Numerical simulation of oblique and multidirectional wave propagation and breaking on steep slope based on FEM model of Boussinesq equations

Creating a representative numerical simulation of the propagation and breaking of waves along slopes is an important problem in engineering design. Most studies on wave breaking have focused on the propagation of normal incident waves on gentle slopes. In practice, however, waves on steep slopes are obliquely incident or multidirectional irregular waves. In this paper, the eddy viscosity term is introduced to the momentum equation of the improved Boussinesq equations to model wave dissipation caused by breaking and friction, and a numerical model based on an unstructured finite element method (FEM) is established based on the governing equations. It is applied to simulate wave propagation on a steep slope of 1:5. Parallel physical experiments are conducted for comparative analysis that considered a large number of cases, including those featuring of normal and oblique incident regular and irregular waves, and multidirectional waves. The heights of the incident wave increase for different periods to represent different kinds of waves breaking. Based on examination, the effectiveness and accuracy of the numerical model is verified through a comprehensive comparison between the numerical and the experimental results, including in terms of variation in wave height, wave spectrum, and nonlinear parameters. Satisfactory agreement between the numerical and experimental values shows that the proposed model is effective in representing the breaking of oblique incident regular waves, irregular waves, and multidirectional incident irregular waves. However, the initial threshold of the breaking parameter η_t^(I) takes different values for oblique and multidirectional waves. This needs to be paid attention when the breaking of waves is simulated using the Boussinesq equations.     

Self-adaptive FEM numerical modeling of the mild-slope equation

Based on the linear wave theory, the mild-slope equation (MSE) is a preferred mathematical model to simulate nearshore wave propagation. A numerical model to solve the MSE is developed here on the basis of a self-adaptive finite element model (FEM) combined with an iterative method to determine the wave direction angle to the boundary and thus to improve the treatment of the boundary conditions. The numerical resolution of the waves into ideal domains and multidirectional waves through a breakwater gap shows that the numerical model developed here is effective in representing wave absorption at the absorbing boundaries and can be used to simulate multidirectional wave propagation. Finally, the simulated wave distribution in a real harbor shows that the numerical model can be used for engineering practice.     

A generalized dynamic model of nanoscale surface acoustic wave sensors and its applications in Love wave propagation and shear-horizontal vibration

A generalized dynamic model to depict the wave propagation properties in surface acoustic wave nano-devices is established based on the Hamilton's principle and variational approach. The surface effect, equivalent to additional thin films, is included with the aid of the surface elasticity, surface piezoelectricity and surface permittivity. It is demonstrated that this generalized dynamic model can be reduced into some classical cases, suitable for macro-scale and nano-scale, if some specific assumptions are utilized. In numerical simulations, Love wave propagation in a typical surface acoustic wave device composed of a piezoelectric ceramic transducer film and an aluminum substrate, as well as the shear-horizontal vibration of a piezoelectric plate, is investigated consequently to qualitatively and quantitatively analyze the surface effect. Correspondingly, a critical thickness that distinguishes surface effect from macro-mechanical behaviors is proposed, below which the size-dependent properties must be considered. Not limited as Love waves, the theoretical model will provide us a useful mathematical tool to analyze surface effect in nano-devices, which can be easily extended to other type of waves, such as Bleustein-Gulyaev waves and general Rayleigh waves.     

Effects of initial stress on guided waves in orthotropic functionally graded plates

Because of the limitation of the manufacturing technology, initial stress in functionally graded materials (FGM) and structures is inevitable. Based on the theory of “Mechanics of Incremental Deformations”, the guided wave propagation in FGM plates under gravity, homogeneous initial stress in the thickness direction and inhomogeneous initial stress in the wave propagation direction is investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. The convergence of the polynomial series method is discussed through the numerical examples. The effects of the initial stress on the Lamb-like wave and on the SH wave are investigated respectively and the numerical results show they are quite distinct. The effect of the gravity on the wave propagation can be ignored. The effects of the initial stress in the thickness direction are very different from those of the initial stress in the wave propagation direction, both on the dispersion curves and on the displacement and stress distributions.     

基于小波的一维线性波动方程的数值解法

小波的紧支性，正交性和二阶以上的Daubechies尺度函数及小波函数的可微性，很适合作为Galerkin方法的基函数。加上快速小波变换，这已成为数值求解偏微分方程的有力工具，本文利用微分算子的小波表示。对一维线性波动方程的小波数值解法进行了讨论。最后用实例说明了波波方法的有效性和快速性。     

Estimation of interface damage of fiber-reinforced composites

The estimation of interface damage of fiber-reinforced composites based on the propagation constants of coherent waves is studied in this paper. First, the relation between the interface damage and the propagation constants is investigated by using the theory of multiple scattering. Next, single and multiple scatterings in the composites in the case of incident P, SV, and SH waves are considered. The propagation constants of coherent waves are computed numerically, and the influence of interface damage on them is discussed. Then, based on the relation between the propagation constants and the interface damage, an inverse method to estimate the interface damage is proposed. Finally, a numerical example is given. The numerical results are obtained by using synthetic experimental data and the genetic algorithm. It is shown by the numerical example that the interface damage can be approximately estimated from the wave propagation constants measured with various degrees of accuracy.     

Detailed simulation of the pulsating detonation wave in the shock-attached frame

The paper is devoted to the numerical investigation of the stability of propagation of pulsating gas detonation waves. For various values of the mixture activation energy, detailed propagation patterns of the stable, weakly unstable, irregular, and strongly unstable detonation are obtained. The mathematical model is based on the Euler system of equations and the one-stage model of chemical reaction kinetics. The distinctive feature of the paper is the use of a specially developed computational algorithm of the second approximation order for simulating detonation wave in the shock-attached frame. In distinction from shock capturing schemes, the statement used in the paper is free of computational artifacts caused by the numerical smearing of the leading wave front. The key point of the computational algorithm is the solution of the equation for the evolution of the leading wave velocity using the second-order grid-characteristic method. The regimes of the pulsating detonation wave propagation thus obtained qualitatively match the computational data obtained in other studies and their numerical quality is superior when compared with known analytical solutions due to the use of a highly accurate computational algorithm.     

Experimental evaluation of phase velocities and tortuosity in fluid saturated highly porous media

In the current contribution, we present a novel method for the determination of the high frequency tortuosity parameter, α_∞ in high porous media. Therefore, time-domain measurements of ultrasonic signals are performed with a transmission technique. Aluminium foams with different pore fluids will be under the scope of experimental investigation. Finally, the experimental results are compared with analytical wave propagation tests. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling concept and numerical simulation of ultrasonic wave propagation in a moving fluid-structure domain based on a monolithic approach

In the present study, we propose a novel multiphysics model that merges two time-dependent problems – the Fluid-Structure Interaction (FSI) and the ultrasonic wave propagation in a fluid-structure domain with a one directional coupling from the FSI problem to the ultrasonic wave propagation problem. This model is referred to as the “eXtended fluid-structure interaction (eXFSI)” problem. This model comprises isothermal, incompressible Navier–Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The ultrasonic wave propagation problem comprises monolithically coupled acoustic and elastic wave equations. To ensure that the fluid and structure domains are conforming, we use the ALE technique. The solution principle for the coupled problem is to first solve the FSI problem and then to solve the wave propagation problem. Accordingly, the boundary conditions for the wave propagation problem are automatically adopted from the FSI problem at each time step. The overall problem is highly nonlinear, which is tackled via a Newton-like method. The model is verified using several alternative domain configurations. To ensure the credibility of the modeling approach, the numerical solution is contrasted against experimental data.     

三维复合介质波动方程多尺度辛几何算法

本文针对三维复合介质波动方程,提出了一类多尺度辛几何算法.其主要内容有:1.快速振荡系数三维波动方程的多尺度渐近分析与收敛性估计;2.均匀化波动方程的辛几何算法;3.多尺度辛几何算法与数值实验结果.     

Determining the limits of geometrical tortuosity from seepage flow calculations in porous media.

Recent investigations have found a distinct correlation of effective properties of porous media to sigmoidal functions, where one axis is the Reynolds number Re and the other is the effective property dependent of Re, Θ_i = S_i(Re). One of these properties is tortuosity. At very low Re (seepage flow), there is a characteristic value of tortuosity, and it is the upper horizontal asymptote of the sigmoidal function. With higher values of Re (transient flow) the tortuosity value decreases, until a lower asymptote is reached (turbulent flow). Estimations of this parameter have been limited to the low Reynolds regime in the study of porous media. The current state of the art presents different numerical measurements of tortuosity, such as skeletization, centroid binding, and arc length of streamlines. These are solutions for the low Re regime. So far, for high Re, only the arc length of stream lines has been used to calculate tortuosity. The present approach involves the simulation of fluid flow in large domains and high Re, which requires numerous resources, and often presents convergence problems. In response to this, we propose a geometrical method to estimate the limit of tortuosity of porous media at Re → ∞, from the streamlines calculated at low Re limit. We test our method by calculating the tortuosity limits in a fibrous porous media, and comparing the estimated values with numerical benchmark results. Ongoing work includes the geometric estimation of different intrinsic properties of porous media. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modeling of seismic and acoustic-gravity waves propagation in an “Earth-Atmosphere” model in the presence of wind in the air

In this paper, an effective numerical algorithm for 2.5D seismic and acoustic-gravitational wave propagation is applied to a combined “Earth-Atmosphere” model in the presence of wind in the air. Seismic wave propagation in an elastic half-space is described by a system of first-order dynamic equations of elasticity theory. The propagation of acoustic-gravitational waves in the atmosphere in the presence of wind is described by the linearized Navier-Stokes equations. The algorithm is based on the integral Laguerre transform with respect to time, the finite integral Fourier transform with respect to a spatial coordinate combined with a finite difference method for the reduced problem.     

Discontinuity Waves, Shock Formation and Critical Temperature in Crystals

The propagation of discontinuity waves in a rigid heat conductor at low temperatures is studied by using a generalized non-linear Maxwell–Cattaneo equation developed in the framework of extended thermodynamics. The critical time (i.e., the instant in which a shock wave formation occurs) is evaluated in both cases of infinite and finite heat conductivity. The critical temperature θ̃, pointed out in our previous papers concerning the propagation of shock and simple waves, once more plays an important role: in fact, now it determines two different regimes for the wave propagation and this phenomenon, from a mathematical point of view, is related to the loss of the genuine non-linearity when θ = θ̃. In the last sections some numerical results are given and a brief analysis about the evolution of a possible initial wave profile is performed.     

Numerical analysis of wave propagation in fluid-filled deformable tubes

The theory of Biot describing wave propagation in fluid saturated porous media is a good effective approximation of a wave induced in a fluid-filled deformable tube. Nonetheless, it has been found that Biot's theory has shortcomings in predicting the fast P-wave velocities and the amount of intrinsic attenuation. These problems arises when complex mechanical interactions of the solid phase and the fluid phase in the micro-scale are not taken into account. In contrast, the approach proposed by Bernabe does take into account micro-scopic interaction between phases and therefore poses an interesting alternative to Biot's theory. A Wave propagating in a deformable tube saturated with a viscous fluid is a simplified model of a porous material, and therefore the study of this geometry is of great interest. By using this geometry, the results of analytical and numerical results have an easier interpretation and therefore can be compared straightforward. Using a Finite Difference viscoelastic wave propagation code, the transient response was simulated. The wave source was modified with different characteristic frequencies in order to gain information of the dispersion relation. It was found that the P-wave velocities of the simulations at sub-critical frequencies closely match those of Bernabe's solution, but at over-critical frequencies they come closer to Biot's solution. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Singular boundary method based on time‐dependent fundamental solutions for active noise control

Active noise control is an efficient strategy of noise control. A numerical wave shielding model to inhibit wave propagation, which can be considered as an extension of traditional active noise control, is established using the singular boundary method using time‐dependent fundamental solutions in this study. Two empirical formulas to evaluate the origin intensity factors with Dirichlet and Neumann boundary conditions are derived respectively. In comparison with other similar numerical methods, the method can obtain highly accurate results using very few boundary nodes and small CPU time. These meet the major technical requirements of simulation of active noise control. The subsequent numerical experiments show that the proposed model can shield efficiently from the wave propagation for both inner and exterior problems. By applying the newly derived empirical formulas, the CPU time of the singular boundary method is further reduced significantly, which makes the method a competitive new and efficient meshless method. In addition, the singular boundary method makes active noise control in an online manner via time‐dependent fundamental solutions as its basis functions.     

Experimental investigation of compression waves in polyurethane foam

The behavior of porous foam plastics under impact loading has been experimentally investigated with reference to the example of polyurethane foam. The specially designed loading mechanism made it possible to measure the propagation velocity of the compression wave, its dependence on the impact velocity, and the absorption. The impact loading velocities varied from 2.5 to 13 m/sec. The results obtained are discussed from the standpoint of nonlinear acoustics.Leningrad Zhdanov State University. Translated from Mekhanika Polimerov, No. 1, pp. 160–162, January–February, 1970.     

Reflected-refracted and head sh waves formed on a thin layer that is in welded contact with two elastic half-spaces

The reflection and refraction of SH waves by an elastic layer sandwiched between two elastic half-spaces are studied by using the numerical simulation on the basis of contour integration in the complex plane of the horizontal component of the slowness vector. The propagation of body, channel, head, and screened body waves are simulated in time and spectral domains. The wave fields associated with the propagation in the layer have strong attenuation, provided that the wave length is smaller than the value of the thickness of the layer. The stationary wave field of such waves is of resonance nature. Moreover, the maximum of the modulus of the spectral function is shifted to higher frequences as the epicentric distance increases. Thus, the attenuation of such waves depends on spectral characteristics of a source-receiver system. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 225, 1997, pp. 91–120. Translated by T. N. Surkova.     

An unstructured FEM model based on Boussinesq equations and its application to the calculation of multidirectional wave run-up in a cylinder group

In this paper, a numerical model based on the improved Boussinesq equations derived by Beji and Nadaoka [5] is first developed using unstructured finite element technique. A locally rotated coordinate system is introduced to improve the treatment for the fully reflective boundaries whose orientation does not coincide with the coordinate system. The Adams–Bashforth–Moulton predictor–corrector scheme is used for time integration. Typical examples are employed to validate the numerical model. Based on the developed model, multidirectional wave propagation through a cylinder group is numerically calculated and the effects of the wave directionality on the waves in the group and the wave run-up on the cylinders are investigated. Numerical results show that the wave directionality has considerable effect on the wave run-up in the cylinder group.     

Application of time reverse modeling on ultrasonic non-destructive testing of concrete

Time reverse modeling (TRM) is applied to localize and characterize acoustic emission using a numerical concrete model. Aim is to transform a method within exploration geophysics to non-destructive testing. In contrast to previous time reverse applications, no single event or first onset time identification is applied. The method is described from a mathematical point of view. So-called source TRM with limited knowledge of boundary values is compared with so-called full TRM where a complete set of boundary conditions is used. The resulting localization accuracy of both approaches is similar. With a known three-dimensional analytical solution we demonstrate the applicability and the limitations of the two-dimensional wave propagation method solving the elastodynamic wave equation. With the help of CT images we are able to digitalize a concrete specimen and to verify a used numerical concrete model. TRM localization using this highly scattering material is feasible using the rotated staggered finite-difference method. We demonstrate the localization of acoustic emission with a limited number of sensors and using effective elastic properties. Source characteristics can also be recovered. Goal is to apply our method to acoustic emissions measured during experiments carried out on concrete and reinforced concrete specimen.     

Propagation of wave packets through resonant quantum systems

We use a previously proposed modified saddle point method to describe the tunneling of a rectangular wave packet through a resonant quantum system. We calculate the shape of the wave packet obtained at the quantum system output analytically for different values of the level width. The result of propagation is a wave packet that is the superposition of complementary error functions. Comparing the result with the exact numerical solution obtained without using any asymptotic methods shows a rather good coincidence. We study the propagation of Gaussian and rectangular wave packets in detail for large values of the resonance level width.