Numerical study on residual current and its impact on mass transport in the Hangzhou Bay and the Changjiang Estuary I. A3-D joint model of the Hangzhou Bay and the Changjiang Estuary

A 3-D numerical model is set up in a large domain covering the Hangzhou Bay and the Changjiang Estuary based on the ECOM model in orthogonal curvilinear coordinates.The numerical schemes for baroclinic pressure gradient (BPG)terms and convective terms are improved in the paper according to the characteristics of velocity field and mass transport in the area.The model is validated by the simulations of residual current and salinity transport in the Hangzhou Bay and the Changjiang Estuary.

Numerical modeling calculation for the spatial distribution characteristics of horizontal field transfer functions

Applying 3-dimension finite difference method, the distribution characteristics of horizontal field transfer functions for rectangular conductor have been computed, and the law of distribution for Re-part and Im-part has been given. The influences of source field period, the conductivity, the buried depth and the length of the conductor on the transfer functions were studied. The extrema of transfer functions appear at the center, the four corners and around the edges of conductor, and move with the edges. This feature demonstrates that around the edges are best places for transfer functions' observation.

Simulation of subcritical flow pattern in 180° uniform and convergent open-channel bends using SSIIM 3-D model

In meandering rivers, the flow pattern is highly complex, with specific characteristics at bends that are not observed along straight paths. A numerical model can be effectively used to predict such flow fields. Since river bends are not uniform-some are divergent and others convergent-in this study, after the SSIIM 3-D model was calibrated using the result of measurements along a uniform 180° bend with a width of 0.6 m, a similar but convergent 180v bend, 0.6 m to 0.45 m wide, was simulated using the SSI1M 3-D numerical model. Flow characteristics of the convergent 180° bend, including lengthwise and vertical velocity profiles, primary and secondary flows, lengthwise and widtbwise slopes of the water surface, and the helical flow strength, were compared with those of the uniform 180° bend. The verification results of the model show that the numerical model can effectively simulate the flow field in the uniform bend. In addition, this research indicates that, in a convergent channel, the maximum velocity path at a plane near the water surface crosses the channel＇s centerline at about a 30° to 40° cross-section, while in the uniform bend, this occurs at about the 50° cross-section. The varying range of the water surface elevation is wider in the convergent channel than in the uniform one, and the strength of the helical flow is generally greater in the uniform channel than in the convergent one. Also, unlike the uniform bend, the convergent bend exhibits no rotational cell against the main direction of secondary flow rotation at the 135° cross-section.

3-D Modelling of the Confederation Bridge Using Data of Full Scale Tests

Long-span bridges are special structures that require advanced analysis techniques to examine their performance. This paper presents a procedure developed to model the Confederation Bridge using 3-D beam elements. The model was validated using the data collected before the opening of the bridge to the public. The bridge was instrumented to conduct fullscale static and dynamic tests. The static tests were to measure the deflection of the bridge pier while the dynamic tests to measure the free vibrations of the pier due to a sudden release of the static load. Confederation Bridge is one of the longest reinforced concrete bridges in the world. It connects the province of Prince Edward Island and the province of New Brunswick in Canada. Due to its strategic location and vital role as a transportation link between these two provinces, it was designed using higher safety factors than those for typical highway bridges. After validating the present numerical model, a procedure was developed to evaluate the performance of similar bridges subjected to traffic and seismic loads. It is of interest to note that the foundation stiffness and the modulus of elasticity of the concrete have significant effects on the structural responses of the Confederation Bridge.

Full 3-D numerical modeling of borehole electric image logging and the evaluation model of fracture

A full 3-D finite element method numerical modeling program is written based on the principle and technical specification of borehole electric image well logging tool. The response of well logging is computed in the formation media model with a single fracture. The effect of changing fracture aperture and resistivity ratio to the logging response is discussed. The identification ability for two parallel fractures is also present. A quantitative evaluation formula of fracture aperture from borehole electric image logging data is set up. A case study of the model well is done to verify the accuracy of the for-mula. The result indicates that the formula is more accurate than the foreign one.

Numerical Si mulation of Transportation of SPMfrom the Yellow River to the Bohai Sea

A 3D diagnostic model including a suspended sediment transport module, ECOMSED, driven by the monthly discharge and sediment load of the Yellow River in 1983 ～ 1984, was applied to the Bohai Sea. The simulation of the temporal-spatial variation of SPM （Suspended Particular Matter） concentration, sediment flux, and deposition rate was carfled out. It could be seen that, the SPM concentration exhibited distinct seasonal variation, and the variation characteristic was similar for two years. Some of the fine sediment of the Yellow River extended to the western bank of the Liaodong Bay, but most of the sediment deposited around the estuary of the Yellow River, the deposition flux rapidly decreasing with the increasing distance to the estuary. The deposition rate kept at 0.05 ～ 0.1 mm/a for most area, close to the insitu data. There were two areas of high SPM concentration in the Bohai Sea, one of which could be attributed to the Yellow River discharge, and another one, located at the seas with intensive resuspension power, to the tidal current energy. The sediment from the Yellow River was transported mainly along the track of the, Lagrangian residual cireulations. In one word, the suspended load transport was basically attributed to the wind-driven and tidal-induced Lagrangian residual circulations. The resuspenslon flux was related to the bottom currents： the larger the current speed, the more the sediment resuspended.

Numerical modeling of 3-D terrain effect on MT field

Using the boundary element method, the numerical modeling problem of three-dimensional terrain effect on magnetotelluric (MT) field is solved. This modeling technique can be run on PC in the case of adopting special net division. The result of modeling test for 2-D terrain by this modeling technique is basically coincident with that by 2-D modeling technique, but there is a great difference between the results of 3-D and 2-D modeling for 3-D terrain.

A Higher-Efficient Non-Hydrostatic Finite Volume Model for Strong Three-Dimensional Free Surface Flows and Sediment Transport

In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection-diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional （2-D） grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.

A New Efficient Finite Volume Modeling of Small Amplitude Free Surface Flows with Unstructured Grid

A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k - c equations in this model. The eddy viscosity is calculated from the k-c turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field, and then applied to simulate the tidal flow in the Bohai Sea.

Influence of complex topography on magnetotelluric-observed data using threedimensional numerical simulation:A case from Guangxi area,China

Fully recognize various problems in the observed magnetotelluric(MT)data is the precondition of inverse solutions.In the paper,according to the geomorphological conditions of the observational MT stations in the Guangxi area,we constructed several different kinds of models to conduct a three-dimensional forward simulation of the MT fi eld using the vector fi nite element method(FEM).First,the variation rule and differences of apparent resistivityρxy andρyx in the xy and yx modes were studied and analyzed,and then the geoelectric information refl ected by the change of apparent resistivityρxx andρyy were discussed.Final,the responses of typical geological structures that cause a static shift problem were presented.The synthetic examples showed thatρxy andρyx were relevant to the layout of the survey line,for instance,ρxy had different values along the west-east profi le compared with that of the southnorth profi le,Moreover,ρxx andρyy could subtly show the abnormal body-host rock interface,which could be used to restrict the anomalous domain in the inversion process.In addition to the scale and depth of the top surface of the anomalous body,the widespread rivers and hills,can simulate static shift.Hence,to reduce the infl uence of static shift on MT data,a reasonable distance between a station and rivers or hills should be considered in accordance with the scale of rivers or hills.

Improved treatments for evaluating horizontal magnetic components through the 3-D FDM in E-polarization induction problems

To improve the accuracy of the numerical evaluation through the 3-D finite difference method, the surface boundary conditions are added to modify the old program. The author has tested the new program by making calculations for the model constructed by Wanamaker, et al (1984). The comparison between the numerical results obtained from this paper and those by Wannamaker, et al (1984) indicates that a pronounced improvement is realized in the evaluation of the horizontal magnetic components. Moreover, better calculations for the vertical magnetic components are also obtainable by using the new program.

The Application of 3-D Visible Technology to Reservoir Management

The paper deals with the application of 3 -D visible technology to reservoir management. Making use of this method for expanding - spread data point in reservoir management, can discard the false and retain the true during data recording. As a result, The quality of data recording is ensured. In reservoir description, the reservoir characteristics, such as space distribution,physical change and fluid distribution may be identified by restoring palaeostructures, building - up 3-D facics tract model and 3-D fracture system model. Seismic interpretation, geologic modeling and numerical simulation are well integrated so that they can be promote reservoir performance management to develop into the intensive management pattern.

A SIMPLIFIED NUMERICAL MODEL OF 3-D GROUNDWATER AND SOLUTE TRANSPORT AT LARGE SCALE AREA

A simplified numerical model of groundwater and solute transport is developed. At large scale area there exists a big spatial scale difference between horizontal and vertical length scales. In the resultant model, the seepage region is particularly divided into several virtual layers along the z direction and vertical 1-D columns covering x-y 2-D area according to stratum properties. The numerical algorithm is replacing the full 3-D water and mass balance analysis as the 2-D Galerkin finite element method in x- and y-directions and 1-D finite differential approach in the z direction. The reasonable method of giving minimum thickness is successfully used to handle transient change of water table, drying cells and problem of rewetting. The solution of the simplified model is preconditioned conjugate gradient and ORTHOMIN method. The validity of the developed 3-D groundwater model is tested with the typical pumping and backwater scenarios. Results of water balance of the computed example reveal the model computation reliability. Based on a representative 3-D pollution case, the solute transport module is tested against computing results using the MT3DMS. The capability and high efficiency to predict non-stationary situations of free groundwater surface and solute plume in regional scale problem is quantitatively investigated. It is shown that the proposed model is computationally effective.

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.

A SEMI-IMPLICIT 3-D NUMERICAL MODEL USING SIGAM-COORDINATE FOR NON-HYDROSTATIC PRESSURE FREE-SURFACE FLOWS

A 3-D numerical formulation is proposed on the horizontal Cartesian, vertical sigma-coordinate grid for modeling non-hydrostatic pressure flee-surface flows. The pressure decomposition technique and 0 semi-implicit method are used, with the solution procedure being split into two steps. First, with the implicit parts of non-hydrostatic pressures excluded, the provisional velocity field and free surface are obtained by solving a 2-D Poisson equation. Second, the theory of the differential operator is employed to derive the 3-D Poisson equation for non-hydrostatic pressures, which is solved to obtain the non-hydrostatic pressures and to update the provisional velocity field. When the non-orthogonal sigma-coordinate transformation is introduced, additional terms come into being, resulting in a 15-diagonal, diagonally dominant but unsymmetric linear system in the 3-D Poisson equation for non-hydrostatic pressures. The Biconjugate Gradient Stabilized （BiCGstab） method is used to solve the resulting 3-D unsymmetric linear system instead of the conjugate gradient method, which can only be used for symmetric, positive-definite linear systems. Three test cases are used for validations. The successful simulations of the small-amplitude wave, a supercritical flow over a ramp and a turbulent flow in the open channel indicate that the new model can simulate well non-hydrostatic flows, supercritical flows and turbulent flows.

3-D VARIABLE PARAMETER NUMERICAL MODEL FOR EVALUATION OF THE PLANNED EXPLOITABLE GROUNDWATER RESOURCE IN RE-GIONAL UNCONSOLIDATED SEDIMENTS

In order to correctly evaluate the exploitable groundwater resottrce in regional complex, thick Quaternary unconsolidated sediments, the whole Quaternary unconsolidated sediments are considered as a unified hydrogeological unit and a 3-D unsteady groundwater flow numerical model is adopted. Meanwhile, with the consideration of the dynamic changes of the porosity, the hydraulic conductivity and the specific storage with the groundwater level dropping during the exploitation process, an improved composite element seepage matrix adjustment method is applied to solve the unsteady flow problem of free surface. In order to eva- luate the exploitable groundwater resource in Cangzhou, Hebei Province, the hydrogeological conceptual model of Cangzhou is generalized to establish, a 3-D variable parameter numerical model of Cangzhou. Based on the prediction of the present groundwater exploitation, and by adjusting the groundwater exploitation layout, the exploitable groundwater resource is predicted. The model enjoys features like good convergence, good stability and high precision.

A NUMERICAL MODEL FOR 3-D FLOW IN OPEN CHANNELS

A 3-D model based on the Reynolds equations with closed k-ε turbulence model is presented in this paper,which can be used to predict surface water flow in open channels.In- stead 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 bot- tom.The velocity,eddy viscosity coefficient,turbulent shear stress,turbulent kinetic energy and elevation of the free surface over the trenches dredged in the main channel,can be obtained. The computed results are in good agreement with existing experimentaing data.

THREE-DIMENSIONAL NUMERICAL MODELLING OF THE WAVE-IN-DUCED RIP CURRENTS UNDER IRREGULAR BATHYMETRY

A process-based 3-D hydrodynamic model is established to simulate the rip current structures under irregular bathymetry. The depth-varying wave-induced residual momentum, the surface rollers, the turbulent mixing and the wave-current interactions are considered. Experimental datasets are used to validate the model, and it is shown that the model can effectively describe the 3-D structures of the rip currents in both normal and oblique wave incident cases. The flow patterns of the rip currents see various characteristics for different incident wave directions. In the normal incident case, pairs of counter-rotating primary circulation cells are formed, and an offshore rip flow occurs in the embayment troughs. The peak seaward velocities occur at the top of the bed boundary layer, and the undertow is incorporated in addition to the rip currents. In the oblique incident case, the longshore currents are dominant, which result in a meandering flow along the depth contour, and the undertow is weaker compared to that in the normal incident condition.

Comparison of Fully 3-D,Simplified 3-D and 2-D Numerical Simulations on a Circulating Fluidized Bed Boiler

Based on the fully three-dimensional(3-D)and two-dimensional(2-D)comprehensive CFD(Computational Fluid Dynamics)combustion models for a circulating fluidized bed boiler,a simplified 3-D computational domain considering the corrections of furnace side wall openings is proposed.It aims to compensate for the deficiencies of the large amount of computation in the fully 3-D model and improve the air and gas flow treatments at the openings in the simplified 2-D model.Three different computational domains,named as the fully 3-D model,simplified 3-D model and 2-D model,were implemented to perform a comparative CFD analysis in an ultra-supercritical circulating fluidized bed boiler including the hydrodynamics,penetration depth of secondary air,temperature and species distribution.The simulation results computed by the simplified3-D model yield better agreement with the fully 3-D simulation results than those of the 2-D model.The simplified 3-D model is recommended as an alternative computational domain for the conventional 2-D model in the numerical simulation of large-scale circulating fluidized bed boiler.

THREE-DIMENSIONAL NUMERICAL MODEL FOR WINDING TIDAL RIVER WITH BRANCHES

Natural rivers are usually winding with branches and shoals, which are difficult to be simulated with rectangular grids. A 3-D current numerical model was established based on the orthogonal curvilinear coordinate system and vertical o coordinate system. The equations were discretisized using a semi-implicit scheme. The ＂predictor＂ and ＂corrector＂ steps were applied for the horizontal momentum equations to meet the basic requirement that the depth-integrated currents obtained from the equations for 2-D and 3-D modes have identical values. And a modification of traditional method of dry/wet discriminance was proposed to determine accurately the boundary and ensure the continuity of variable boundary in the simulation. This model was verified with the data measured in a winding tidal river with branches in April, 2004. The simulated data of water levels and velocities agree well with the measured ones, and the computed results reveal well the practical flow characteristics, including the vertical secondary flow in a winding reach.