剖面二维非恒定悬移质泥沙扩散方程的数值方法

通过讨论剖面二维非恒定泥沙扩散方程的数值方法，建立了一种用于求解含沙量分布沿程变化的差分格式（Ｚ－Ｃ格式）并通过一个具体的数值例子说明了计算的方法步骤。     

任意流场中稀疏颗粒运动方程的数值解法及其应用

任意流场中稀疏颗粒运动方程是一非线性的微分积分方程，极难获得解析解。本文首先对方程中Ｂａｓｓｅｔ力项构造了适当的计算格式，然后详细研究了颗粒运动方程的数值计算方法并提出称之为Ｐ（ＥＣ）＾ｋ多步法的差分格式，简要分析了该格式的收敛性和代数精度，给出了时域离散长长必满足的条件。     

一维对流扩散方程的一类新型高精度紧致差分格式

本文对一维无源线性对流扩散方程给出了4种高精度(O(h^2)-O(h^5))三点紧致差分格式，其中每一种格式都是在前一格式基础上进行简单修正得到的，故而计算起来很简便。数值算例表明本文方法优于以往的几种高精度差分格式，且适用于对流占优问题。     

基于有限体积法的伴随数值模型研究

传统上认为伴随数值模型的构造应先设计正向方程的数值格式,然后由数值格式推导伴随数值格式建立伴随模型,但利用该方法过程繁杂繁琐,且从正数值模型直接得到伴随模型,制约了对伴随模型数值格式的具体设计,如利用该方法就无法构造有限体积法的伴随数值模型.为发挥有限体积法在数值格式和边界拟合方面的优势,和检验对伴随方程进行数值格式选取和设计的可行性,本文直接从深度平均的非线性守恒型浅水方程出发,先利用Lagrange法推导得到其伴随方程,然后再对浅水方程和伴随方程的数值通量分别采用二阶精度的Roe格式和一阶精度的Lax-Friedrichs流函数格式,建立正模型和伴随模型采用不同数值格式的无结构三角网格有限体积法的伴随模型.进行的一系列数值实验,正确反演出了顺直河道和概化河口的开边界,结果表明该方法构造伴随模型是可行的,为伴随模型的构造方法开辟了一条新的途径.     

对流方程数值解法比较及分析研究

归纳总结了求解对流方程的几种常用数值解法的格式，如迎风格式、四点时空偏心Preissmann格式、杨一贡日格式等，并从相容性、稳定性、收敛特性分析出发，对各种数值解法的特点进行了比较与分析，同时将各种解法应用到两种典型算例的验算中进行比较与分析，期望对于实际工作中在面临如何正确合理的选择一种合适的求解对流方程的数值解法的问题时能有一定的参考作用。     

停泵水锤预测中的直接迭代格式与电算方法

针对水锤数值计算中的特征线方程和边界条件方程，设计了一种简单实用的直接迭代格式，并编写了计算软件，为停泵水锤数值计算提供了基础。同时就泵阀计算参数进行了探讨，工程实践应用表明，其技术上是可行的。     

对流-扩散方程的差分格式设计(Ⅱ) 纯扩散方程和对流-扩散方程

文[1]给出了一种设计差分格式的通用方法,并以纯对流方程为例,详尽地描述了设计的方法和过程,同时给出了许多新的格式。本文是文[1]的第二部份,着重对纯扩散方程和一般的对流-扩散方程,给出了差分格式的设计过程和许多新的格式。最后,文中还对几个有精确解的算例进行了各种设计格式的数值计算和比较试验。     

船舶螺旋桨周围粘流场数值预报与流场分析

本文叙述了通过直接求解雷诺平均应力方程（ＲＡＮＳ）来获得船舶螺旋桨粘流场数值解的方法与数值求解步骤，该方法采用非交错网格系统，利用幂函数格式离散动量方程，预报－校正方法求解速度－压力耦合问题，应用Ｂａｌｄｗｉｎ－Ｌｏｍａｘ代数湍流模式求解雷诺应力项使方程组封闭，以此来获得螺旋桨粘流场，为了验证数值方法的稳定性和可靠性，文中以ＤＴＲＣ４１１９桨为算例，对螺旋桨粘流场进行了数值求解，通过对计算结果的分     

扩展型Boussinesq水波方程的一种改进有限体积/有限差分混合算法

为高效数值求解扩展型Boussinesq水波方程,采用一种近似变换方法,将动量方程中的混合导数项变换为纯空间导数项,建立了一种基于原始变量的新的守恒形式方程。对守恒形式方程中的通量项采用基于二阶迎风TVD格式的有限体积方法进行求解,时间导数项采用具有TVD性质的三阶龙格-库塔多步积分方法进行时间积分,剩余项采用中心差分方法进行计算,发展了扩展型Boussinesq水波方程的一种简单高效的混合有限体积/有限差分求解方法。该方法具有数值格式构造过程简单、无需可调参数、数值稳定性强等优点。利用典型波浪传播算例对数值模型进行了验证,计算结果与文献实验数据吻合良好。     

基于WENO-Z重构的Osher-Solomon格式求解浅水波方程

浅水波方程在水利、海洋和环境工程中有着非常重要的应用。该文提出一种求解浅水波方程的高分辨算法,对单元交界面处守恒变量进行三阶WENO-Z重构。空间方向上采用三阶WENO-Z重构的Osher-Solomon数值通量,时间方向上采用三阶强稳定的Runge-Kutta方法,将新格式应用于一维和二维不同初值问题的浅水波方程数值求解中,并分析与比较了研究格式的分辨率。数值结果表明:与原格式相比,三阶WENO-Z重构的Osher-Solomon格式分辨率更高。     

3-D numerical simulations of violent sloshing by CIP-based method

The violent sloshing flow inside a rectangular tank is computed by the CIP (Constrained Interpolation Profile) ^[1] based Cartesian grid method. Two kinds of CIP scheme, the original CIP scheme and the RCIP scheme, have been applied to the flow solver. 2-D and 3-D computations using the two CIP schemes are carried out and their performances are discussed by comparing the results of the impact pressures on the wall and the free surface profiles to the experimental measurements.

     

Numerical Simulation of Sediment Transport Following a Dam Break

For the computation of the morphological changes on reservoir beds, in scale model experiments, a hydrodynamic model is combined with the sediment continuity equation. The hydrodynamic model is based upon the equations of mass and momentum conservation. The sediment transport capacity appearing in the sediment continuity equation is calculated by using the relationship proposed by Smart. For the solution of the above system of three partial differential equations, the explicit numerical schemes of Lax and Wendroff and MacCormack are tested. The whole mathematical model is applied to the experimental case of sediment release from a reservoir after a dam break.     

NUMERICAL SIMULATION OF TURBULENT SPOTS IN INCLINED OPEN-CHANNEL FLOW

The generation and evolution of turbulent spots in the open-channel flow are simulated numerically by using the Navier-Stokes equations. An effective numerical method with high accuracy and high resolution is developed.The fourth order time splitting methods with high accuracy is proposed. Thre-dimensional coupling difference methods are presented for the spatial discretization of the Poisson equation of pressure and Hemholtz equations of velocity, therefore, the fourth-order thre-dimensional coupling central difference schemes are constituted. The fourth-order explicit upwind-biased compact difference schemes are designed to overcome the difficulty for the general higher-order central differences cheme which is inadaptable in the boundary neighborhood.The iterative algorithm and overall time marching is used to enhance efficiency. The method is applied in the numerical simulation of turbulent spots at various complex boundary conditions and flow domains. The generation and the developing process of turbulent spots are given, and the basic char acteristics of turbulent spots are shown by simulating the evolution of the wall pulse in inclined open-channel flow.     

高雷诺数流动的平均化差分格式

本文在N—S方程涡量一流函数形式的经典ADI格式和SOR松驰迭代公式的基础上,对其“外来项”进行平均化处理,构造出了平均化差分格式及迭代求解程序。对雷诺数Re=100,1000,10000的空腔流动分别进行了数值计算,并与各数值方法的结果及实验资料进行了比较,结果令人满意。     

桃源水电站机组大件吊装技术与场地布置

结合桃源水电站贯流式机组电站厂房的设计形式,考虑到大件设备安装场地受限的具体条件,在进行大量分析、计算的基础上,提出了符合实际条件的机组大件吊装方案和适宜的场地布置方法。重点介绍了大件吊装方案的设计和优选过程,以及吊装过程中遇到的一些技术难题和现场组装工位的布置情况。通过实践和研究,总结出了一套成熟的安装工艺和方法,可以有效缩短安装工期,在同行业中具有比较高的推广价值。     

污染物移流扩散方程的高精度分裂格式

提出了污染物移流扩散方程的一种高精度分裂格式, 该格式将多维移流扩散方程分裂为多个一维方程进行求解, 在每个方向上仅涉及三个空间节点而达到空间四阶精度. 采用该格式对几个经典的纯移流、移流扩散问题进行了数值模拟, 数值结果表明, 该格式比经典的移流扩散方程格式的精度要高得多, 此外该格式还具有编程简单、求解十分快速的优点.     

THE FINITE VOLUME PROJECTION METHOD WITH HYBRID UNSTRUCTURED TRIANGULAR COLLOCATED GRIDS FOR INCOMPRESSIBLE FLOWS

In this article a finite volume method is proposed to solve viscous incompressible Navier-Stokes equations in two-dimensional regions with corners and curved boundaries. A hybrid collocated-grid variable arrangement is adopted, in which the velocity and pressure are stored at the centroid and the circumcenters of the triangular control cell, respectively. The cell flux is defined at the mid-point of the cell face. Second-order implicit time integration schemes are used for convection and diffusion terms. The second-order upwind scheme is used for convection fluxes. The present method is validated by results of several viscous flows.     

THE COMPACT SECOND-ORDER UPWIND FINITE DIFFERENCE SCHEMES FOR THE CONVECTION-DIFFUSION EQUATIONS

The compact second-order upwind finite difference schemes free of ceil Reynoldsnumber limitation are developed in this paper for the one-to three-dimensional steady convection-diffusion equations,using a perturbational technique applied to the classical first-order upwindschemes.The present second-order schemes take essentially the same form as those of the first-order schemes,but involve a simple modification to the diffusive coefficients.Numerical exam-ples including one-to three-dimensional model equations of fluid flow and a problem of naturalconvection with boundary-layer effect are given to illustrate the excellent behavior of the presentschemes.     

水击波数值模拟中高分辨率TVD格式优选

TVD方法特别适合数值模拟双曲型偏微分方程间断波问题,选用4种典型的TVD格式应用于水击方程的数值模拟。通过水击实例计算,将数值结果与理论解比较,揭示4种不同构造形式的TVD格式在捕捉水击波方面耗散性和压制性数值性能的差异,且TVD格式均优于常规的差分方法;改变计算库朗数条件下的计算结果表明:Harten修正通量TVD格式、TVD-MC格式以及全离散TVD格式在大范围库朗数条件下计算稳定性较差,优选Sweby反扩散TVD格式模拟水击,其计算稳定性良好,精度较高。     

A NEW FINITE DIFFERENCE SCHEME FOR 2-D FLOWS AT LARGE Re

Based on the conventional ADI method and SOR method for solving the Navier-Stokes equations, averaging those linkage terms which also are the terms of vary-ing coefficients of the equations, a new finite difference scheme-Averaging Finite Diffe-rence (AFD) scheme for 2-D flows was proposed. A 2-D driven cavity flow was calculated numerically as an example with the presented scheme at Re= 100, 1000, 2000, 3200, 10000. The results were discussed and compared to those obtained with the conventional methods as well as experimental data. It showed that a slight change of the approximation pattern of the conventional scheme in the terms of varying-coefficients of the governing equations seems to have an obvious influence on the solutions at high Re which will be erro- neous if the conventional schemes was employed.