THREE-DIMENSIONAL NON-HYDROSTATIC MODEL FOR FREE-SURFACE FLOWS WITH UNSTRUCTURED GRID

The three-dimensional Navier-Stokes equations were solved with the fractional step method where the hydrostatic pressure component was determined first, while the non-hydrostatic component of the pressure was computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric. The eddy viscosity was calculated from the efficient k-ε turbulence model. The resulting model is computationally efficient and unrestricted to the CFL condition. Computations with and without hydrostatic approximation were compared for the same cases to test the validity of the conventional hydrostatic pressure assumption. The model was verified against analytical solutions and experimental data, with excellent agreement.     

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 ispresented 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 inthe velocity-pressure iterative procedure on the basis of the conventional SIMPLE method.Thismodel 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 energyand 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 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 σ 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.     

NUMERICAL MODELLING OF FREE-SURFACE FLOWS WITH BOTTOM AND SURFACE-LAYER PRESSURE TREATMENT

A new non-hydrostatic numerical model with the three-dimensional Navier-Stokes equations on structured grids was constructed and discussed. The algorithm is based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid. The eddy viscosity coefficient was calculated by the efficient k-ε turbulence model. A new surface-layer non-hydrostatic treatment and a local cell bottom treatment were introduced so that the three-dimensional model is fully non-hydrostatic and is free of any hydrostat...     

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.     

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 resource 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 HIGHER-ORDER NON-HYDROSTATIC MODEL FOR SIMULATING WAVE PROPAGATION OVER IRREGULAR BOTTOMS

A higher-order non-hydrostatic model is developed to simulate the wave propagation over irregular bottoms based on a vertical boundary-fitted coordinate system.In the model,an explicit projection method is adopted to solve the unsteady Euler equations.Advection terms are integrated explicitly with the MacCormack's scheme,with a second-order accuracy in both space and time.Two classical examples of surface wave propagation are used to demonstrate the capability of the model.It is found that the model with on...     

SIGMA-COORDINATE NUMERICAL MODEL FOR SIDE-DISCHARGE INTO NATURAL RIVERS

Due to large topography slopes in natural rivers, pollutant concentration embodies a property of three-dimensional distribution when wastewater is discharged from effluents along the bank. With the sigma coordinate along the vertical dimension fitted to both the moving free surface and the bed topography, a three-dimensional numerical model was developed in the present work to address pollutant transport processes in the above-mentioned cases. To avoid the reduction in accuracy caused by spurious diffusion in the case of steep bottom slopes, a formula for horizontal diffusion in the sigma coordinate system was derived. A case study for the side discharge into a straight open-channel flow shows that numerical results are verified well by experimental data. Furthermore, the present model is also verified by the simulation of discharging wastewater from Fuling Phosphorus Factory effluent into the Three Gorges Reservoir and the agreement between the numerical simulation results and field observation data is satisfactory. The change of the mixing zone scope in the water surface versus the layers along the vertical dimension was also discussed in detail. The study shows that a more realistic calculation for pollutant discharge has been provided by the present model than by the depth-average model which predicts an unrealistically smaller mixing zone.     

A SPLIT-CHARACTERISTIC FINITE ELEMENT MODEL FOR 1-D UNSTEADY FLOWS

An efficient and accurate solution algorithm was proposed for 1-D unsteady flow problems widely existing in hydraulic engineering. Based on the split-characteristic finite element method, the numerical model with the Saint-Venant equations of 1-D unsteady flows was established. The assembled finite element equations were solved with the tri-diagonal matrix algorithm. In the semi-implicit and explicit scheme, the critical time step of the method was dependent on the space step and flow velocity, not on the wave celerity. The method was used to eliminate the restriction due to the wave celerity for the computational analysis of unsteady open-channel flows. The model was verified by the experimental data and theoretical solution and also applied to the simulation of the flow in practical river networks. It shows that the numerical method has high efficiency and accuracy and can be used to simulate 1-D steady flows, and unsteady flows with shock waves or flood waves. Compared with other numerical methods, the algorithm of this method is simpler with higher accuracy, less dissipation, higher computation efficiency and less computer storage.     

3-D SHALLOW WATER FLOW COMPUTATION BY A SEMIIMPLICIT FINITE ELEMENT METHOD

A simi-implicit finite element method is developed for three-dimensional shallow water flow. By using water depth to scale the vertical coordinate, the governing equation is transformed into fixed computational domain. An efficient generalized conjugate gradient scheme is adopted for the solution of finite element analogy.     

A 2-D HYDRODYNAMIC MODEL FOR THE RIVER, LAKE AND NETWORK SYSTEM IN THE JINGJIANG REACH ON THE UNSTRUCTURED QUADRANGLES

The main river,the Dongting Lake and river networks in the Jingjiang reach of the Yangtze River constitute a complex water system,for which a full 2-D hydrodynamic model is established instead of the traditional 1-D or compound models for simulation of such complex systems,based on the latest developments of computer technologies and numerical methods.To better handle irregular boundaries and keep the computation cost well in a reasonable limit,unstructured grids of moderate scale are used. In addition,a dynamic boundary tracking method is proposed to simulate variable flow domains at different floods,especially,when the moderate scale gird can not describe flows in narrow river-network channels at low water levels.Theθsemi-implicit method and the Eulerian-Lagrangian Method(ELM)are adopted,which make the model unconditionally stable with respect to the gravity wave speed and Courant number restrictions.Properties and efficiency of the model are discussed,and it is concluded that the new model is robust and efficient enough for the simulation of a big,complex water system.Validation tests show that the simulation results agree well with field data.It takes about 0.96 h to complete the computation of a 76 d flood,which indicates that the model is efficient enough for engineering applications.     

A VERTICAL 2-D NUMERICAL SIMULATION OF SUSPENDED SEDIMENT TRANSPORT

Numerical simulation of sediment transport and bed evolution has become an important technique in the sediment research. In this article,a numerical model of suspended sediment transport was proposed,which was established in the vertical σ coordinate for fitting the free surface and bottom. In the research of the sediment transport,the predominant factors were found to be the eddy diffusion,the settling velocity,the bed condition and so on. By the aid of the model in the article,the contribution of the Rouse parameter to the vertical profile of sediment concentration was clarified,which was identical to the theoretical results. In the comparison of the numerical results with laboratory data,the agreement between experimental data and numerical results was reached except for some data. And the possible reasons for the disagreement were discussed.     

A NUMERICAL PRESSURE TRANSIENT MODEL FOR MULTILAYERED GAS RESERVOIRS WITH PSEUDOSTEADY STATE FORMATION CROSSFLOW

ＮＯＭＥＮＣＬＡＴＵＲＥＡＤｊ=Ａｊ·ｒ2 ｗ(ｋｈ) ｔＣＤｅ =ＴＶｗ2πＴｗｒｗ2 (ｈ) ｔｒＤ =ｒｒｗｐＤｊ=2π(ｋｈ) ｔＴｓｃｐｓｃｑｓｃＴ (Ｐμｚ) ｊ(φ0 - φｊ)ＴａＤ =(ｋｈ) ｔｔａ(ｈ) ｔ(μＣｇ) 0 ｒｗ2ｑＤｊ=ｑｊｑＷＤｊ=(ｋｈ) ｊ(ｋｈ) ｔωｊ=(     

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 – ? 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.     

EXPERIMENTAL STUDY OF 3-D TURBULENT BEND FLOWS IN OPEN CHANNEL

1.INTRODUCTION Mostnaturalflowsareturbulent,andthenat uralriversareprevalentlymeandering.Mostofthe riverbendsarethosewithnot fully developedcir culationcurrentsonly,inwhichcentralanglesfor thebendsaresmallerthan180°,even90°.These bendflowsarecharacterizedbythedevelopmentoflateralcirculationcurrentsandbythenot fully offsetsofmainflow,withobvious3Dfeatures.Soinhydraulicengineeringandnavigationengi neering,itisimportantandnecessarytoinvesti gatethe3Dturbulentcharactersofbendflow.Be causet…     

具有复杂计算域的三维非静压流动数值模拟

建立了基于非结构化网格的表层静压假设的三维流动非静压数值模型。模型中采用半隐式分步法求解Navier-Stokes控制方程。运用满足自由表面运动学边界条件的水位演化方程来计算自由表面,动量方程中的对流项和水平扩散项采用Semi-Lagrangian方法离散。模型能有效求解正压的、斜压的、静压和非静压三维流动问题,并具有质量守恒、无条件稳定等优点。通过孤立波在缓变底坡上的传播和渤海潮流运动两个算例对模型进行检验,通过数值计算结果和实测结果的比较,验证了模型能够准确的模拟具有强三维流动特性的自由表面流动问题的能力和具有良好的复杂边界适应性。     

NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS OF PLUNGE POOL AND ENERGY DISSIPATION ANALYSIS

A 3-D numerical model for simulating the complicated turbulent flows was developed and the code was made. A numerical calculation of the plunge pool of Laxiwa project in China was carried on. Those 3-D distributions of velocity,pressure on bottom wall,turbulence kinetic energy and turbulence energy dissipation rate are revealed in detail and the detailed flow patterns of plunge pool were shown. By studying on the characteristics of turbulent diffusion and energy dissipation,the calculated results show that the major turbulence and energy dissipation are taken place near the axis of water jet. The calculated results also indicated that the calculated maximum impact pressures on the bottom wall of the plunge pool have a good agreement with those obtained by physical hydraulic model test.     

A MODEL FOR FIXED ALGAE MANAGEMENT IN OPEN CHANNELS USING FLUSHING FLOWS

The management of regulated rivers and canals involves new objectives of water quality preservation. Among water quality aspects, the development of benthic algae induces impacts on both the quantitative and the qualitative management. In open‐channel networks, their growth causes accumulation of biomass on the substratum, which decreases the hydraulic performance. Their detachment induces increases of drift biomass and particles likely to cause clogging issues. To manage these benthic algae developments, we study an original strategy that consists of performing hydraulic flushes in order to detach a part of the algal cover. The principle is to create a controlled hydrodynamic perturbation thanks to hydraulic control structures and to limit the quantity of fixed and drift algae simultaneously. We propose a comprehensive model of the flushes based on coupled hydrodynamic and algae detachment models in order to analyse and improve the management procedure. This model was applied on two real canals located in southern France. Copyright © 2011 John Wiley & Sons, Ltd.     

A NUMERICAL MODEL FOR FLOW-SALT-SEDIMENT MOVEMENT IN TIDAL ESTUARIES

Ａ　ＮＵＭＥＲＩＣＡＬ　ＭＯＤＥＬ　ＦＯＲ　ＦＬＯＷ－ＳＡＬＴ－ＳＥＤＩＭＥＮＴ　ＭＯＶＥＭＥＮＴ　ＩＮ　ＴＩＤＡＬ　ＥＳＴＵＡＲＩＥＳＡＮＵＭＥＲＩＣＡＬＭＯＤＥＬＦＯＲＦＬＯＷ－ＳＡＬＴ－ＳＥＤＩＭＥＮＴＭＯＶＥＭＥＮＴＩＮＴＩＤＡＬＥＳＴＵＡＲ...     

NUMERICAL INVESTIGATION ON EXTRUDATE SWELL FOR VISCOELASTIC FLUID： USING MAXWELL MODEL

The numerical investigation on extrudate swell through capillary die for viscoelastic fluid characteried by integral-type Maxwell constitutive equation was conducted by employing the finite element method with the calculation of viscoelastic extra stress in the conventional finite element. The method of avoiding singularity was also adopted by integrating the strain history of the Gauss points for each element near the wall and the free surface. The convergence solutions at high Weissenberg number can be obtained by using the appropriate methods to reduce errors and improve the speed of convergence of the calculation, which include adding a relaxation factor of velocity in iteration process, or enlarging the reference viscosity, or reducing the elapsed time. The highest Weissenberg number obtained here is up to 3. 8, while the solution at the Weissenberg number of 3. 75 was given in the previous work with similar extrudate swell ratio and the exit pressure drop by using differential Maxwell model with Elastic-Viscous Stress Split (EVSS) combined with Streamline Upwind Petrov-Galerkin (SUPG) scheme. The calculations indicated that the method of dealing with integral consti- tutive equation introduced in this paper is suitable in simulating viscoelastic flow characterized by integral constitutive equation at high elastic level.