations and error norm analysis of acoustic pressure. CPU time reduction of up to 40% has been observed without sacrificing accuracy. Any penalty in numerical accuracy incurred by using serendipity elements rather than Lagrangian elements is far outweighed by the gains in dimensionality. The computational gains for calculation of acoustic potential are considerably less. Analytical expressions for the modal and convective effects on the propagating wavelength have been formulated and compared to numerical results. Preliminary assessment of alternative finite element approaches to model the convective potential formulation has been conducted. Stabilization and wave approximation methods have been implemented to solve simple one-dimensional problems.

A study is made of computational accuracy and efficiency for finite element modeling of acoustic radiation in a nonuniform moving medium. For a given level of accuracy for acoustic pressure, cubic serendipity elements are shown to require a less dense mesh than quadratic elements. These elements have been applied to the near field of inlet and aft acoustic radiation models for a turbofan engine and they yield considerable reduction in the dimensionality of the problem without sacrificing accuracy. The results show that for computation of acoustic pressure the cubic element formulation model is superior to the quadratic. Performance gains in computation of acoustic potential are not as significant. In the external radiated field, improved convergence using cubic serendipity elements is shown by comparison of contours of constant pressure magnitude.

In this work, we are interested in the modelling of the acoustic attenuation of exhaust mufflers including perforated ducts, and its numerical computation. The study is worked out in harmonic time regime, for the two-dimensional case. The hole diameter and the center-to-center distance between consecutive holes are supposed of same order, and small compared to the size of the muffler. The formulation is derived by using multiscale techniques and matching the asymptotic expansions. The numerical method couples finite elements in the muffler with modal decomposition in the inlet and the outlet of the duct.