Exact solution and the multidimensional Godunov scheme for the acoustic equations

The acoustic equations derived as a linearization of the Euler equations are a valuable system for studies of multi-dimensional solutions. Additionally they possess a low Mach number limit analogous to that of the Euler equations. Aiming at understanding the behaviour of the multi-dimensional Godunov scheme in this limit, first the exact solution of the corresponding Cauchy problem in three spatial dimensions is derived. The appearance of logarithmic singularities in the exact solution of the 4-quadrant Riemann Problem in two dimensions is discussed. The solution formulae are then used to obtain the multidimensional Godunov finite volume scheme in two dimensions. It is shown to be superior to the dimensionally split upwind/Roe scheme concerning its domain of stability and ability to resolve multi-dimensional Riemann problems. It is shown experimentally and theoretically that despite taking into account multi-dimensional information it is, however, not able to resolve the low Mach number limit.

Effective Acoustic Equations for a Layered Material Described by the Fractional Kelvin-Voigt Model

The paper is devoted to the construction of effective acoustic equations for a two-phase layered viscoelastic material described by the Kelvin–Voigt model with fractional time derivatives. For this purpose, the theory of two-scale convergence and the Laplace transform with respect to time are used. It is shown that the effective equations are partial integro-differential equations with fractional time derivatives and fractional exponential convolution kernels. In order to find the coefficients and the convolution kernels of these equations, several auxiliary cell problems are formulated and solved

Recovering Density and Speed of Sound Coefficients in the 2D Hyperbolic System of Acoustic Equations of the First Order by a Finite Number of Observations

We consider the coefficient inverse problem for the first-order hyperbolic system, which describes the propagation of the 2D acoustic waves in a heterogeneous medium. We recover both the denstity of the medium and the speed of sound by using a finite number of data measurements. We use the second-order MUSCL-Hancock scheme to solve the direct and adjoint problems, and apply optimization scheme to the coefficient inverse problem. The obtained functional is minimized by using the gradient-based approach. We consider different variations of the method in order to obtain the better accuracy and stability of the appoach and present the results of numerical experiments.

Taking into account the fluid saturation of bottom sediments in marine seismic survey problem

The problem of the numerical simulation of the seismic response from the marine bottom is considered. Acoustic equations are used for the description of the water dynamic behavior. Bottom sediments are described with the porous fluid-filled medium. The Dorovsky model is used. The algorithm for solving all hyperbolic equation systems with the grid-characteristic method was proposed. The distinctive feature of this approach is the ability to set explicitly necessary contact conditions between media with different rheology.

Numerical simulation of aberrated medical ultrasound signals

Transcranial ultrasound examination is hampered by the skull which acts as an irregular aberrator of the ultrasound signal. Numerical recovery of the ultrasound field can help in elimination of aberrations induced by the skull. In this paper, we address the simulation of medical phantom scanning through silicon aberrators with wave notching. The numerical model is based on the 2D acoustic equations which are solved by the wavefront construction raytracing method. Numerical B-scan images are compared with experimental B-scan images.

Stochastic Response Analysis of a Built-Up Vibro-Acoustic System with Parameter Uncertainties

In this paper, the quantification of uncertainty effects on stochastic responses of interior vibro-acoustic interaction systems with moderate geometry complexities and uncertain design parameters is investigated. A variational-based stochastic model is developed to predict the vibro-acoustic responses submitted to probabilistic parameters, and it is illustrated by application to a built-up system consisting of an irregular acoustic cavity backed up a plate assembly. The model is derived from the combination of the multi-domain Rayleigh–Ritz approach, used to solve the deterministic structural–acoustic equations, together with the generalized polynomial chaos expansion (gPCE) to represent propagation of uncertainty and estimate the statistical characteristics of the responses. Benchmark comparisons are made with the Monte Carlo simulations (MCS) to demonstrate the tremendous computational advantage of the present methodology. Uncertainty analysis is performed to ascertain the influence of random parameters on responses. The results reveal that system uncertainty is significant enough to affect the vibro-acoustic behaviors and hence the consideration of input uncertainties is necessary in analyses and designs to ensure the sustainable system performance.