Numerical Simulation and Parallel Computing of Acoustic Wave Equation in Isotropic-Heterogeneous Media

In this paper,we consider the numerical implementation of the 2D wave equation in isotropic-heterogeneous media.The stability analysis of the scheme using the von Neumann stability method has been studied.We conducted a study on modeling the propagation of acoustic waves in a heterogeneous medium and performed numerical simulations in various heterogeneous media at different time steps.Developed parallel code using Compute Unified Device Architecture(CUDA)technology and tested on domains of various sizes.Performance analysis showed that our parallel approach showed significant speedup compared to sequential code on the Central Processing Unit(CPU).The proposed parallel visualization simulator can be an important tool for numerous wave control systems in engineering practice.

The viscous strip approach to simplify the calculation of the surface acoustic wave generated streaming

In recent decades,the importance of surface acoustic waves,as a biocompatible tool to integrate with microfluidics,has been proven in various medical and biological applications.The numerical modeling of acoustic streaming caused by surface acoustic waves in microchannels requires the effect of viscosity to be considered in the equations which complicates the solution.In this paper,it is shown that the major contribution of viscosity and the horizontal component of actuation is concentrated in a narrow region alongside the actuation boundary.Since the inviscid equations are considerably easier to solve,a division into the viscous and inviscid domains would alleviate the computational load significantly.The particles'traces calculated by this approximation are excellently alongside their counterparts from the completely viscous model.It is also shown that the optimum thickness for the viscous strip is about 9-fold the acoustic boundary layer thickness for various flow patterns and amplitudes of actuation.

A Numerical Investigation of the Effect of Boundary Conditions on Acoustic Pressure Distribution in a Sonochemical Reactor Chamber

The intensification of physicochemical processes in the sonochemical reactor chamber is widely used in problems of synthesis,extraction and separation.One of the most important mechanisms at play in such processes is the acoustic cavitation due to the non-uniform distribution of acoustic pressure in the chamber.Cavitation has a strong impact on the surface degradation mechanisms.In this work,a numerical calculation of the acoustic pressure distribution inside the reactor chamber was performed using COMSOL Multiphysics.The numerical results have revealed the dependence of the structure of the acoustic pressure field on the boundary conditions for various thicknesses of the piezoelectric transducer.In particular,the amplitude of the acoustic pressure is minimal in the case of absorbing boundaries,and the attenuation becomes more significant as the thickness of the piezoelectric transducer increases.In addition,reflective boundaries play a significant role in the formation and distribution of zones of maximum cavitation activity.

Numerical simulation of the blast wave of a multilayer composite charge

The numerical simulation of a blast wave of a multilayer composite charge is investigated.A calculation model of the near-field explosion and far-field propagation of the shock wave of a composite charge is established using the AUTODYN finite element program.Results of the near-field and far-field calculations of the shock wave respectively converge at cell sizes of 0.25-0.5 cm and 1-3 cm.The Euler--fluxcorrected transport solver is found to be suitable for the far-field calculation after mapping.A numerical simulation is conducted to study the formation,propagation,and interaction of the shock wave of the composite charge for different initiation modes.It is found that the initiation mode obviously affects the shock-wave waveform and pressure distribution of the composite charge.Additionally,it is found that the area of the overpressure distribution is greatest for internal and external simultaneous initiation,and the peak pressure of the shock wave exponentially decays,fitting the calculation formula of the peak overpressure attenuation under different initiation modes,which is obtained and verified by experiment.The difference between numerical and experimental results is less than 10%,and the peak overpressure of both internal and external initiation is 56.12% higher than that of central single-point initiation.

Numerical Simulation of the Protective Effect of Complex Boundaries Toward Shock Waves in a 3D Explosive Field

A numerical method is presented that simulates 3D explosive field problems. A code MMIC3D using this method can be used to simulate the propagation and reflected effects of all kinds of rigid boundaries to shock waves produced by an explosive source. These numerical results indicate that the code MMIC3D has the ability in computing cases such as 3D shock waves produced by air explosion, vortex region of the shock wave, the Mach wave, and reflected waves behind rigid boundaries.

Numerical simulation of the propagation of electromagnetic waves in ionospheric irregularities

The characteristics of high-frequency(HF)electromagnetic(EM)wave propagation can be affected when EM waves propagate in the ionosphere.When ionospheric irregularities appear in the ionosphere,they can have a serious impact on the propagation of HF EM waves.In this study,the propagation of HF EM waves in ionospheric irregularities was investigated by numerical simulation.First,a twodimensional model of plasma bubbles was used to produce ionospheric irregularities in the ionosphere.A ray-tracing method was then utilized to simulate the propagation of HF radio waves in these ionospheric irregularities.Results showed that the propagation of HF radio waves in the ionosphere was more complex in ionospheric irregularities than without ionospheric irregularities.In addition,corresponding ionograms were synthesized by radio rays propagated in the ionosphere with these irregularities.The synthesized ionograms were then compared with the experimental ionograms recorded by an ionosonde.Results showed that spread F could be simulated on the ionograms when ionospheric irregularities occurred in the ionosphere.This result was consistent with the ionosonde observations.

A simple method of depressing numerical dissipation effects during wave simulation within the Euler model

Numerical wave tanks are widely-acknowledged tools in studying waves and wave-structure interactions. They can generate waves under realistic scales and offers more information on the fluid field. However, most numerical wave tanks suffer from issues known as the numerical dissipation and numerical dispersion. The former causes wave energy to be slowly dissipated and the latter shifts wave frequencies during wave propagation. This paper proposes a simple method of depressing numerical dissipation effects on the basis of solving Euler equations using the finite difference method(FDM). The wave propagation solutions are solved analytically taking into account the influence of the damping terms. The main idea of the method is to append a source term to the momentum equation, whose strength is determined by how strong the numerical damping effect is. The method is verified by successfully depressing numerical effects during the simulation of regular linear waves, Stokes waves and irregular waves. By applying the method, wave energy is able to be close to its initial value after long distance of travel.

THE EFFECTS OF THE PLATEAU'S TOPOGRAPHIC GRADIENT ON ROSSBY WAVES AND ITS NUMERICAL SIMULATION

By using barotropic model equations, this article analyzed the characteristics of Rossby waves, the propaga- tion features of wave energy and the influence of dynamic and thermal effects of the Tibetan Plateau on Rossby waves, and the focus is on discussing the plateau＇s topographic gradient effects on atmospheric Rossby waves. Then based on the WRF3.2 and the NCEP/NCAR FNL reanalysis data, we devised comparative tests of changing the plateau＇s topo- graphic gradient and simulated a process of persistent heavy rain that happened in May 2010 in South China. The re- sults are shown as follows. The Tibetan Platean＇s topography is conducive to the formation of atmospheric Rossby waves, while the platean＇s terrain, its friction and heating effects can all make the atmospheric Rossby waves develop into the planetary waves; The effects of platean＇s north and south slopes on the Rossby wave＇ phase velocity is opposite, and when the slope reached a certain value can the quasi-steady normal fluctuations be generated; Simultaneously, due to the plateau＇s topographic gradient, descending motion appears at the west side of the plateau while ascending motion appears at the east side, and the vertical movement increased with the amplification of topographic gradients. The plateau＇s topographic gradient also obviously amplified the precipitation in South China, and the rainfall area increased with the amplification of topographic gradients and gradually moved from south to north and from west to east, which is conducive to the occurrence and development of convective activities in the downstream areas of the Tibetan Plateau; Moreover, for the plateau＇s dynamic and thermal effects, the Rossby wave＇ propagation shows upstream effects of ener- gy dispersion, so the plateau can then affect the weather in downstream areas. Moreover, the wave group velocity in- creased with the degree of topographic slope.

Numerical Simulation of Surface Acoustic Wave and Detection of Surface Crack in Steel

The surface acoustic wave （SAW） propagating in a sample of steel is simulated by using finite element method （FEM）. The waves are excited by a load function with propagation properties such as phase velocity disper- sion and wide bandwidth. A two-dimensional model consisting of surface defects loaded with a wideband 50--200 M Hz and short time 0.1 gs displacement function is investigated in the time and frequency domains. By transient dy- namic analysis, Fourier transform and dispersion calculation, snapshots of propagating wave and responses from sens- ing points are presented. It is indicated that this supervision approach is sensitive to the surface cracks and reflections.

Numerical Simulation of Wave Field at the Kemena River Mouth in Kalimantan Island

By use of the parabolic equation of numerical simulation of wave which is suitable for large-angle propagation anti Crank-Nicolson differential method, the wave field at the Kemema River mouth has been studied for analysis of sediment movement in the area. In order to reflect wave energy loss accurately, the Bretchneider-Reid formula is quoted and the friction coefficient in the formula is discussed in this paper. The calculation results indicate that the wave becomes a little damped at the mouth of Kemena River influenced by the topography and bottom friction, and the wave at the east beach is higher than that at the west beach, because the east beach extends out.

Numerical simulation of acoustic pressure field for ultrasonic grain refinement of AZ80 magnesium alloy

Ultrasound with different intensities was applied to treating AZ80 alloy melt to improve its solidification structure.The average grain size of the alloy could be decreased from 303 to 148 μm after the ultrasound with intensity of 30.48 W/cm2 was applied.To gain insight into the mechanism of ultrasonic treatment which affected the microstructure of the alloy,numerical simulations were carried out and the effects of different ultrasonic pressures on the behaviors of cavitation bubble in the melt were studied.The ultrasonic field propagation in the melt was also characterized.The results show that samples from different positions are subjected to different acoustic pressures and the effect of grain refinement by ultrasonic treatment for these samples is different.With the increase of ultrasonic intensity,the acoustic pressure is increased and the grain size is decreased generally.

The numerical simulation on electromagnetic wave attenuation characteristics of coal face in time-frequency domain

This paper took the abnormal geological objects with high or low resistivity in the coal face as the background to establish the physical model. 2D forward numerical simulation for electromagnetic wave equation was implemented by the finite-difference scheme. According to the simulative results, the attenuation-absorption coefficient were calculated respectively based on field intensity and frequency shift parameter. Research result indicates, when coal-bed contains high electric resistivity geological abnormal object or low electric resistivity geological abnormal object, absorption attenuation function researched by frequency shift parameter of electromagnetic wave signal is more sensitive than by electromagnetic field intensity parameter.

Numerical Simulation of the Three-Dimensional Wave-Induced Currents on Unstructured Grid

By coupling the three-dimensional hydrodynamic model with the wave model, numerical simulations of the three- dimensional wave-induced current are carried out in this study. The wave model is based on the numerical solution of the modified wave action equation and eikonal equation, which can describe the wave refraction and diffraction. The hydrodynamic model is driven by the wave-induced radiation stresses and affected by the wave turbulence. The numerical implementation of the module has used the finite-volume schemes on unstructured grid, which provides great flexibility for modeling the waves and currents in the complex actual nearshore, and ensures the conservation of energy propagation. The applicability of the proposed model is evaluated in calculating the cases of wave set-up, longshore currents, undertow on a sloping beach, rip currents and meandering longshore currents on a tri-cuspate beach. The results indicate that it is necessary to introduce the depth-dependent radiation stresses into the numerical simulation of wave-induced currents, and comparisons show that the present model makes better prediction on the wave procedure as well as both horizontal and vertical structures in the wave-induced current field.

Numerical simulation of seismic wave propagation in complex media by convolu-tional differentiator

We apply the forward modeling algorithm constituted by the convolutional Forsyte polynomial differentiator pro-posed by former worker to seismic wave simulation of complex heterogeneous media and compare the efficiency and accuracy between this method and other seismic simulation methods such as finite difference and pseudospec-tral method. Numerical experiments demonstrate that the algorithm constituted by convolutional Forsyte polyno-mial differentiator has high efficiency and accuracy and needs less computational resources, so it is a numerical modeling method with much potential.

Effects of mesoscale gravity waves on sporadic E simulated by a one-dimensional dynamic model

In addition to being driven by tidal winds,the sporadic E(Es)layers are modulated by gravity waves(GWs),although the effects are not yet comprehensively understood.In this article,we discuss the effects of mesoscale GWs on the Es layers determined by using a newly developed model,MISE-1D(one-dimensional Model of Ionospheric Sporadic E),with low numerical dissipation and high resolution.Driven by the wind fields resolved by the high-resolution version of the Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension(WACCM-X),the MISE-1D simulation revealed that GWs significantly influence the evolution of the Es layer above 100 km but have a very limited effect at lower altitudes.The effects of GWs are diverse and complex,generally including the generation of fluctuating wavelike structures on the Es layer with frequencies similar to those of the GWs.The mesoscale GWs can also cause increases in the density of Es layers,or they can disperse or diffuse the Es layers and increase their thickness.In addition,the presence of GWs is a key factor in sustaining the Es layers in some cases.

DIRECT NUMERICAL SIMULATION OF VIBRATIONINDUCED T-S WAVE ON BOUNDARY LAYER WALL

The spatial growth of the disturbance in the boundary layer is directly numerically simulated, and the receptivity of the Blasius basic flow to the local two-dimensional （2-D） sustainable micro-vibration is investigated. Results show that the disturbance velocity presents the sine vibration features with the change of time, and the vibration period is identical to the vibration of the local wall. The disturbance velocity presents the fluctuation feature downstream, and the streamwise wave length approximates to the results from the Orr-Sommerfeld equation （OSE）. The growth rate from direct numerical simulation（DNS） is a little greater than that from OSE, and their trends are almost consistent. Under the condition of Re= 2 800, the disturbance amplitude gradually grows in the given computational region with the period T=30. However, it firstly increases and then decreases with the period T= 20. The disturbance harmonic of the former is obviously larger than that of the latter. The maximum streamwise and vertical disturbance velocities from DNS do not fully coincide with those from OSE at the vicinity of the local vibration wall, but coincide well with the former when they travel downstream. The 2-D disturbance induced by the local micro-vibration represents the form of Tollmien-Schlichting （T-S） wave on the boundary layer.

Hybrid-Vlasov simulation of soft X-ray emissions at the Earth’s dayside magnetospheric boundaries

Solar wind charge exchange produces emissions in the soft X-ray energy range which can enable the study of near-Earth space regions such as the magnetopause,the magnetosheath and the polar cusps by remote sensing techniques.The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)and Lunar Environment heliospheric X-ray Imager(LEXI)missions aim to obtain soft Xray images of near-Earth space thanks to their Soft X-ray Imager(SXI)instruments.While earlier modeling works have already simulated soft X-ray images as might be obtained by SMILE SXI during its mission,the numerical models used so far are all based on the magnetohydrodynamics description of the space plasma.To investigate the possible signatures of ion-kinetic-scale processes in soft Xray images,we use for the first time a global hybrid-Vlasov simulation of the geospace from the Vlasiator model.The simulation is driven by fast and tenuous solar wind conditions and purely southward interplanetary magnetic field.We first produce global X-ray images of the dayside near-Earth space by placing a virtual imaging satellite at two different locations,providing meridional and equatorial views.We then analyze regional features present in the images and show that they correspond to signatures in soft X-ray emissions of mirrormode wave structures in the magnetosheath and flux transfer events(FTEs)at the magnetopause.Our results suggest that,although the time scales associated with the motion of those transient phenomena will likely be significantly smaller than the integration time of the SMILE and LEXI imagers,mirror-mode structures and FTEs can cumulatively produce detectable signatures in the soft X-ray images.For instance,a local increase by 30%in the proton density at the dayside magnetopause resulting from the transit of multiple FTEs leads to a 12%enhancement in the line-of-sight-and time-integrated soft X-ray emissivity originating from this region.Likewise,a proton density increase by 14%in the magnetosheath associated with mirror-mode structures can result in an enhancement in the soft X-ray signal by 4%.These are likely conservative estimates,given that the solar wind conditions used in the Vlasiator run can be expected to generate weaker soft X-ray emissions than the more common denser solar wind.These results will contribute to the preparatory work for the SMILE and LEXI missions by providing the community with quantitative estimates of the effects of small-scale,transient phenomena occurring on the dayside.

Freak wave simulation based on nonlinear model and the research on the time-frequency energy spectrum of simulation results

VOF （volume of fluid） method has been used to make the numerical simulation of freak wave come true. The comparisons between the numerical results and linear theoretical results corresponding to Eq.（5） have been carried out to show that the numerical results have a better exhibition of nonlinear characteristics. Wavelet analysis method has been adopted to investigate the time-frequency energy spectrum of simulation freak waves and the results reveal strong nonlinear interaction enables energy to be transferred to high harmonics during the progress of its formation. Varying water depth can enhance the nonlinear interaction, making much more energy be transferred to high harmonics and freak waves with higher asymmetry be generated.

Effect of Wave Nonlinearity on the Instantaneous Seabed Liquefaction

The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.

Simulating the evolution of focused waves by a two-layer Boussinesq-type model

Accurate simulation of the evolution of freak waves by the wave phase focusing method requires accurate linear and nonlinear properties,especially in deep-water conditions.In this paper,we analyze the ability to simulate deep-water focused waves of a two-layer Boussinesq-type(BT)model,which has been shown to have excellent linear and nonlinear performance.To further improve the numerical accuracy and stability,the internal wavegenerated method is introduced into the two-layer Boussinesq-type model.Firstly,the sensitivity of the numerical results to the grid resolution is analyzed to verify the convergence of the model;secondly,the focused wave propagating in two opposite directions is simulated to prove the symmetry of the numerical results and the feasibility of the internal wave-generated method;thirdly,the limiting focused wave condition is simulated to compare and analyze the wave surface and the horizontal velocity of the profile at the focusing position,which is in good agreement with the measured values.Meanwhile the simulation of focused waves in very deep waters agrees well with the measured values,which further demonstrates the capability of the two-layer BT model in simulating focused waves in deep waters.