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.

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 Two-Dimensional Shock/Boundary-Layer Interaction between a Rocket and Booster

A two-dimensional Reynolds-averaged Navier-Stokes solver is applied to analyze the aerodynamic behavior of the Shock/Boundary-Layer interaction of rocket with a boosted The K-ε turbulence model and a finite volume method in a unstructured body-fitted curvilinear coordinates have been used. The results indicate that the separation and the reattachment occur in the Boundary-Layer of the main rocket because of the shock interaction. The shape of the booster nose effects the flow field obviously. In the case of the hemisphere booster nose the pressure has complicate distributions and the separation is very clear. The distance between the booster and main rocket has the evident effect on the flow field. If the distance is smaller the pressure coefficient is bigger the separation zone even the separation bubble occurs.

Propagation Properties of Shock Waves in Polyurethane Foam based on Atomistic Simulations

Porous materials are widely used in the field of protection because of their excellent energy absorption characteristics.In this work,a series of polyurethane microscopic models are established and the effect of porosity on the shock waves is studied with classical molecular dynamics simulations.Firstly,shock Hugoniot relations for different porosities are obtained,which compare well with the experimental data.The pores collapse and form local stress wave,which results in the complex multi-wave structure of the shock wave.The microstructure analysis shows that the local stress increases and the local velocity decreases gradually during the process of pore collapse to complete compaction.Finally,it leads to stress relaxation and velocity homogenization.The shock stress peaks can be fitted with two exponential functions,and the amplitude of attenuation coefficient decreases with the increase of density.Besides,the pore collapse under shock or non-shock are discussed by the entropy increase rate of the system.The energy is dissipated mainly through the multiple interactions of the waves under shock.The energy is dissipated mainly by the friction between atoms under non-shock.

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.

MULTI-MATERIAL NUMERICAL SIMULATION OF MOVING SHOCK INTERACTING WITH CONSECUTIVE BUBBLES

Numerical simulations are performed on the interface with large deformation induced by the interaction between a moving shock and two consecutive bubbles. The high performance of the level set method for multi-material interfaces is demonstrated. Discontinuous Galerkin finite element method is used to solve Euleri- an equations. And the fifth-order weighted essentially non-oscillatory （WENO） scheme is used to solve the level set equation for capturing multi-material interfaces. The ghost fluid method is used to deal with the interfacial boundary condition. Results are obtained for two bubble interacting with a moving shock. The contours of the constant density and the pressure at different time are given. In the computational domain, three different cases are considered, i.e. two helium bubbles, a helium bubble followed by an R22 bubble in the direction of the moving shock, and an R22 bubble followed by a helium bubble. Computational results indicate that multi-mate- rial interfaces can be properly captured by the level set method. Therefore, for problems involving the flow of three different materials with two different interfaces, each interface separating two different materials can be similarly handled.

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.

Numerical Simulation of Nonlinear Three-Dimensional Waves in Water of Arbitrary Varying Topography

The numerical simulation is based on the authors' high-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth. Corresponding finite-difference equations and general conditions for open and fixed natural boundaries with an arbitrary reflection coefficient and phase shift are also given in this paper. The systematical tests of numerical simulation show that the theoretical models, the finite-difference algorithms and the boundary conditions can give good calculation results for the wave propagating in shallow and deep water with an arbitrary slope varying from gentle to steep.

2-D Composite Model for Numerical Simulations of Nonlinear Waves

A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Omega is divided into two subregions. In the near-field around a structure, Omega(2), the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-epsilon equations and numerically solved by the improved VOF method; whereas in the subregion Omega(1) (Omega(1) = Omega - Omega(2)) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.

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.

Mesh Size Effect in Numerical Simulation of Blast Wave Propagation and Interaction with Structures

Numerical method is popular in analysing the blast wave propagation and interaction with structures.However,because of the extremely short duration of blast wave and energy trans-mission between different grids,the numerical results are sensitive to the finite element mesh size.Previous numerical simulations show that a mesh size acceptable to one blast scenario might not be proper for another case,even though the difference between the two scenarios is very small,indicating a simple numerical mesh size convergence test might not be enough to guarantee accu-rate numerical results.Therefore,both coarse mesh and fine mesh were used in different blast scenarios to investigate the mesh size effect on numerical results of blast wave propagation and interaction with structures.Based on the numerical results and their comparison with field test re-sults and the design charts in TM5-1300,a numerical modification method was proposed to correct the influence of the mesh size on the simulated results.It can be easily used to improve the accu-racy of the numerical results of blast wave propagation and blast loads on structures.

Numerical simulations of full-wave fi elds and analysis of channel wave characteristics in 3-D coal mine roadway models

Currently, numerical simulations of seismic channel waves for the advance detection of geological structures in coal mine roadways focus mainly on modeling two- dimensional wave fields and therefore cannot accurately simulate three-dimensional （3-D） full-wave fields or seismic records in a full-space observation system. In this study, we use the first-order velocity-stress staggered-grid finite difference algorithm to simulate 3-D full-wave fields with P-wave sources in front of coal mine roadways. We determine the three components of velocity Vx, Vy, and Vz for the same node in 3-D staggered-grid finite difference models by calculating the average value of Vy, and Vz of the nodes around the same node. We ascertain the wave patterns and their propagation characteristics in both symmetrical and asymmetric coal mine roadway models. Our simulation results indicate that the Rayleigh channel wave is stronger than the Love channel wave in front of the roadway face. The reflected Rayleigh waves from the roadway face are concentrated in the coal seam, release less energy to the roof and floor, and propagate for a longer distance. There are surface waves and refraction head waves around the roadway. In the seismic records, the Rayleigh wave energy is stronger than that of the Love channel wave along coal walls of the roadway, and the interference of the head waves and surface waves with the Rayleigh channel wave is weaker than with the Love channel wave. It is thus difficult to identify the Love channel wave in the seismic records. Increasing the depth of the receivers in the coal walls can effectively weaken the interference of surface waves with the Rayleigh channel wave, but cannot weaken the interference of surface waves with the Love channel wave. Our research results also suggest that the Love channel wave, which is often used to detect geological structures in coal mine stopes, is not suitable for detecting geological structures in front of coal mine roadways. Instead, the Rayleigh channel wave can be used for the advance detection of geological structures in coal mine roadways.

Evaluation of numerical wave model for typhoon wave simulation in South China Sea

The simulating waves nearshore(SWAN) model has typically been designed for wave simulations in near-shore regions. In this study, the model's applicability to the simulation of typhoon waves in the South China Sea(SCS) was evaluated. A blended wind field, consisting of an interior domain based on Fujita's model and an exterior domain based on Takahashi's model, was used as the driving wind field. The waves driven by Typhoon Kai-tak over the SCS that occurred in 2012 were selected for the numerical simulation research. Sensitivity analyses of time step, grid resolution, and angle resolution were performed in order to obtain optimal model settings. Through sensitivity analyses, it can be found that the time step has a large influence on the results, while grid resolution and angle resolution have a little effect on the results.

EXPERIMENTAL RESEARCH AND NUMERICAL SIMULATION OF LASER SHOCK FORMING OF TA2 TITANIUM SHEET

Laser shock forming （ISF） was a new technique realized by applying an impulsive pressure generated by laser-induced shock wave on the surface of metal sheet. LSF of metal sheet was investigated with experiments and numerical simulation. The basic theories were introduced; the surface quality and deformation of the processed titanium sample （TA2） were examined; ABAQUS was used to simulate ISF and the central displacement of the shocked region was measured and compared with the simulation. Overlapped ISF treatment was experimentally carried out to produce groove and simulation. The results showed that the surface quality and the microstructure with single laser pulse had no remarkable change, and ablation was observed on the surface of the sample with overlapped pulses. The deformation observed in the numerical simulation agreeed with that observed in the experimental measurement quite well.

Numerical simulation of characteristics of semidiurnal tidal waves in sea region around Taiwan

POM97, an oceanic model, has been used for the first time to the numerical study on the tidal waves of the as Regions around Taiwan. In this paper, we have got the result that the semidiurnal tidal waves of these area mainly are the co-operating tides which come from the south of 23'N of the western Pacific. Those semidiurnal tidal waves affecting the Taiwan Straits come respectively from the south and the north entrance of the channel, and the north tidal wave is stronger than the south one. The strongest tidal field is the area from the Meizhou Bay to the Xinhua Bay along the coast of Fujian Province, where the biggest amplitude of the M2 partial tide can reach 240 cm. The strongest tidal cur- rent fields lie in the Penghu watercourse, where the maximum velocity of the M2 partial tide can arrive at 196 m/s. In the horizontal structure of the tidal currets, we have found that there is a stream dot in the north of the channel, besides, there still exist four new ones. As for the vertical structure, it mainly is biassed to the right at the surface, and to the left near the bottom layer.

A numerical simulation of surface wave excitation in a rectangular planar-type plasma source

The principle of surface wave plasma discharge in a rectangular cavity is introduced simply based on surface plasmon polariton theory. The distribution of surface-wave electric field at the interface of the plasma-dielectric slab is investigated by using the three-dimensional finite-difference time-domain method （3D-FDTD） with different slotantenna structures. And the experimental image of discharge with a novel slot antenna array and the simulation of the electric field with this slot antenna array are both displayed. Combined with the distribution of surface wave excitation and experimental results, the numerical simulation performed by using 3D-FDTD is shown to be a useful tool in the computer-aided antenna design for large area planar-type surface-wave plasma sources.

Numerical simulation and inversion of offshore area depth based on x-band microwave radar

A detection method of offshore area depth utilizing the x-band microwave radar is proposed. The method is based on the sea clutter imaging mechanism of microwave radar, and combined with dispersion equation of the liner wave theorem and least square method （LSM）, consequently get the inversion results of water depth in the detected region. The wave monitoring system OSMAR-X exploited by the Ocean State Laborato-ry, Wuhan University, based on a microwave radar has proven to be a powerful tool to monitor ocean waves in time and space. Numerical simulation and inversion of offshore area depth are carried out here; since JONSWAP model can give description of stormy waves in different growth phase, it is suitable for simulation. Besides, some results from measured data detected by OSMAR-X x-band radar located at Longhai of Fujian Province, China, validates this method. The tendency of the average water depths inferred from the radar images is in good agreement with the tide level detected by Xiamen tide station. These promising results suggest the possibility of using OSMAR-X to monitor operationally morphodynamics in coastal zones. This method can be applied to both shore-based and shipborne x-band microwave radar.

An explicit method for numerical simulation of wave equations

In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.

Numerical Simulation of Wave Height and Wave Set-Up in Nearshore Regions

Based on the time dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation, and then a practical method for the simulation of wave height and wave set- up in nearshore regions is presented. The variation of the complex wave amplitude is numerically simulated by use of the parabolic mild slope equation including the effect of wave energy dissipation due to wave breaking. The components of wave radiation stress are calculated subsequently by new expressions for them according to the obtained complex wave amplitude, and then the depth-averaged equation is applied to the calculation of wave set-up due to wave breaking. Numerical results are in good agreement with experimental data, showing that the expression for the energy dissipation factor is reasonable and that the new method is effective for the simulation of wave set-up due to wave breaking in nearshore regions.

Numerical Simulation of Local Scour Around A Large Circular Cylinder Under Wave Action

A horizontal two-dimensional numerical model is developed for estimation of sediment transport and sea bed change around it large circular cylinder tinder wave action, The wave model is based on an elliptic mild slope equation. The wave-induced current by the gradient of radiation stress is considered and a depth integrated shallow water equation is applied to the calculation of the current. The mass transport velocity and the bed shear stress due to streaming are considered, which are important factors affecting the sediment transport around a structure due to waves, especially in reflective areas. Wave-current interaction is taken into account in the model for computing the bed shear stress. The model is implemented by it finite element method, The results of this model are compared with those from other methods and agree well with experimental data.