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.

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.

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.

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 INVESTIGATION OF THREE-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS IN DIVERGENT CURVED CHANNELS AND TURBULENT MODEL STUDY

In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density-weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flown in divergent curved channels was carried out by means of parabolizeil computation method. The calculating results were used to analyze and investigate the aerodynamic performance of talor cascades in compressors preliminarily.

Three-dimensional numerical simulation of crown spike due to coupling effect between bubbles and free surface

The motion of gas bubbles beneath a free surface will lead to a spike of fluid on the free surface. The distance of the bubbles to the free surface is the key factor to different phenomena. When the inception distance varies in some range, crown phenomenon would happen after the impact of weak buoyancy bubbles, so this kind of spike is defined as crown spike in the present paper. Based on potential flow theory, a three-dimensional numerical model is established to simulate the motion of the free-surface spike generated by one bubble or a horizontal line of two in-phase bubbles. After the downward jet formed near the end of the collapse phase, the simulation of the free surface is performed to study the crown spike without regard to the toroidal bubble＇s effect. Calculations about the interaction between one bubble and free surface agree well with the experimental results conducted with a high-speed camera, and relative error is within 15%. Crown spike in both single- and two-bubble cases are simulated numerically. Different features and laws of the motion of crown spike, depending on the bubble-boundary distances and the inter-bubble distances, have been investigated.

The numerical simulation for a 3D two-phase anisotropic medium based on BISQ model

Biot-flow and squirt-flow are the two most important fluid flow mechanisms in porous media containing fluids. Based on the BISQ （Biot-Squirt） model where the two mechanisms are treated simultaneously, the elastic wave-field simulation in the porous medium is limited to two-dimensions and two-components （2D2C） or two-dimensions and three-components （2D3C）. There is no previous report on wave simulation in three- dimensions and three-components. Only through three dimensional numerical simulations can we have an overall understanding of wave field coupling relations and the spatial distribution characteristics between the solid and fluid phases in the dual-phase anisotropic medium. In this paper, based on the BISQ equation, we present elastic wave propagation in a three dimensional dual-phase anisotropic medium simulated by the staggered-grid high-order finite-difference method. We analyze the resulting wave fields and show that the results are an improvement.

A Three-Dimensional Water Quality Model and Its Application to Jiaozhou Bay, China

A three-dimensional coupled physical and water quality model was developed and applied to the Jiaozhou Bay to study water quality involving nutrients, biochemical oxygen demand, dissolved oxygen, and phytoplankton that are closely related to eutrophication process. The physical model is a modified ECOM-si version with inclusion of flooding/draining processes over the intertidal zone. The water quality model is based on WASP5 which quantifies processes governing internal nutrients cycling, dissolved oxygen balance and phytoplankton growth. The model was used to simulate the spatial distribution and the temporal variation of water quality in the Jiaozhou Bay for the period of May 2005 to May 2006. In addition, the effect of reduction of riverine nutrients load was simulated and evaluated. The simulated results show that under the influence of nutrients discharged from river, the concentrations of nutrients and phytoplankton were higher in the northwest and northeast of the bay, and decreased from the inner bay to the outer. Affected by strong tidal mixing, the concentrations of all state variables were vertically homogeneous except in the deeper regions where a small gradient was found. Obvious seasonal variation of phytoplankton biomass was found, which exhibited two peaks in March and July, respectively. The variation of riverine waste loads had remarkable impact on nutrients concentration in coastal areas, but slightly altered the distribution in the center of the bay.

NUMERICAL SIMULATION OF SOUTH CHINA SEA MONSOON ONSET BASED ON GRAPES MODEL AND EXPERIMENTS ON INITIAL MODEL FIELDS

The Global and Regional Assimilation and Prediction System (GRAPES), a limited-area regional model, was used to simulate the onset of South China Sea summer monsoon. In view of the relatively insufficient information about the initial field in simulation predictions, the Advanced Microwave Sounding Unit-B (AMSU-B) data from a NOAA satellite were introduced to improve the initial values. By directly using the 3-dimensional variational data assimilation system of GRAPES, two schemes for assimilation tests were designed. In the design, Test 1 (T1) assimilates both sounding and AMSU-B data, and Test 2 (T2) assimilates only the conventional sounding data, before applying the model in simulation forecasts. Comparative experiments showed that the model was very sensitive to initial fields and successful in reproducing the monsoon onset, allocation of high- and low-level wind fields during the pentad of onset, and the northward advancement of the monsoon and monsoon rain bands. The scheme, however, simulated rainfall and the location of the subtropical high with deviations from observations. The simulated location of the subtropical high was more westward and northward and the simulated rainfall for the South China Sea was larger and covered a broader area.

Optimal Evacuation Scheme Based on Dam-Break Flood Numerical Simulation

The optimal evacuation scheme is studied based on the dam-break flood numerical simulation. A three- dimensional dam-break mathematical model combined with the volume of fluid （VOF） method is adopted. According to the hydraulic information obtained from numerical simulation and selecting principles of evacuation emergency scheme, evacuation route analysis model is proposed, which consists of the road right model and random degree model. The road right model is used to calculate the consumption time in roads, and the random degree model is used to judge whether the roads are blocked. Then the shortest evacuation route is obtained based on Dijstra algorithm. Gongming Reservoir located in Shenzhen is taken as a case to study. The results show that industrial area I is flooded at 2 500 s, and after 5 500 s, most of industrial area II is submerged. The Hushan, Loucun Forest and Chaishan are not flooded around industrial area I and II. Based on the above analysis, the optimal evacuation scheme is determined.

3-D NUMERICAL SIMULATION OF FRACTURE PROCESSES IN HETEROGENEOUS BRITTLE MATERIALS

By using the lattice model combined with finite element methods andstatistical techniques, a numerical approach is developed to establish mechanical models ofthree-dimensional heterogeneous brittle materials. A special numerical code is introduced, in whicha lattice model and statistical approaches are used to simulate the initial heterogeneity ofmaterial properties. The size of displacement-load step is adap-tively determined so that only fewelements would fail in each load step. When the tensile principal strain in an element exceeds theultimate strain of this element, the element is considered broken and its Young's modulus is set tobe very low. Some important behaviors of heterogeneous brittle materials are indicated using thiscode. Load-displacement curves and figures of three-dimensional fracture patterns are alsonumerically obtained, which are similar to those observed in laboratory tests.

A FULLY ELLIPTIC CALCULATING PROCEDURE FOR THREE-DIMENSIONAL THERMAL POLLUTION

The use of the mathematical models so far for three-dimensional flow has some limitations because of their simplifications. Many characteristics of the flow field can not be predicted by these models. In this paper the three dimensional elliptic governing equations are solved by finite-volume methods; the buoyancy extensions of the widely tested k-?. model is adapted. The method is first applied to calculate the field of side discharge into open channel flow. The results are in good agreement with those of ref. [7]. Then it is further used to the intake discharge problem which is of a typical layout in cooling-water projects, and the calculated results, which predict in detail the charactreistics of flow field, are reasonable.

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

THREE-DIMENSIONAL NUMERICAL MODELLING OF SUBMERGED DIKE ALIGNMENT IN CURVED ESTUARINE CHANNEL

Submerged dikes were frequently built in curved estuarine channels to improve navigational conditions. A three-dimensional numerical model of tidal motions was developed to simulate flows through the submerged dike alignment in curved estuarine reach of complex bathymetry on the basis of satisfactory calibrations. Through the analysis of the morphological characteristics of the curved channel of the Huangpu River mouth in the Yangtze River Delta, a submerged dike alignment project was examined. The effect of the navigation channel improvement project and its influence on the flow regimes, the navigational conditions, the flood control and the operating conditions of harbours within the adjacent water area were evaluated, and the technical feasibility of the navigation channel improvement scheme was demonstrated.

EVALUATION OF THREE-DIMENSIONAL NUMERICAL MODEL FOR SALINE INTRUSION AND PURGING IN SEWAGE OUTFALLS

Saline intrusion into sewage outfalls will greatly decrease the efficiency of the structures. The numerical model for this flow has been limited to one- and two-dimensional ones. In this article, a three-dimensional numerical model for saline intrusion and purging in sewage outfalls was developed. The flow was modeled in three dimensions under turbulent conditions with the RNG k-ε turbulence model. The numerical results provided quantitative evidence of the fundamental flow mechanisms that took place during saline intrusion and purging. The comparisons of the results with that of two-dimensional model and that of experiments indicate that the three-dimensional numerical model developed in this article is more effective in predicting the internal flow in outfalls.

THREE-DIMENSIONAL ELASTIC ATMOSPHERIC NUMERICAL MODEL AND THE SIMULATION OF A SEVERE STORM CASE

A three-dimensional meso-γ,scale elastic atmospheric numerical model has been established and used to simulate a severe storm case.The important characteristics of the modeled storm are close to those of the observed case.

NUMERICAL INVESTIGATION OF THREE-DIMENSIONAL FLOW AND BED SHEAR STRESS DISTRIBUTION AROUND THE SPAN SHOULDER OF PIPELINE

Three-dimensional flow around a pipeline span shoulder is simulated using afractional step finite element method. The Reynolds number, based on the pipe-diameter and theapproaching flow velocity, is set at 500 and 5 x 10~5 to simulate both laminar and turbulent flow.In high Reynolds number case, Smagorinsky SGS closure is used to model the turbulent flows. The flowfield visualization by vorticity iso-surfaces shows that a spiral vortex tube is formed around thespan shoulder and extends around the span shoulder. The vortex cores defined by the eigenvalues ofthe symmetric tensor S^2 + Ω~2 (S and Ω are respectively the symmetric and antisymmetric parts ofthe velocity gradient tensor) gives more details of the flow field. It is also found that there aresignificant bed shear stress concentrations in the span shoulder area. The reasons for the shearstress concentration are discussed.

Modeling of the Mixture of Wastewater Discharged from A Submerged Multiport Diffuser in Nantong Sea-Area

Laboratory experiments were conducted to investigate the mixture of wastewater discharged from a submerged multiport diffuser in the Nantong sea-area. The process was then simulated with a three-dimensional numerical model. The plane or line patch was used to impose the discharge momentum flux in the near field. A comparison of model simulation with laboratory experiments shows that the proposed model can be used to simulate the shapes of pollution plumes, the distributions of excess concentration, and the velocity induced by a coflowing diffuser in proximity to a shoreline boundary. From the numerical simulation and laboratory experiments, it is recommended that the multiport diffuser be placed in a hydrodynamically active sea-area.

THREE-DIMENSIONAL NUMERICAL SIMULATIONS OF THE EFFECTS OF ICE PHASE PROCESSES ON EVOLUTION OF CONVECTIVE STORMS

The numerical experiments on sensitivity of two types of convective storms to ice phasemicrophysical processes have been made by using a fully elastic three-dimensional cloud mod-el with a more detailed ice phase parameterization scheme. The simulations show that, ingeneral, inclusion of ice phase processes in the model leads to more intensive modelingstorms--the total latent heat released and the total precipitation increase obviously, the cloudtop rises, and the maximum ground precipitation rate is reached earlier. These effects of icephase processes can be much more significant in some relatively cold environments, in whichthey even modify the dynamic structures and life cycle of simulating storms. The mecha-nisms and favourable conditions of ice phase influences on storms are also discussed.

行人荷载下乐山大佛九曲栈道赋存岩体稳定性研究

针对乐山大佛九曲栈道地形崎岖多变、长年游人如织的特点,为分析行人荷载对九曲栈道赋存岩体稳定性的影响,建立了九曲栈道区域的精细化模型,采用数值计算方法研究了行人静、动荷载作用下九曲栈道赋存岩体的受力状态及变形特征。结果表明,九曲栈道满载行人时赋存岩体整体稳定,仅局部表层岩体发生破坏。静荷载下L1裂隙底部、L15中下部及栈道底部佛龛的表层岩体受拉破坏;栈道中下部两转角处崖壁、佛脚平台及临江面底部凸出部位的表层岩体易发展为受拉破坏。动荷载下栈道赋存岩体的振动速度均超过规范容许值,在行人动荷载长期作用下易疲劳破坏;栈道上部转角处凸出部位的表层岩体还可能发生瞬时受拉破坏。研究结果对掌握行人荷载下九曲栈道赋存岩体的稳定性现状及预防性加固有指导意义。