Four dimensional wave propagation simulation in liquid metal with realistic thermal fluctuation.

In this paper, we performed a four-dimensional numerical simulation to calculate wave propagation in a thermal fluctuating liquid metal in order to obtain detailed knowledge on a wave propagation in coolant material of a Sodium-cooled Fast reactor (SFR). The wave and the medium are described in three spatial and one temporal dimensions. We made use of a massive data set to describe the fluctuating situation of the medium. This data set was provided by Computational Fluid Dynamics (CFD) with a Large-Eddy Simulation (LES) model, which calculated the temperature field with a higher spatial resolution than Reynolds-Averaged Navier-Stokes turbulence models (RANS). This data set was furthermore obtained from other studies on a numerical and physical experiment called PLAJEST that created mixing jets of liquid metal in order to simulate the status of running SFRs. Because of the limitation of computational resources, previous acoustic studies applied to such a medium could only use the spatial-temporally averaged fluctuating heterogeneity of a medium calculated by RANS turbulence model. This limitation may overlook wave fluctuation because of the difference of the resolution between computational fluid dynamics and acoustic wave length. Our numerical effort allowed us to study the most realistic acoustic wave propagation in liquid metal than in any former studies. A new important result was obtained in this work as we demonstrated that ultrasonic measurements could follow thermal-hydraulic fluctuations in an opaque liquid with high sensitivity. This result was obtained through the definition of descriptors to analyze medium fluctuations along the wave path. We defined a very new measurement index, called hereafter Cumulated Temperature Fluctuation Intensity (CTFI), to correlate the variations in the thermal-hydraulic conditions to the wave variations. We demonstrated a good correlation between the second derivative of this index and the second derivative of several acoustic measurements, then we discussed the easiest measurements to be used in practice in an industrial setup.

Simulations of ultrasonic wave propagation in concrete based on a two-dimensional numerical model validated analytically and experimentally.

Several non-destructive evaluation techniques to characterize concrete structures are based on ultrasonic wave propagation. The interpretation of the results is often limited by the scattering phenomena between the ultrasonic wave and the high concentration aggregates contained in the cement matrix. Numerical simulations allow for further insights. This study aims to build a two-dimensional numerical model in order to reproduce and interpret ultrasonic wave propagations in concrete. The model is built in a spectral-element software package called SPECFEM2D. The validation of the numerical tool is based on the use of resin samples containing different amount of aluminum rods from low (5%) to high concentration (40%), the last one being representative of aggregate concentration in concrete. These samples are characterized using an ultrasonic testing bench (ultrasonic water tank) from 150 kHz to 370 kHz. The measured results are analyzed in terms of phase velocity and attenuation which are the main parameters of coherent waves. As homogenization models such as the Waterman-Truell or Conoir-Norris models are usually used to model coherent waves in two-phase systems, we also compare the experimental and numerical results against them. We confirm that the use of these homogenization models is limited to low concentration of scattering phase, which is not adapted to applications to concrete. Finally, we use our numerical tool to carry out a parametric study on scatterer concentration, shape, orientation and size distribution of aggregates in concrete. We show that aggregate orientation has an influence on coherent wave parameters, but aggregate shape has not.

Broadband transmission losses and time dispersion maps from time-domain numerical simulations in ocean acoustics.

In this letter, a procedure for the calculation of transmission loss maps from numerical simulations in the time domain is presented. It can be generalized to arbitrary time sequences and to elastic media and provides an insight into how energy spreads into a complex configuration. In addition, time dispersion maps can be generated. These maps provide additional information on how energy is distributed over time. Transmission loss and time dispersion maps are generated at a negligible additional computational cost. To illustrate the type of transmission loss maps that can be produced by the time-domain method, the problem of the classical two-dimensional upslope wedge with a fluid bottom is addressed. The results obtained are compared to those obtained previously based on a parabolic equation. Then, for the same configuration, maps for an elastic bottom and maps for non-monochromatic signals are computed.

Ultrasonic computed tomography based on full-waveform inversion for bone quantitative imaging.

We introduce an ultrasonic quantitative imaging method for long bones based on full-waveform inversion. The cost function is defined as the difference in the L 2-norm sense between observed data and synthetic results at a given iteration of the iterative inversion process. For simplicity, and in order to reduce the computational cost, we use a two-dimensional acoustic approximation. The inverse problem is solved iteratively based on a quasi-Newton technique called the Limited-memory Broyden-Fletcher-Goldfarb-Shanno method. We show how the technique can be made to work fine for benchmark models consisting of a single cylinder, and then five cylinders, the latter case including significant multiple diffraction effects. We then show pictures obtained for a tibia-fibula bone pair model. Convergence is fast, typically in 15 to 30 iterations in practice in each frequency band used. We discuss the so-called 'cycle skipping' effect that can occur in such full waveform inversion techniques and make them remain trapped in a local minimum of the cost function. We illustrate strategies that can be used in practice to avoid this. Future work should include viscoelastic materials rather than acoustic, and real data instead of synthetic data.

An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics.

The numerical simulation of acoustic waves in complex three-dimensional (3D) media is a key topic in many branches of science, from exploration geophysics to non-destructive testing and medical imaging. With the drastic increase in computing capabilities this field has dramatically grown in the last 20 years. However many 3D computations, especially at high frequency and/or long range, are still far beyond current reach and force researchers to resort to approximations, for example, by working in two dimensions (plane strain) or by using a paraxial approximation. This article presents and validates a numerical technique based on an axisymmetric formulation of a spectral finite-element method in the time domain for heterogeneous fluid-solid media. Taking advantage of axisymmetry enables the study of relevant 3D configurations at a very moderate computational cost. The axisymmetric spectral-element formulation is first introduced, and validation tests are then performed. A typical application of interest in ocean acoustics showing upslope propagation above a dipping viscoelastic ocean bottom is then presented. The method correctly models backscattered waves and explains the transmission losses discrepancies pointed out in F. B. Jensen, P. L. Nielsen, M. Zampolli, M. D. Collins, and W. L. Siegmann, Proceedings of the 8th International Conference on Theoretical and Computational Acoustics (ICTCA) (2007). Finally, a realistic application to a double seamount problem is considered.

A perfectly matched layer for fluid-solid problems: Application to ocean-acoustics simulations with solid ocean bottoms.

A time-domain Legendre spectral-element method is described for full-wave simulation of ocean acoustics models, i.e., coupled fluid-solid problems in unbounded or semi-infinite domains, taking into account shear wave propagation in the ocean bottom. The technique can accommodate range-dependent and depth-dependent wave speed and density, as well as steep ocean floor topography. For truncation of the infinite domain, to efficiently absorb outgoing waves, a fluid-solid complex-frequency-shifted unsplit perfectly matched layer is introduced based on the complex coordinate stretching technique. The complex stretching is rigorously taken into account in the derivation of the fluid-solid matching condition inside the absorbing layer, which has never been done before in the time domain. Two implementations are designed: a convolutional formulation and an auxiliary differential equation formulation because the latter allows for implementation of high-order time schemes, leading to reduced numerical dispersion and dissipation, a topic of importance, in particular, in long-range ocean acoustics simulations. The method is validated for a two dimensional fluid-solid Pekeris waveguide and for a three dimensional seamount model, which shows that the technique is accurate and numerically long-time stable. Compared with widely used paraxial absorbing boundary conditions, the perfectly matched layer is significantly more efficient at absorbing both body waves and interface waves.

Some illustrative examples of the use of a spectral-element method in ocean acoustics.

Some numerical results in the time domain obtained with the spectral-element method are presented in order to illustrate the high potential of this technique for modeling the propagation of acoustic waves in the ocean in complex configurations. A validation for a simple configuration with a known solution is shown, followed by some simulations of the propagation of acoustic waves over different types of ocean bottoms (fluid, elastic, and porous) to emphasize the wide variety of media that can be considered within the framework of this method. Finally, a movie illustrating upslope propagation over a viscoelastic wedge is presented and discussed.

Elastic surface waves in crystals--part 2: cross-check of two full-wave numerical modeling methods.

We obtain the full-wave solution for the wave propagation at the surface of anisotropic media using two spectral numerical modeling algorithms. The simulations focus on media of cubic and hexagonal symmetries, for which the physics has been reviewed and clarified in a companion paper. Even in the case of homogeneous media, the solution requires the use of numerical methods because the analytical Green's function cannot be obtained in the whole space. The algorithms proposed here allow for a general material variability and the description of arbitrary crystal symmetry at each grid point of the numerical mesh. They are based on high-order spectral approximations of the wave field for computing the spatial derivatives. We test the algorithms by comparison to the analytical solution and obtain the wave field at different faces (stress-free surfaces) of apatite, zinc and copper. Finally, we perform simulations in heterogeneous media, where no analytical solution exists in general, showing that the modeling algorithms can handle large impedance variations at the interface.

Elastic surface waves in crystals. Part 1: review of the physics.

We present a review of wave propagation at the surface of anisotropic media (crystal symmetries). The physics for media of cubic and hexagonal symmetries has been extensively studied based on analytical and semi-analytical methods. However, some controversies regarding surfaces waves and the use of different notations for the same modes require a review of the research done and a clarification of the terminology. In a companion paper we obtain the full-wave solution for the wave propagation at the surface of media with arbitrary symmetry (including cubic and hexagonal symmetries) using two spectral numerical modeling algorithms.

The spectral-element method, Beowulf computing, and global seismology.

The propagation of seismic waves through Earth can now be modeled accurately with the recently developed spectral-element method. This method takes into account heterogeneity in Earth models, such as three-dimensional variations of seismic wave velocity, density, and crustal thickness. The method is implemented on relatively inexpensive clusters of personal computers, so-called Beowulf machines. This combination of hardware and software enables us to simulate broadband seismograms without intrinsic restrictions on the level of heterogeneity or the frequency content.