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A fast algorithm for the boundary element method is developed to handle problems in underwater acoustics. The algorithm employs the multipole and local expansions to approximate far-field potentials, and exploits the discrete convolution nature of mapping multipole to local expansions to accelerate the potential evaluation process. The speedup in the solution process is achieved by fast Fourier transform on the multipole and local expansion coefficients on a regular grid. The method is demonstrated by a three-dimensional underwater acoustics scattering problem, and it is found to achieve accurate results with relatively low order of expansion.

Range-dependency in the background sound speed structure for deep ocean propagation scenarios is typical. Here a special case is considered when there is a gradual transition between single and double minimum sound speed profiles. Ray stability, an important measure for many applications, is analyzed. It is done by studying the unperturbed autonomous ray equations in the quasistatic limit. The wave guide is mapped out in terms of constant action curves in the vertical plane of propagation, which reveals a bifurcation effect in the studied wave guides. Conditions for the constancy or a sudden change of the action of a ray trajectory, an effect that impacts on the "use" of a ray, are given.

Parabolic equations written in terms of energy flux are inherently immune to the problem of energy conservation at vertical interfaces. Mikhin [J. Comp. Acoust. 9 (2001) 183–203] achieved exact reciprocity and energy conservation in a finite-difference PE model following this approach. However, his model used the implicit Crank–Nicolson scheme in range that requires a small range step for accurate solution. The present paper generalizes the exponential propagator of Collins [J. Acoust. Soc. Am. 93 (1993) 1736–1742] to solve the energy-flux PE. The obtained solution remains strictly reciprocal and energy conserving, while allowing large range steps. The numerical efficiency is improved by one or two orders of magnitude. A technique is proposed to calculate the acoustic pressure within the large steps, so the solution combines fast advance in range with dense range sampling. Numerical examples are provided.

We compare the results of a coupled mode method with those of a finite element method and also of COUPLE on two test problems of sound propagation and scattering in cylindrically symmetric, underwater, multilayered acoustic waveguides with range-dependent interface topographies. We observe, in general, very good agreement between the results of the three codes. In some cases in which the frequency of the harmonic point source is such that an eigenvalue of the local vertical problem remains small in magnitude and changes sign several times in the vicinity of the interface nonhomogeneity, the discrepancies between the results of the three codes increase, but remain small in absolute terms.

The acoustic propagation problem is modeled via the parabolic approximation. The physical domain consists of the water column with a horizontal water–bottom interface and the bottom region consists of N-strata with horizontal interfaces. The computational domain is restricted to the water column, while the stratified bottom region is modeled by a nonlocal boundary condition applied along the water–bottom interface, and having the form of a Neumann to Dirichlet map (NtD). The discrete analog of the NtD has been implemented in a finite difference scheme for the general wide angle PE model, and successfully tested for several benchmark problems. The stratification of the media can be either physical, e.g. sediment formulation in the bottom, or artificial/computational, e.g. forced by sparse distribution of environmental data measurements in the water column. It should be emphasized that the sound speed may vary from layer to layer, but is constant within each layer. The proposed NtD map can be used in geoacoustic inversion via the optimal control adjoint method.

We extend the Huygens wavefront tracing algorithm, which is a part of an open source Madagascar project, to sound propagation in inhomogeneous, moving media and apply it to a series of benchmark tasks. One set of tasks admits exact analytic solutions and serves the purpose of validation of the new algorithm. Another set of calculations demonstrates applicability of the algorithm to the studies of wavefront dynamics and stability in ocean and atmospheric acoustics. The method is based on a system of differential equations equivalent to the eikonal equation, but formulated in the ray coordinate system. In this paper, we present a first-order, two-dimensional discretization scheme that is interpreted very simply in terms of the Huygens' principle. The method has proved to be a convenient alternative to conventional ray tracing.

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.

We present a numerical implementation of an alternative formulation of the geometrical, or ray, acoustics, where wavefronts rather than rays are the primary objects. Rays are recovered as a by-product of wavefront tracing. The alternative formulation of the geometrical acoustics is motivated, first, by the observation that wavefronts are often more stable than rays at long-range sound propagation, and, second, by a need for computationally efficient modeling of high-frequency acoustic fields in three-dimensionally inhomogeneous, moving or motionless fluids. Wavefronts are found as a finite-difference solution to a system of partial differential equations, which is equivalent to the eikonal equation and is a direct implementation of the intuitive Huygens' wavefront construction. The finite-difference algorithm is an extension of the approach originally developed in the framework of an open source Madagascar project. Benchmark problems, which admit exact, analytic solutions of the eikonal equation, are formulated and utilized to verify the finite-difference wavefront tracing algorithm. Huygens' wavefront tracing (HWT) is applied to modeling sound propagation in three-dimensionally inhomogeneous ocean and atmosphere.

Models of acoustic scattering that predict the echo time history of targets are essential tools for the development of signal processing algorithms in underwater active detection systems. Realistic simulation of echoes requires a multi-frequency evaluation of acoustic scattering. This can be achieved by numerically modeling the surface of the object of interest as a collection of facets and calculating the scattered field using the Helmholtz-Kirchhoff approximation. Time and frequency domain analysis of a simple object (e.g. a sphere) and a complex structure using this technique in monostatic and bistatic configurations are given as examples.

The underwater acoustics is primary and most effective method for underwater object detection and the complex underwater acoustics battlefield environment can be visually described by the three-dimensional (3D) energy field. Through solving the 3D propagation models, the traditional underwater acoustics volume data can be obtained, but it is large amount of calculation. In this paper, a novel modeling approach, which transforms two-dimensional (2D) wave equation into 2D space and optimizes energy loss propagation model, is proposed. In this way, the information for the obtained volume data will not be lost too much. At the same time, it can meet the requirements of data processing for the real-time visualization. In the process of volume rendering, 3D texture mapping methods is used. The experimental results are evaluated on data size and frame rate, showing that our approach outperforms other approaches and the approach can achieve better results in real time and visual effects.

Models of acoustic scattering that predict the echo time history of targets are essential tools for the development of signal processing algorithms in underwater active detection systems. Realistic simulation of echoes requires a multi-frequency evaluation of acoustic scattering. This can be achieved by numerically modelling the surface of the object of interest as a collection of facets and calculating the scattered field using the Helmholtz-Kirchhoff approximation. Time and frequency domain analysis of a simple object (e.g. a sphere) and a complex structure using this technique in monostatic and bistatic configurations are given as examples.