非定常不可压 N-S 方程的一种有效预处理数值方法

本文发展了一非定常不可压流的有效预处理求解方法。应用预处理技术，对不可压N－S方程使用双时间推进法求解。当沿物理时间层推进时，连续性方程和动量方程沿伪时间方向迭代求解。在沿伪时间方向迭代时，设计了一简化的有效标量隐式线（Gauss－Sidel）迭代算法。对流项采用三阶迎几差分法离散，同时对数值通量项进行了预处理。数值分析了预处理对数值解精度和收敛性的影响。对振荡平板的非定常流动及不同Re数下定常、非定常驱动方腔流动的数值模拟结果表明，本文发展的非定常不可压流的预处理求解方法，不但提高了计算效率，而且减小了人工粘性，改善了数值解的精度。     

河道及河口一维及二维嵌套泥沙数学模型

建立了一种河道及河口一、二维嵌套的泥沙数学模型，对基本的控制方程、方程的离散和求解方法、嵌套连接条件以及非均匀沙的处理等问题进行了研究。以非恒定非均匀不平衡输沙理论作为本文建模的基础，为方便处理，通过交界面的水位、流量和含沙量等的传递，在每一迭代内进行耦合计算。数值模拟结果与实测资料吻合较好，且计算省时，表明本文建立的嵌套模型是一种解决某些实际工程问题的可靠的和高效的工具。     

三维方腔拖曳流的数值模拟

本文推导出一种适用于定常和不定常粘性不可压缩Navier-Stokes方程的分裂步方法。采用Taylor-Galerkin有限元格式进行求解，对有限元等式中关于速度的时间项进行三点向后差分，深入考虑粘性不可压缩流Navier-Stokes方程中对流项的作用，利用二阶Taylor展开完成时间项向空间项的转化，采用张量分析的方法推导了N-S方程分裂步方法的有限元离散格式，并采用低Reynolds数三维方腔拖曳粘性流^[23][24]作为基本算例，检验了这种分裂步方法的稳定性和有效性，同时与大涡模拟相结合对Reynolds数为10000的三维方腔拖曳湍流流场进行了相关的分析，进一步揭示了方腔回流运动的非定常非对称性、流动结构表现为竖轴环流与立面环流相叠加、流速沿垂线分布相对均匀等流动规律，显示了该方法与大涡模拟相结合能够有效地捕捉涡系及其时变过程。     

Effect of channel shape on selection of time marching scheme in the discontinuous Galerkin method for 1-D open channel flow

One-dimensional open channel flows are simulated using the discontinuous Galerkin finite element method. Three different explicit time marching schemes, including multistep/multistage schemes, are evaluated for different channel shapes for accuracy and efficiency. The Forward Euler, second-order Adam-Bashforth(multistep), and second-order total variation diminishing(TVD) Runge-Kutta(multistage) time marching schemes are utilized. The role of monotonized central, minmod, and zero TVD slope limiters for each of the time marching scheme is investigated. The numerical flux is approximated using HLL function. The accuracy and robustness of different time marching schemes are evaluated for steady and unsteady flows using analytical and measured data. The unsteady flows include dam break tests with wet and dry beds downstream of the dam in prismatic(rectangular, trapezoidal, triangular, and parabolic cross-sections) and non-prismatic(natural river) channels. The steady flow test involves simulation of hydraulic jump in a diverging rectangular channel. The various schemes are evaluated by comparing accuracy using statistical measures and efficiency using maximum possible time step size as well as CPU runtime. The second-order Adam-Bashforth time marching scheme is found to have the best accuracy and efficiency among the time stepping schemes tested.     

基于FD/MLSFD的混合算法计算 二维浅水方程

将基于最小二乘法的无网格有限差分方法(MLSFD方法)和传统有限差分方法(FDM)相结 合,生成了一种混合算法。研究并解决了差分网格/无网格混合算法的藕合问题,将混合算法运用于 求解二维浅水方程,通过计算高雷诺数(Re =105)条件下的圆柱绕流模型揭示了该混合算法在进行二 维浅水模型的数值模拟方面具有较高的精确度。     

中间渠道内非恒定流数值模拟

利用平面二维非恒定流数值模型，来研究中间渠道内非恒定流问题，该模型基于任意三角形计算网络，采用隐式求解自由表面的剖开算子法，离散求解控制方程，有效地处理了非线性混合算子和计算自由表面的困难，避免人工滤波措施，提高了计算精度和计算稳定性，并在三峡通航工程方案比较中得到应用。计算结果表明，该模型能较好地反映中间渠道内水流特征，与分析模拟船闸不同运行方式下渠道内水流波动特性，达到优化运行方案，改善渠道内航行条件的目的。     

NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS IN A CUT-OFF VALVE AND ANALYSIS OF FLOW CHARACTERISTICS IN PIPE

1 .　INTRODUCTIONThevalvehasbeenplayinganimportantroleinthe pipeengineeringandisalsooneofmaincomponentsgeneratingtheheadloss .Becauseofthecomplexgeometry ,thedesignwasusuallyeval uatedempiricallyinthepast,whichcausesmuchenergyloss .Toreducetheenergyloss ,itisessen tialforadesignertoknowthedetailsofflowfieldinthevalvepipe .Recently ,withtheremarkableprogressintheComputationalFluidDynamics(CFD)andcomputerhardware ,itisexpectedthatCFDwillbecomeapowerfultoolinthedesignofvalve .Intheactual…     

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of SaintVenant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.     

地下水流与河网水流的耦合模型

从河道水流一维不稳定流(扩展的圣维南方程组)有限差分的递代方程和地下水的有限元数值方法出发，通过河道四周地下水流与河道水流的交换流量把两个模型数值计算的矩阵方程从理论上耦合起来.理想水文流域系统的计算结果表明，模型的设计是合理的     

基于最小二乘的N-S方程算子分裂有限元法

提出一种新的求解N S方程的有限元法,即基于最小二乘的N S方程算子分裂有限元法。该算法采用算子分裂法将N S方程分解成扩散项和对流项:扩散项时间离散采用向后差分格式,空间离散采用标准Galerkin有限元法;对流项时间离散采用向后差分格式,空间离散采用最小二乘有限元法。应用该算法对方腔流和后台阶流进行数值模拟,方腔流数值计算结果与标准解吻合很好;在后台阶流数值模拟中给出了不同雷诺数下的流场特征和速度对比曲线,所得计算结果与试验结果吻合较好,表明基于最小二乘的N S方程算子分裂有限元法具有较好的收敛性和较高的精度。     

明满交替流数值模拟中的精细积分法

建立具有统一形式的明满交替流控制方程。由于系统阵刚性而导致明满交替流数值模拟的计算精度低和收敛性差。在交错网格上对控制方程进行空间上的数值离散后，加入伪时间导数项进行预处理，改善系统阵的刚性。通过采用系统阵增维的方法将非齐次状态空间方程转化为齐次方程，避免了矩阵求逆运算，增强计算的稳定性；预处理后系统方程每一个物理时间步的求解都相当于一个稳态问题，需要花费大量的计算时间，借助于精细积分法可以采用大步长的优势来加快求解速度。有效地解决了明满交替流建模中由于刚性而引起的数值稳定性问题和预处理引起的积分时间较慢的问题。而且这一方法具有程序容易实现的优点。     

1-D coupled non-equilibrium sediment transport modeling for unsteady flows in the discontinuous Galerkin framework

A high-resolution,1-D numerical model has been developed in the discontinuous Galerkin framework to simulate 1-D flow behavior,sediment transport,and morphological evaluation under unsteady flow conditions.The flow and sediment concentration variables are computed based on the one-dimensional shallow water flow equations,while empirical equations are used for entrainment and deposition processes.The sediment transport model includes the bed load and suspended load components.New formulations for Harten-Lax-van Leer(HLL) and Harten-Lax-van Contact(HLLC) are presented for shallow water flow equations that include the bed load and suspended load fluxes.The computational results for the flow and morphological changes after two dam break events are compared with the physical model tests.Results show that the modified HLL and HLLC formulations are robust and can accurately predict morphological changes in highly unsteady flows.     

Application of CLEAR-VOF method to wave and flow simulations

A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid (CLEAR-VOF) method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.     

FINITE VOLUME METHOD FOR SIMULATION OF VISCOELASTIC FLOW THROUGH A EXPANSION CHANNEL

A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell (UCM) fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.     

NUMERICAL SIMULATIONS OF 2D PERIODIC UNSTEADY CAVITATING FLOWS

1. INTRODUCTION Cavitation is a natural phenomenon especially existing in liquids. A cavitating flow generally involves a large number of vapor structures such as bubbles or vortices which are convecting downstream. When they reach high pressure zones, th…     

NUMERICAL SIMULATIONS OF CAVITATING FLOWS

BRIEFINTRODUCTIONOFTHEPAPER :　Thisthesismainlyresearchesonthehydrodynamiccharacteristicsandmechanismfor 3Dcavitatingflowsaroundaxisymmetricbodies ,aswellasthe2Dcavitatingflowsaroundhydrofoils .Anewcavi tatingflowmodel,whichinvolvesviscousandmul ti phaseeffects,isestablishedintwo phaseflowcategory .Accordingtothelocalizedvariationofdensitywithinpredominantlyincompressiblewatermediumandthecharacteristicsofsoundspeedinwater vapormixture ,arelationbetweendensityandpressureisassumed ,in…     

An iterative Rankine boundary element method for wave diffraction of a ship with forward speed

A 3-D time-domain seakeeping analysis tool has been newly developed by using a higher-order boundary element method with the Rankine source as the kernel function. An iterative time-marching scheme for updating both kinematic and dynamic free-surface boundary conditions is adopted for achieving numerical accuracy and stability. A rectangular computational domain moving with the mean speed of ship is introduced. A damping beach at the outer portion of the truncated free surface is installed for satisfying the radiation condition. After numerical convergence checked, the diffraction unsteady problem of a Wigley hull traveling with a constant forward speed in waves is studied. Extensive results including wave exciting forces, wave patterns and pressure distributions on the hull are presented to validate the efficiency and accuracy of the proposed 3-D time-domain iterative Rankine BEM approach. Computed results are compared to be in good agreement with the corresponding experimental data and other published numerical solutions.     

多区非均质油藏的有限元法理论分析

建立了单相流体在非均质油藏中、在不稳定渗流条件下的有限元方程,同时考虑了井筒储存效应和表皮效应的影响。将井壁视为内边界,在空间上用任意四边形单元对求解区域进行剖分,在时间上用向后差分法进行离散。用二区非均质油藏的解析解对方法进行了验证,而后对三区非均质油藏和四区非均质油藏进行了模拟分析,说明用有限元法模拟分析多区非均质油藏是准确、方便的。实际上,本模拟器可以适用于任意非均质油藏。     

多尺度有限元法在地下水模拟中的应用

本文详细介绍了多尺度有限元法的基本原理，并将其应用于非均质多孔介质中的流动问题，对水文地质参数按函数连续变化、渐变和突变3种非均质多孔介质中的二维地下水稳定流、非稳定流分别用多尺度有限元法和传统有限元法进行了计算。计算结果的对比表明，多尺度有限元法比传统有限元法有效，既节省计算量又有较高的精度。     

安康枢纽下游非恒定流数学模型研究

由于安康电站未设置满足航运设计流量要求的小型发电机组,无法保证常年带系统基荷运行,导致安康下游枯水期通航受到严重破坏.为兼顾发电与航运利益,尽可能发挥有限水资源综合利用的最佳效益,对安康电站日调节泄流过程进行科学调度.采用有限元方法,将流量和水位相耦合,采用水位修正算法计算水位,建立了一维非恒定流数学模型,该模型放宽了时间步长的限制,数值稳定性好,计算速度快.将模型应用到汉江安康电站坝下至白河160 km河段的恒定流与非恒定流计算和验证,结果表明该模型准确、可靠,可以进行实际应用.