自由液面流体在晃动有限元方法

本文给出了一种以ALE描述N－S方程为基础的，求解具有自由液面流体大晃动的有限元方法。文中首先给出了ALE描述的N－S方程、自由液面边界条件和相应的有限元方程；然后分别采用经典Galerkin格式和Newmark法进行空间和时域的离散化，得到了相的Newmark－压力修正求解格式，并由预测－校正直接求解。分析实例表明这是一种简单可靠的方法。     

Level Set方法求解三维大幅晃动问题的分步有限元法

取与容器固结的坐标系，将外激励视为质量力，针对刚性容器内流体三维非线性大幅晃动问题，提出了在时间和空间上均具有二阶精度的两步Taylor—Galerkin分步有限元方法。该法首先显式地求解忽略压力梯度项的中间速度场，然后由压力泊松方程求得压力场，再根据求得的压力对速度场进行修正。求解中利用Level—Set方法隐式地追踪自由面，即在每个时间步求解Level—Set函数随水流的输运方程，并通过迭代的方法对其进行重新初始化，以保持为距离的函数，从而达到捕捉自由面的目的。控制方程统一采用简单方便且具有较高精度的两步Taylor—Galerkin格式进行离散，并通过两个算例验证了本文数值方法的正确性和有效性。     

自由液面流体大晃动有限元方法

本文给出了一种以ALE描述N-S方程为基础的,求解具有自由液面流体大晃动的有限元方法.文中首先给了ALE描述的N-S方程、自由液面边界条件和相应的有限元方程;然后分别采用经典Galerkin格式和Newmark法进行空间和时域的离散化,得到了相的Newmark-压力修正求解格式,并由预测-校正法直接求解.分析实例表明这是一种简单可靠的方法.     

水平井油藏数值模拟的有限元方法

本文对底水油藏水平井三维两相渗流的数学模型给出了一种有限单元解法。在求解过程中，对压力场采用基于Ｇａｌｅｒｋｉｎ方法的经典有限元技术，对饱和度场，引入了非标准的不连续有限元方法，以反映实际油藏中水驱前缘的含水饱和度不连续跃度的性质。整个过程采用计算功能极强的ＮＤＰ－ＦＯＲＴＲＡＮ语言编程实现，对有限元整体刚度矩阵采用变带宽一维压缩存储，以节省数组存储空间，进一步提高程序的运算能力和运行速度。     

水工混凝土带缝结构渗流场的扩展有限元分析

水工混凝土结构常带缝运行于水压与渗流共同作用的复杂工况下,在处理其结构渗流场与位移场耦合问题时,为了避免经典有限元法确定两场间变量对应关系的麻烦和不同网格分析的协调问题,将扩展有限元引入水工裂缝结构稳定渗流场的分析中,通过研究渗流场分析中裂缝单元水头的节点加强方式,构造出能使裂缝位置处渗透压力连续并反映裂缝内传导系数矩阵特点的节点加强函数,从而得出渗流场的扩展有限元逼近形式,建立扩展有限元法求解渗流场的离散方程和求解步骤,将渗流场和位移场统一在扩展有限元框架下求解。实例分析表明,裂缝的存在对裂缝区渗流场的影响较大,裂缝内水流渗透坡降较小,与实际情况相符,验证了该方法求解渗流场的可行性和所编程序的正确性。     

挡土结构中土体被动临界滑动场及被动土压力的数值计算

本文将边坡临界滑动场方法进行推广和改进，计算挡土结构中土体被动临界滑动场PCSF和被动土压力。首先建立土体极限平衡方程并引入条间力函数，给出平衡方程求解格式；介绍改进的土体临界滑动场数值模拟技术；最后给出实用的被动土压力计算图。本文方法原理简单、精度高，可应用于工程计算。     

三维定常船尾绕流的不定常数值计算

本文采用有限体积法非正交贴体会标下对求解三维不定常船尾绕流做了进一步的研究，将Ｃａｒｒｔｅｅｉａｎ坐标系下的Ｎ－Ｓ方程和连续方程变换到非正交贴坐标系下的方程，用ＳＩＭＰＬＥＣ方法迭代求解速度和压力耦合的有限差分方程组，最后给出了用该方法计算的ＳＳＰＡ７２０例子。     

用变分不等式理论求解渗流问题的截止负压法

提出了用变分不等式的理论求解一般稳定渗流问题的新方法－截止负压法，它直接以压力场为未知函数，采用罚函数有限元并结合固定网格迭代确定自由面，能求解任意边界、任意结构的非均质各向异性渗流问题。     

二维粘性流动的边界元方法

本文叙述了粘性流动边界元方法，并研究了动力润滑，涡旋发生以及生物力学等问题。该方法基于用Ｓｔｏｌｅｓ方程的基本解作为格林函数，将Ｎ－Ｓ方程归结为求解区域边界上的积分方程，使用边界单元，数值求解积分方程，给出了应力分布、压力分布及速度场。数值结果与理论结果和实验结果十分符合，方法具有很高的精度，比起目前的差分法和有限元法，在某些问题上更有效，也更灵活。     

管道内绕物体的三维粘性流

本文研究了管道内绕物体的三维粘性流动。采用Green函数方法将基本方程化为求解区域边界上的积分方程,使用空间曲面三角形离散边界,用六节点等参数元数值地求解了积分方程,确定了速度场、压力场和边界应力,算例与解析解比较有较高的精度,一些典型问题的计算结果也是满意的。     

求解不可压层流的一种全隐数值格式

该文基于SMAC(simplified marker and cell)方法,发展了一种在任意曲线坐标系中求解不可压黏性层流的全隐数值格式。基本方程是以逆变速度为未知变量的动量方程和关于压力修正量的Poisson方程。所有方程离散在MAC交错网格系统中进行。根据构造的全隐数值格式自编程序对一可简化成二维层流的后台阶流场进行计算,通过与已有的实验结果和计算结果进行比较,确认目前的计算结果优于比较的计算结果,和实验结果也相当吻合。为进一步验证该数值格式的可靠性,扩展程序对三维后台阶层流进行计算,结果表明,三维计算结果比二维计算结果更加接近实验结果。     

基于非结构化网格上的三维微幅自由表面流动非静压数值模型

建立了基于非结构化网格求解三维微幅自由表面流动非静压数值模型。一种有限差分法和有限体积法相结合的方法被用来在非结构化网格上离散控制方程。模型中采用分步法,以使压力项分解为静水压力项和动水压力项来单独处理。在每一时间步,得到关于水位和由压力泊松方程得到的动水压力的稀疏的线性方程组。模型是质量守恒的和对于重力波速、风应力、底摩阻、垂向黏性无条件稳定的。通过三个非恒定微幅自由表面流动算例的数值解和解析解的比较,验证了本文所建立的模型能够准确有效的预测三维微幅自由表面流动。     

NUMERICAL SIMULATION OF TWO-DIMENSIONAL DAM-BREAK FLOWS IN CURVED CHANNELS

Two-dimensional transient dam-break flows in a river with bends were theoretically studied. The river was modeled as a curved channel with a constant width and a flat bottom. The water was assumed to be an incompressible and homogeneous fluid. A channel-fitted orthogonal curvilinear coordinate system was established and the corresponding two-dimensional shallow-water equations were derived for this system. The governing equations with well-posed initial and boundary conditions were numerically solved in a rectangular domain by use of the Godunov-type finite-difference scheme, which can capture the hydraulic jump of dam-break flows. The comparison between the obtained numerical results and the experimental data of Miller and Chaudry in a semicircle channel shows the validity of the present numerical scheme. The mathematical model and the numerical method were applied to the dam-break flows in channels with various curvatures. Based on the numerical results, the influence of river curvatures on the dam-break flows was analyzed in details.     

ANALYTICAL AND NUMERICAL SOLUTIONS FOR THE FLOW IN MICROTUBE WITH THREE-DIMENSIONAL CORRUGATED SURFACE,PART 1:STEADY FLOW

The influences of three-dimensional corrugated wall on the fully-developed steady no-slip flows in microtube are studied by analytical and numerical methods in this article. Detailed analytical solutions for the space-averaged equations and the numerical method for the solutions of the disturbance equations are given. An iterative arithm of coupled equations with respect to space-averaged velocities and disturbance velocities is suggested. The study shows that a three-dimensional subsidiary stress layer exists in the near-wall region. The relative roughness, wavenumber and Reynolds number are three important parameters influencing the subsidiary stresses and the space-averaged pressure drop. The space-averaged pressure drop subject to an invariable flow rate mainly depends on the position of datum surface. When the datum surface is taken at the balance position of wall function, the value of pressure drop is determined by the dynamic characteristics of the flow.     

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…     

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.     

三峡水库近坝区三维流场及温度场的数值模拟

基于三维不可压缩流动的N-S方程建立水流水温模型,模型在动量方程中考虑浮力作用并取消了静水压力假定,采用大涡模拟紊流模型计算紊动扩散,并考虑水面散热及其太阳辐射的影响因素,适合于对复杂流态及其有密度分层流动的数值模拟。应用所建立的数学模型对三峡近坝区从庙河至坝前水域的三维流场及温度场进行了数值模拟,计算出的水温分布与坝前观测的水温分布二者符合良好。模拟结果表明,三峡水库在蓄水至139 m水位时,垂向没有明显的水温分层,与实测结果相符。     

HIGH ACCURATE SOLUTION OF INCOMPRESSIBLE VISCOUS FLOW WITH PRIMATIVE VARIABLE

This paper presents a higher order difference scheme for the computationof the incompressible viscous flows.The discretization of the two-dimensional incompress-ible viscous Navier-Stokes equations,in generalized curvilinear coordinates and tensor for-mulation,is based on a non-ataggered grid.The momentum equations are integrated intime using the four-stage explicit Runge-Kutta algorithm [1]and discretized in space us-ing the fourth-order accurate compact scheme[2]The pressure-Poisson equation is dis-cretized using the nine-point compact scheme.In order to satisfy the continuity constraintand ensure the smoothness of pressure field,an optimum procedure to derive a discretepressure equation is proposed [9][3]The method is applied to calculate the driven cavityflow on a stretched grid with the Reynolds numbers from 100 to 10000.The numerical re-sults are in very good agreement with the results obtained by Ghia et al [7]and includethe periodic solutions for high Reynolds numbers.     

LIQUID-GAS TWO PHASE FLOW RATES METERING BY DUAL PRESSURE DIFFERENTIAL MEASUREMENTS

The measurement of the overall mass flow rates in a two phase, gas/liquid pipeline is considered on the basis of dual pressure differential measurements for a combined contraction/frictional pipe type of flow meter and a numerical model to predict overall mass flow rates from pressure differentials measured from this type of flow meter is presented. The experiments generally conform with the predictions of the flow rates prediction model. Whilst the practicability of such metering of two phase flows is clearly demonstrated, application of the method would require careful calibration to allow for the influence of nozzle coefficients, pipe Reynolds number and void fraction upon the one dimensional compressible flow equations through wall friction factor and interphase slip effects.     

缝洞型油藏三重介质油水两相流数值试井解释方法

基于多重介质渗流的概念模型和数学模型,建立了缝洞型油藏油水两相流三重介质数值试井模型;对模型进行数值求解,得到三重介质油藏两相流试井响应曲线并分析其特征。指出三重介质油水两相条件下的压恢曲线与单相时的不重合,并随着初始油水饱和度的变化而变化,不能直接用单相试井模型来解释两相流试井曲线;提出了先拟合油水产量曲线,再拟合压力恢复曲线的试井解释方法。