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.

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.

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.

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.

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 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 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 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 surface movement laws under different unconsolidated layers thickness

Based on specific geology and mining conditions of certain coal working face in China, a series of numerical models under different unconsolidated layers thickness were respectively established by employing FLAC3D. The relationship between the unconsolidated layers thickness and surface movement laws was studied. Maximum surface subsidence, Maximum horizontal displacement and surface subsidence degree were obtained. Contours of surface subsidence/horizontal displacement and curves were drawn. Some laws of surface subsidence/horizontal displacement were analyzed. The role of the unconsolidated layers in surface subsidence was revealed. It is significant to predict surface subsidence of thick unconsolidated layers for coal mine and take effective measures to control surface subsidence.

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.

Numerical simulation and analysis of solid-liquid two-phase threedimensional unsteady flow in centrifugal slurry pump

Based on RNG k-ε turbulence model and sliding grid technique, solid-liquid two-phase three-dimensional(3-D) unsteady turbulence of full passage in slurry pump was simulated by means of Fluent software. The effects of unsteady flow characteristics on solid-liquid two-phase flow and pump performance were researched under design condition. The results show that clocking effect has a significant influence on the flow in pump, and the fluctuation of flow velocity and pressure is obvious, particularly near the volute tongue, at the position of small sections of volute and within diffuser. Clocking effect has a more influence on liquid-phase than on solid-phase, and the wake-jet structure of relative velocity of solid-phase is less obvious than liquid-phase near the volute tongue and the impeller passage outlet. The fluctuation of relative velocity of solid-phase flow is 7.6% smaller than liquid-phase flow at the impeller outlet on circular path. Head and radial forces of the impeller are 8.1% and 85.7% of fluctuation, respectively. The results provide a theoretical basis for further research for turbulence, improving efficient, reducing the hydraulic losses and wear. Finally, field tests were carried out to verify the operation and wear of slurry pump.

3D Modeling and Simulation of Fancy Fabrics in Weft Knitting

Weft knitted fancy fabrics are widely used in knitted garment design. Due to the complexity of the structures, their modeling and simulation needs to be solved in three-dimensional (3D) CAD developments. In this paper, 3D loop geometrical models of weft knitted fancy structures, including tuck stitch, jacquard stitch, transfer stitch and fleecy stitch, were developed based on an improved model of plain loop, and their central axes as some 3D space curves were achieved by using Non-Uniform Rational B-Splines (NURBS). The 3D visual simulation programme was written in C++ programming language using OpenGL, which was a function library of 3D graphics. Some examples of weft knitted fancy fabrics were generated and practical application of 3D simulation was discussed.

HEXAHEDRAL ELEMENT REFINEMENT FOR THE PREDICTION- CORRECTION ALE FEM SIMULATION OF 3D BULKINGFORMING PROCESS

Based on the characteristics of 3D bulk forming process, the arbitrary Lagrangian-Eulerian (ALE) formulation-based FEM is studied, and a prediction-correction ALE-based FEM is proposed which integrates the advantages of precisely predicting the boundary configuration of the deformed material, and of efficiently avoiding hexahedron remeshing processes. The key idea of the prediction-correction ALE FEM is elaborated in detail. Accordingly, the strategy of mesh quality control, one of the key enabling techniques for the 3D bulk forming process numerical simulation by the prediction-correction ALE FEM is carefully investigated, and the algorithm for hexahedral element refinement is formulated based on the mesh distortion energy.

Numerical modeling of 3D DC resistivity method in the mixed space-wavenumber domain

Forward modeling is the basis of inversion imaging and quantitative interpretation for DC resistivity exploration.Currently,a numerical model of the DC resistivity method must be finely divided to obtain a highly accurate solution under complex conditions,resulting in a long calculation time and large storage.Therefore,we propose a 3D numerical simulation method in a mixed space-wavenumber domain to overcome this challenge.The partial differential equation about abnormal potential is transformed into many independent ordinary differential equations with different wavenumbers using a 2D Fourier transform along the x axis and y axis direction.In this way,a large-scale 3D numerical simulation problem is decomposed into several 1D numerical simulation problems,which significantly reduces the computational and storage requirements.In addition,these ordinary 1D differential equations with different wavenumbers are independent of each other and high parallelelism of the algorithm.They are solved using a finite-element algorithm combined with a chasing method,and the obtained solution is modified using a contraction operator.In this method,the vertical direction is reserved as the spatial domain,then grid size can be determined flexibly based on the underground current density distribution,which considers the solution accuracy and calculation efficiency.In addition,for the first time,we use the contraction operator in the integral equation method to iterate the algorithm.The algorithm takes advantage of the high efficiency of the standard Fourier transform and chasing method,as well as the fast convergence of the contraction operator.We verified the accuracy of the algorithm and the convergence of the contraction operator.Compared with a volume integral method and goal-oriented adaptive finite-element method,the proposed algorithm has lower memory requirements and high computational efficiency,making it suitable for calculating a model with large-scale nodes.Moreover,different examples are used to verify the high adaptability and parallelism of the proposed algorithm.The findings show that the 3D numerical simulation method of DC resistivity method in a mixed space-wavenumber domain is highly efficient,precise,and parallel.

Numerical Study on Hydraulic Characteristics and Discharge Capacity of Modified Piano Key Weir with Various Inlet/Outlet Width Ratio

A modified piano key weir with a rounded nose and a parapet wall (MPKW) can improve the discharge capacity significantly compared to a standard piano key weir. However, the optimum of the inlet/outlet width ratio (Wi/Wo) on the discharge efficiency of MPKW is still not investigated numerically. The present work utilized the numerical modeling to investigate and analyze the effects of the inlet/outlet key width ratios on the hydraulic characteristics and discharge capacity of the MPKW. To validate the numerical model with the experimental data, the results indicate that the average relative error is 2.96%, which confirms that the numerical model is fairly well to predictthe specifications of flow over on the MPKW. Numerical simulation results indicated that the discharge capacity of the MPKW can be improved up to 8.5% by optimizing the Wi/Wo ratio ranging from 1.53 to 1.67 even if the other parameters of the MPKW keep unchanged. A big Wi/Wo ratio generally leads to an increase in discharge capacity at low heads and a little effect on the discharge efficiency at high heads. The discharge efficiency of the inlet and outlet crests increases up to 9.6% for high heads, while discharge efficiency of the lateral crest decreases up to 23.5% compared with the reference model. The findings of the study revealed that the intrinsic influencing mechanism of the Wi/Wo ratio on the discharge performance of MPKWs.

Numerical and Experimental Study of the 3D Effect on Connecting Arm of Vertical Axis Tidal Current Turbine

Vertical axis tidal current turbine is a promising device to extract energy from ocean current. One of the important components of the turbine is the connecting arm, which can bring about a significant effect on the pressure distribution along the span of the turbine blade, herein we call it 3D effect. However, so far the effect is rarely reported in the research, moreover, in numerical simulation. In the present study, a 3D numerical model of the turbine with the connecting arm was developed by using FLUENT software compiling the UDF（User Defined Function） command. The simulation results show that the pressure distribution along the span of blade with the connecting arm model is significantly different from those without the connecting arm. To facilitate the validation of numerical model, the laboratory experiment has been carried out by using three different types of NACA aerofoil connecting arm and circle section connecting arm. And results show that the turbine with NACA0012 connecting arm has the best start-up performance which is 0.346 m/s and the peak point of power conversion coefficient is around 0.33. A further study has been performed and a conclusion is drawn that the aerofoil and thickness of connecting arm are the most important factors on the power conversion coefficient of the vertical axis tidal current turbine.

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.

A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.

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.