An explicit method for numerical simulation of wave equations: 3D wave motion

In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order （M=1） recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.

Image processing based three-dimensional model reconstruction for cross-platform numerical simulation

Numerical simulation is the most powerful computational and analysis tool for a large variety of engineering and physical problems.For a complex problem relating to multi-field,multi-process and multi-scale,different computing tools have to be developed so as to solve particular fields at different scales and for different processes.Therefore,the integration of different types of software is inevitable.However,it is difficult to perform the transfer of the meshes and simulated results among software packages because of the lack of shared data formats or encrypted data formats.An image processing based method for three-dimensional model reconstruction for numerical simulation was proposed,which presents a solution to the integration problem by a series of slice or projection images obtained by the post-processing modules of the numerical simulation software.By means of mapping image pixels to meshes of either finite difference or finite element models,the geometry contour can be extracted to export the stereolithography model.The values of results,represented by color,can be deduced and assigned to the meshes.All the models with data can be directly or indirectly integrated into other software as a continued or new numerical simulation.The three-dimensional reconstruction method has been validated in numerical simulation of castings and case studies were provided in this study.

Study of 3-D Numerical Simulation for Gas Transfer in the Goaf of the Coal Mining

In order to simulate field distribution rules,mathematical models for 3-D air flows and gas transfer in the goaf of the coal mining are established,based on theories of permeability and dynamic dispersion through porous media. A gas dispersion equation in a 3-D field is calculated by use of numerical method on a weighted upstream multi-element balance. Based on data of an example with a U type ventilation mode,surface charts of air pressure distribution and gas concentration are drawn by Graphtool software. Finally,a comparison between actually measured results in the model test and the numerical simulation results is made to proves the numerical implementation feasible.

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 2D and 3D Sloshing Waves in a Regularly and Randomly Excited Container

In this paper,various aspects of the 2D and 3D nonlinear liquid sloshing problems in vertically excited containers have been studied numerically along with the help of a modified-transformation.Based on this new numerical algorithm,a numerical study on a regularly and randomly excited container in vertical direction was conducted utilizing four different cases： The first case was performed utilizing a 2D container with regular excitations.The next case examined a regularly excited 3D container with two different initial conditions for the liquid free surface,and finally,3D container with random excitation in the vertical direction.A grid independence study was performed along with a series of validation tests.An iteration error estimation method was used to stop the iterative solver（used for solving the discretized governing equations in the computational domain） upon reaching steady state of results at each time step.In the present case,this method was found to produce quite accurate results and to be more time efficient as compared to other conventional stopping procedures for iterative solvers.The results were validated with benchmark results.The wave elevation time history,phase plane diagram and surface plots represent the wave nonlinearity during its motion.

Quasi-3D Numerical Simulation of Tidal Hydrodynamic Field

Based on the 2D horizontal plane numerical model, a quasi-3D numerical model is established for coastal regions of shallow water. The characteristics of this model are that the velocity profiles;can be obtained at the same time when the equations of the value of difference between the horizontal current velocity and its depth-averaged velocity in the vertical direction are solved and the results obtained are consistent with the results of the 2D, model. The circulating flow in the rectangular area induced by wind is simulated and applied to the tidal flow field of the radial sandbanks in the South Yellow Sea. The computational results from this quasi-3D model are in good agreement with analytical results and observed data. The solution of the finite difference equations has been found to be stable, and the model is simple, effective and practical.

Numerical simulation of intermediate phase growth in Ti/Al alternate foils

To investigate the diffusion reaction between Ti/Al solid diffusion couple, Ti/Al alternate foils formed by hot pressing were annealed at 525, 550, 575 and 600 °C for time ranging from 1 to 40 h. The experimental results show that TiAl3 was the only observed phase at Ti/Al interface. The interface thermodynamics favored the preferential formation of TiAl3 in Ti/Al couple. The growth of TiAl3 layer occurred mainly towards Al foil side and exhibited a parabolic law. Using the interdiffusion coefficients calculated based on the contribution of grain boundary diffusion, the growth of TiAl3 was simulated numerically with the finite difference method, and the simulated results were in good agreement with the experimental ones.

Numerical Simulation of Injection Molding Cooling Process Based on 3D Surface Model

The design of the cooling system of injection molds directly affects both productivity and the quality of the final part. Using the cooling process CAE system to instruct the mold design, the efficiency and quality of design can be improved greatly. At the same time, it is helpful to confirm the cooling system structure and optimize the process conditions. In this paper, the 3D surface model of mold cavity is used to replace the middle-plane model in the simulation by Boundary Element Method, which break the bottleneck of the application of the injection molding simulation softwares base on the middle-plane model. With the improvements of this paper, a practical and commercial simulation software of injection molding cooling process named as HsCAE3D6.0 is developed.

NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS OVER DREDGED TRENCHES

A 3- D free surface flow in open channels based on the Reynolds equations with the k-ε turbulence closure model is presented in this paper. Insted of the 'rigid lid' approximation, the solution of the free surface equation is implemented in the velocity-pressure iterative procedure on the basis of the conventional SIMPLE method. This model was used to compute the flow in rectangular channels with trenches dredged across the bottom. The velocity, eddy viscosity coefficient, turbulent shear stress, turbulent kinetic energy and elevation of the free surface can be obtained. The computed results are in good agreement with previous experimental data.

3-D Finite-Element Numerical Simulation of Centrifugal Induction Electrosalg Casting Solidification Process

A 3-D finite-element numerical simulation model of temperature field for CIESC casting solidification process was developed with the aid of ANSYS software and a series of corresponding experiments were made. The results showed that the good agreement was obtained between the numerical simulation and the experiments. Based on the numerical simulation results, the characteristics of temperature distribution in the castings during CIESC solidification process were analyzed and summarized. According to the G/R-1/2 method and numerical simulation results, there is no any shrinkage defect in the CIESC casting and structure or casting is fine and compact.

Numerical Simulation Study on the Detection of Weak Structural Plane of Rock Slope by Using 3D Electrical Resistivity Tomography

The weak structure plane is an important factor affecting the stability of rock slope, and detecting the spatial structure of the weak structural plane is beneficial to analyze the stability of the slope and estimate the quantity of the landslide. Based on 3D electrical resistivity tomography, a model of rock slope with weak structure plane is established, and the characteristics of three-dimensional resistivity imaging of weak structure plane under different ground water conditions are simulated. The results show that the weak structural plane has a better reflection in 3D electrical resistivity tomography;the distribution of weak structural plane of 3D resistivity imaging can be roughly determined under different ground water conditions;the three-dimensional electrical resistivity tomography is feasible in the detection of weak structural plane of rock slope.

Temperature Distributions in Single Cell of Polymer Electrolyte Fuel Cell Simulated by an 1D Multi-plate Heat-Transfer Model and a 3D Numerical Simulation Model

The purpose of this study is to verify an 1D multi-plate heat-transfer model estimating the temperature distribution on the interface between polymer electrolyte membrane and catalyst layer at cathode in single cell of polymer electrolyte fuel cell, which is named as reaction surface in this study, with a 3D numerical simulation model solving many governing equations on the coupling phenomena in the cell. The results from both models/simulations agreed well. The effects of initial operation temperature, flow rate, and relative humidity of supply gas on temperature distribution on the reaction surface were also investigated. It was found in both 1D and 3D simulations that, the temperature rise （i.e., Treact-Tini） of the reaction surface from initial operation temperature at 70℃ was higher than that at 80℃ irrespective of flow rate of supply gas. The effect of relative humidity of supply gas on Treact- Tini near the inlet of the cell was small. Compared to the previous studies conducted under the similar operation conditions, the Treact - Tini calculated by 1D multi-plate heat-transfer model in this study as well as numerical simulation using 3D model was reasonable.

3D simulation of image-defined complex internal features using the numerical manifold method

The numerical simulation of internal features,such as inclusions and voids,is important to analyze their impact on the performance of composite materials.However,the complex geometries of internal features and the induced continuous-discontinuous(C-D)deformation fields are challenges to their numerical simulation.In this study,a 3D approach using a simple mesh to simulate irregular internal geometries is developed for the first time.With the help of a developed voxel crack model,image models that are efficient when recording complex geometries are directly imported into the simulation.Surface reconstructions,which are usually labor-intensive,are excluded from this approach.Moreover,using image models as the geometric input,image processing techniques are applied to detect material interfaces and develop contact pairs.Then,the C-D deformations of the complex internal features are directly calculated based on the numerical manifold method.The accuracy and convergence of the developed3D approach are examined based on multiple benchmarks.Successful 3D C-D simulation of sandstones with naturally formed complex microfeatures demonstrates the capability of the developed approach.

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.

Numerical simulation for influence of excavation and blasting vibration on stability of mined-out area

Dynamic analysis steps and general flow of fast lagrangian analysis of continua in 3 dimensions(FLAC3D) were discussed. Numerical simulation for influence of excavation and blasting vibration on stability of mined-out area was carried out with FLAC3D. The whole analytical process was divided into two steps, including the static analysis and the dynamic analysis which were used to simulate the influence of excavation process and blasting vibration respectively. The results show that the shape of right upper boundary is extremely irregular after excavation, and stress concentration occurs at many places and higher tensile stress appears. The maximum tensile stress is higher than the tensile strength of rock mass, and surrounding rock of right roof will be damaged with tension fracture. The maximum displacement of surrounding rock is 4.75 mm after excavation. However, the maximum displacement increases to 5.47 mm after the blasting dynamic load is applied. And the covering area of plastic zones expands obviously, especially at the foot of right upper slope. The analytical results are in basic accordance with the observed results on the whole. Damage and disturbance on surrounding rock to some degree are caused by excavation, while blasting dynamic load increases the possibility of occurrence of dynamic instability and destruction further. So the effective supporting and vibration reducing measures should be taken during mining.

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.

Numerical simulation of protection range in exploiting the upper protective layer with a bow pseudo-incline technique

The developing processes of stress and deformation fields of a protected layer after mining an upper-protective layer with a bow pseudo-incline technique were simulated to locate the protection region. The pressure relief of the protected layer was analyzed after mining the upper-protective layer. The pressure relief angle along the strike and incline were located according to the roles of protection of the deformation and stress pressure-relief of the protective layer after mining. This results show that the upper-protective layer with the bow pseudo-incline technique have an upper and downside pressure relief angle of 85 and 68 degrees respectively; the distribution of strike pressure relief angles along the pseudo-incline working face is uneven and their values range from 38.3 to 51 degrees. The pressure relief angle of the inclined middle location was the largest. The distribution of the protection region of the upper-protective layer with the bow pseudo-incline teelmique located by practical tests and numerical simulation is essentially consistent, compared with the results obtained by these methods.

Numerical simulation of involutes spline shaft in cold rolling forming

Design of forming dies and whole process of simulation of cold rolling involutes spline can be realized by using of CAD software of PRO-E and CAE software of DEFORM-3D. Software DEFORM-3D provides an automatic and optimized remeshing function, especially for the large deformation. In order to use this function sufficiently, simulation of cold rolling involutes spline can be implemented indirectly. The relationship between die and workpiece, forming force and characteristic of deformation in the forming process of cold rolling involutes spline are analyzed and researched. Meanwhile, reliable proofs for the design of dies and deforming equipment are provided.

Numerical simulation of asphalt mixture based on three-dimensional heterogeneous specimen

In order to verify the validity of finite element numerical simulation method for asphalt mixture, which consists of aggregates, mastic （where mastic is a kind of fine mixture composed of asphalt binder mixed with fines and fine aggregates） and air voids, based on three-dimensional （3D） heterogeneous specimen, X-ray computerized tomography （X-ray CT） was used to scan the asphalt specimens to obtain the real internal microstrnctures of asphalt mixture. CT images were reconstructed to build up 3D digital specimen, and the viscoelastic properties of mastic were described with Burgers model The uniaxial creep numerical simulations of three different levels of aggregate gradation were conducted. The simulation results agree well with the experimental results. The numerical simulation of asphalt mixture incorporated with real 3D microstructure based on finite element method is a promising application to conduct research of asphalt concrete. Additionally, this method can increase the mechanistic understanding of global viscoelastic properties of asphalt mixtures by linking the real 3D microstructure.