Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in spacewavenumber mixed domain

In gravity-anomaly-based prospecting, the computational and memory requirements for practical numerical modeling are potentially enormous. Achieving an efficient and precise inversion for gravity anomaly imaging over large-scale and complex terrain requires additional methods. To this end, we have proposed a new topography-capable By performing a two-dimensional Fourier transform in the horizontal directions, threedimensional partial differential equations in the spatial domain were transformed into a group of independent, one-dimensional differential equations engaged with different wave numbers. These independent differential equations are highly parallel across different wave numbers. differential equations with different wave numbers, and the efficiency of solving fixedbandwidth linear equations was further improved by a chasing method. In a synthetic test, a prism model was used to verify the accuracy and reliability of the proposed algorithm by comparing the numerical solution with the analytical solution. We studied the computational precision and efficiency with and without topography using different Fourier transform methods. The results showed that the Guass-FFT method has higher numerical precision, while the standard FFT method is superior, in terms of computation time, for inversion and quantitative interpretation under complicated terrain.

Three-Dimensional Numerical Modeling of an Ar-N_2 Plasma Arc Inside a Non-Transferred Torch

A three-dimensional numerical model is developed to study the behaviour of an argon-nitrogen plasma arc inside a non-transferred torch. In this model, both the entire cathode and anode nozzle are considered to simulate the plasma arc. The argon-nitrogen plasma arc is simulated for different arc currents and gas flow rates of argon. Various combinations of arc core radius and arc length, which correspond to a given torch power, are predicted. A most feasible combination of the same, which corresponds to an actual physical situation of the arc inside the torch, is identified using the thermodynamic principle of minimum entropy production for a particular torch power. The effect of the arc current and gas flow rate on the plasma arc characteristics and torch efficiency is explained. The effect of the nitrogen content in the plasma gas on the torch power and efficiency is clearly detected. Predicted torch efficiencies are comparable to the measured ones and the effect of the arc current and gas flow rate on predicted and measured efficiencies is almost similar. The efficiency of the torch, cathode and anode losses and core temperature and velocity at the nozzle exit are reported for five different cases.

THREE-DIMENSIONAL NUMERICAL MODELING OF SECONDARY FLOWS IN A WIDE CURVED CHANNEL

Most natural rivers are curved channels, where the turbulent flows have a complex helical pattern, as has been extensively studied both numerically and experimentally. The helical flow structure in curved channels has an important bearing on sediment transport, riverbed evolution, and pollutant transport study. In this article, different turbulence closure schemes i.e., the mixing-length model and the k-ε model with different pressure solution techniques i. e., hydrostatic assumptions and dynamic pressure treatments are applied to study the helical secondary flows in an experiment curved channel. The agreements of vertically-averaged velocities between the simulated results obtained by using different turbulence models with different pressure solution techniques and the measured data are satisfactory. Their discrepancies with respect to surface elevations, superelevations and secondary flow patterns are discussed.

Three-dimensional numerical modeling of single geocellreinforced sand

This paper summarizes the development of a three-dimensional numerical model for analyzing single geocell-reinforced soil.In this model,the infill soil was modeled using the Duncan-Chang model,which can simulate non-linearity and stress-dependency of soil.Geocell was modeled using linearly elastic plate elements,which can carry both bending and membrane stresses.A linear interface stress-strain relationship with a MohrCoulomb yield criterion was adopted to model the interface friction between the geocell wall and the soil.By modeling the geocell and the soil separately,the interaction between the soil and the geocell can be accurately simulated.To verify this model,a plate load test was conducted in the laboratory,in which a 12-cmthick sand layer reinforced by a single geocell was subjected to a vertical load from a circular steel plate.The load-displacement curves and the horizontal tensile strain of the geocell were recorded during the test.A numerical model was created according to the setup of the load test.The numerical results compared reasonably well with the test data.

A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

Progressive fragmentation of granular assemblies within rockslides: Insights from discrete-continuous numerical modeling

Rock fragmentation plays a critical role in rock avalanches,yet conventional approaches such as classical granular flow models or the bonded particle model have limitations in accurately characterizing the progressive disintegration and kinematics of multi-deformable rock blocks during rockslides.The present study proposes a discrete-continuous numerical model,based on a cohesive zone model,to explicitly incorporate the progressive fragmentation and intricate interparticle interactions inherent in rockslides.Breakable rock granular assemblies are released along an inclined plane and flow onto a horizontal plane.The numerical scenarios are established to incorporate variations in slope angle,initial height,friction coefficient,and particle number.The evolutions of fragmentation,kinematic,runout and depositional characteristics are quantitatively analyzed and compared with experimental and field data.A positive linear relationship between the equivalent friction coefficient and the apparent friction coefficient is identified.In general,the granular mass predominantly exhibits characteristics of a dense granular flow,with the Savage number exhibiting a decreasing trend as the volume of mass increases.The process of particle breakage gradually occurs in a bottom-up manner,leading to a significant increase in the angular velocities of the rock blocks with increasing depth.The simulation results reproduce the field observations of inverse grading and source stratigraphy preservation in the deposit.We propose a disintegration index that incorporates factors such as drop height,rock mass volume,and rock strength.Our findings demonstrate a consistent linear relationship between this index and the fragmentation degree in all tested scenarios.

A Hybrid Dung Beetle Optimization Algorithm with Simulated Annealing for the Numerical Modeling of Asymmetric Wave Equations

In the generalized continuum mechanics(GCM)theory framework,asymmetric wave equations encompass the characteristic scale parameters of the medium,accounting for microstructure interactions.This study integrates two theoretical branches of the GCM,the modified couple stress theory(M-CST)and the one-parameter second-strain-gradient theory,to form a novel asymmetric wave equation in a unified framework.Numerical modeling of the asymmetric wave equation in a unified framework accurately describes subsurface structures with vital implications for subsequent seismic wave inversion and imaging endeavors.However,employing finite-difference(FD)methods for numerical modeling may introduce numerical dispersion,adversely affecting the accuracy of numerical modeling.The design of an optimal FD operator is crucial for enhancing the accuracy of numerical modeling and emphasizing the scale effects.Therefore,this study devises a hybrid scheme called the dung beetle optimization(DBO)algorithm with a simulated annealing(SA)algorithm,denoted as the SA-based hybrid DBO(SDBO)algorithm.An FD operator optimization method under the SDBO algorithm was developed and applied to the numerical modeling of asymmetric wave equations in a unified framework.Integrating the DBO and SA algorithms mitigates the risk of convergence to a local extreme.The numerical dispersion outcomes underscore that the proposed SDBO algorithm yields FD operators with precision errors constrained to 0.5‱while encompassing a broader spectrum coverage.This result confirms the efficacy of the SDBO algorithm.Ultimately,the numerical modeling results demonstrate that the new FD method based on the SDBO algorithm effectively suppresses numerical dispersion and enhances the accuracy of elastic wave numerical modeling,thereby accentuating scale effects.This result is significant for extracting wavefield perturbations induced by complex microstructures in the medium and the analysis of scale effects.

Resistance of full-scale beams against close-in explosions.Numerical modeling and field tests

This paper explores the performances of a finite element simulation including four concrete models applied to a full-scale reinforced concrete beam subjected to blast loading. Field test data has been used to compare model results for each case. The numerical modelling has been, carried out using the suitable code LS-DYNA. This code integrates blast load routine(CONWEP) for the explosive description and four different material models for the concrete including: Karagozian & Case Concrete, Winfrith, Continuous Surface Cap Model and Riedel-Hiermaier-Thoma models, with concrete meshing based on 10, 15, and 20 mm. Six full-scale beams were tested: four of them used for the initial calibration of the numerical model and two more tests at lower scaled distances. For calibration, field data obtained employing pressure and accelerometers transducers were compared with the results derived from the numerical simulation. Damage surfaces and the shape of rupture in the beams have been used as references for comparison. Influence of the meshing on accelerations has been put in evidence and for some models the shape and size of the damage in the beams produced maximum differences around 15%. In all cases, the variations between material and mesh models are shown and discussed.

Understanding the spatial interaction of ultrasounds based on three-dimensional dual-frequency ultrasonic field numerical simulation

A transient 3D model was established to investigate the effect of spatial interaction of ultrasounds on the dual-frequency ultrasonic field in magnesium alloy melt.The effects of insertion depth and tip shape of the ultrasonic rods,input pressures and their ratio on the acoustic field distribution were discussed in detail.Additionally,the spacing,angle,and insertion depth of two ultrasonic rods significantly affect the interaction between distinct ultrasounds.As a result,various acoustic pressure distributions and cavitation regions are obtained.The spherical rods mitigate the longitudinal and transversal attenuation of acoustic pressure and expand the cavitation volume by 53.7%and 31.7%,respectively,compared to the plate and conical rods.Increasing the input pressure will enlarge the cavitation region but has no effect on the acoustic pressure distribution pattern.The acoustic pressure ratio significantly affects the pressure distribution and the cavitation region,and the best cavitation effect is obtained at the ratio of 2:1(P15:P20).

Seismic modeling by combining the finite-difference scheme with the numerical dispersion suppression neural network

Seismic finite-difference(FD) modeling suffers from numerical dispersion including both the temporal and spatial dispersion, which can decrease the accuracy of the numerical modeling. To improve the accuracy and efficiency of the conventional numerical modeling, I develop a new seismic modeling method by combining the FD scheme with the numerical dispersion suppression neural network(NDSNN). This method involves the following steps. First, a training data set composed of a small number of wavefield snapshots is generated. The wavefield snapshots with the low-accuracy wavefield data and the high-accuracy wavefield data are paired, and the low-accuracy wavefield snapshots involve the obvious numerical dispersion including both the temporal and spatial dispersion. Second, the NDSNN is trained until the network converges to simultaneously suppress the temporal and spatial dispersion.Third, the entire set of low-accuracy wavefield data is computed quickly using FD modeling with the large time step and the coarse grid. Fourth, the NDSNN is applied to the entire set of low-accuracy wavefield data to suppress the numerical dispersion including the temporal and spatial dispersion.Numerical modeling examples verify the effectiveness of my proposed method in improving the computational accuracy and efficiency.

The study on three-dimensional numerical model and fronts of the Jiulong Estuary and the Xiamen Bay

Applying the methods of on-site observation and dynamic model, the research on the fronts at the Jiulong Estuary has been carried out, during which spatial and temporal distribution, dynamic characteristics and formation mechanism of salinity fronts are analyzed and discussed. The research shows that the estuarine fronts mainly lie in the area from the Jiyu Islet to the Haimen Island, outside of Yuweizai to Hulishan cross-section, the near coast of Yuweizai and the south of the Songyu-Gulangyu Channel. The fronts in the former two regions are formed directly by plume, while the one near the coast of Yuweizai is a tidal intrusion front caused by flood current and the one at the south of the Songyu-Gulangyu Channel is the result of current shear transformation. Under normal circumstances, fresh water of the Jiulong River mainly influences the inside of the Xiamen Bay, and when it is in typhoon seasons, plume front can affect the Taiwan Strait and has an effect on the biogeochemical Drocesses in the strait.

Numerical Simulation of Saline Intrusion and Purging in Long SeaOutfalls with Three-Dimensional Model

Saline intrusion into marine sewage ouffalls will greatly decrease the efficiency of sewage disposal. In order to investigate the mechanisms of this flow, in this paper, a three-dimensional numerical model based on FVM （Finite Volume Method） is established, The RNG κ-ε model is selected for turbulence modeling. The time-averaged vohtme fraction equations are introduced to simulate the stratification and inteffaeial exchange of sewage and seawater in outfalls. Validity of the established three-dimensional numerical model is evaluated by comparisons of numerical results with experimental data. With this three-dimensional numerical model, the internal flow characteristics in ouffalls for different sewage discharges are simulated. The results indicate that for a low sewage discharge, saline circulates in the outfall due to intrusion and both the inflowing momentum and the inteffaeial turbulent mixing are important mechanisms to extrude the saline. For a high sewage discharge, saline intrusion could be avoided. The inflow momentum is the main mechanism to extrude the saline and the inteffacial turbulent mixing is nut important relatively. Even at a high sewage discharge, the saline wedge would be retained in the main ouffall pipe after the risers are purged. It takes a long time for this saline wedge to be extruded by interracial turbulent mixing.

Numerical Simulation of the Whole Three-Dimensional Flow in a Stirred Tank with Anisotropic Algebraic Stress Model

In accordance to the anisotropic feature of turbulent flow, ananisotropic algebraic stress model is adopted to predict theturbulent flow field and turbulent characteristics generated by aRushton disc turbine with the improved inner-outer iterativeprocedure. The predicted turbulent flow is compared with experimentaldata and the simulation by the standard k-ε turbulence model. Theanisotropic algebraic stress model is found to give better predictionthan the standard k-ε turbulence model. The predicted turbulent flowfield is in accordance to experimental data and the trend of theturbulence intensity can be effectively reflected in the simulation.

Three-dimensional tidal current numerical model of the Oujiang Estuary

The characteristics of three-dimensional （3-D） tidal current in the Oujiang Estuary are investigated according to in situ observations. The Oujiang Estuary has features of irregular coastline, complex topography, many islands, moveable boundary, and submerged dyke, therefore, σ 3-D numerical model oil an unstructured triangular grid has been degeloped. The σ coordinate transforination, the moveable boundary and submerged dyke treatment techniques were employed in the model so it is suitable for the tidal simulations in the Oujing Estuary with submerged dyke and moveable boundary problems. The model is evaluated with the in situ data, and the results show that the calculated water elevations at 19 stations and currents at 19 profiler stations are in good agreement with measured data both in magnitude and phase. This numerical model is applied to the 3-D tidal circulation simulations of experiments in stopping flow transport through the South Branch of the Oujiang Estuary, and the feasibility to cutoff the flow in the South Branch of the Oujiang Estuary is demonstrated by numerical simulation experiments. The developed numerical model simulated the 3-D tidal current circulations in complicated coastal and estuarine waters very well.

Three-Dimensional Tidal Model and Its Application to Numerical Simulation of Water Quality in Coastal Waters

The turbulence mechanism plays an important part in the mixing process and momentum transfer of turbulence. A three-dimensional Prandtl mixing length tidal model has been developed to simulate tidal flows and water quality. The eddy viscosities and diffusivities are computed from the Prandtl mixing length model. In order to model the water quality of an estuary or coastal area many interdependent processes need to be simulated. These may be conveniently separated into three main groups: transport and mixing processes, biochemical interaction of water quality variables and the utilization and re-cycling of nutrients by living matter. The model simulates full oxygen and nutrient balance, primary productivity and the transport, reaction mechanism and fate of pollutants over tidal time-scales. The model is applied to numerical simulation of tidal flows and water quality in Dalian Bay. The model has been calibrated against a limited data set of historical water quality observations and in general demonstrates excellent agreement with all available data.

NUMERICAL SIMULATION OF THE KUROSHIO USING NESTED MODEL OF THREE-DIMENSIONAL BAROCLINIC CIRCULATION

As a western boundary current, the Kuroshio is closely related to the large scale oceanic circulation and at the same time, is greatly influenced by the local topography because of its narrow width. Numerical studies of the Kuroshio are usually confined to portions of it in different geographical regions since the computer execution time required to run a numerical model of the Pacific using a sufficiently fine grid to resolve adequately the flow structure of the Kuroshio is enormous. In order to circumvent the problems of multiple spatial scales and consistent boundary conditions, nested models are employed in which a coarse grid model of the Pacific is used to supply the open boundary conditions for a finer grid model of the northwestern Pacific to simulate the flow and temperature fields of the Kuroshio in summer and winter. The major features of the Kuroshio have in general been successfully simulated by the nested models.

Benchmarking of two three-dimensional numerical models in time/space domain to predict railway-induced ground vibrations

In the last 30 years,the scientific community has developed and proposed different models and numerical approaches for the study of vibrations induced by railway traffic.Most of them are formulated in the frequency/wave number domain and with a 2.5D approach.Three-dimensional numerical models formulated in the time/space domain are less frequently used,mainly due to their high computational cost.Notwithstanding,these models present very attractive characteristics,such as the possibility of considering nonlinear behaviors or the modelling of excess pore pressure and non-homogeneous and non-periodic geometries in the longitudinal direction of the track.In this study,two 3D numerical approaches formulated in the time/space domain are compared and experimentally validated.The first one consists of a finite element approach and the second one of a finite difference approach.The experimental validation in an actual case situated in Carregado(Portugal)shows an acceptable fitting between the numerical results and the actual measurements for both models.However,there are some differences among them.This study therefore includes some recommendations for their use in practical soil dynamics and geotechnical engineering.

A Higher-Efficient Three-Dimensional Numerical Model for Small Amplitude Free Surface Flows

A higher-efficient three-dimensional non-hydrostatic model is developed to simulate small amplitude free surface flows based on a staggered unstructured grid. In this model, a fractional step algorithm is adopted to solve the Navier-Stokes equations in two major steps. A top-layer pressure method is proposed to minimize the number of vertical layers and subsequently the computational cost. Three classical examples of small amplitude free surface flows are used to demonstrate the capability and efficiency of the model. The satisfactory results demonstrated the capability and efficiency of modelling a range of small amplitude free surface flows with only a small number of vertical layers.

Numerical investigation of radio-frequency negative hydrogen ion sources by a three-dimensional fluid model

A three-dimensional fluid model is developed to investigate the radio-frequency inductively coupled H2 plasma in a reactor with a rectangular expansion chamber and a cylindrical driver chamber,for neutral beam injection system in CFETR.In this model,the electron effective collision frequency and the ion mobility at high E-fields are employed,for accurate simulation of discharges at low pressures(0.3 Pa-2 Pa)and high powers(40 kW-100 kW).The results indicate that when the high E-field ion mobility is taken into account,the electron density is about four times higher than the value in the low E-field case.In addition,the influences of the magnetic field,pressure and power on the electron density and electron temperature are demonstrated.It is found that the electron density and electron temperature in the xz-plane along permanent magnet side become much more asymmetric when magnetic field enhances.However,the plasma parameters in the yz-plane without permanent magnet side are symmetric no matter the magnetic field is applied or not.Besides,the maximum of the electron density first increases and then decreases with magnetic field,while the electron temperature at the bottom of the expansion region first decreases and then almost keeps constant.As the pressure increases from 0.3 Pa to 2 Pa,the electron density becomes higher,with the maximum moving upwards to the driver region,and the symmetry of the electron temperature in the xz-plane becomes much better.As power increases,the electron density rises,whereas the spatial distribution is similar.It can be summarized that the magnetic field and gas pressure have great influence on the symmetry of the plasma parameters,while the power only has little effect.

Three-Dimensional Numerical Model for Tsunami Propagation Passing Through An Obstacle

A three-dimensional numerical tsunami model is developed to analyze the nonlinear behavior of flow around obstacles with the Marker and Cell （MAC） method based on the Navier-Stokes equations. Tnrough a comparison with experimental data for the cases of dam break and solitary wave propagation, verification of the three-dimensional numerical model is given. Numerical experiment is performed for the analysis of the nonlinear behavior of flow around obstacles and compared with experimental data. The velocity and pressure around obstacles are presented with sufficient accuracy for tstmami propagation passing through an obstacle.