定常对流扩散方程的修正积分因子方法

本文在积分因子方法的基础上，提出了所谓修正积分因子方法，成功地解决了对流占优的对液扩散方程：εｙ＇＇＋ｆ（ｘ，ｙ）ｙ＇＋ｇ（ｘ）ｙ＝ｓ（ｘ），ａ＜ｘ＜ｂ，０＜ε＜＜１（１）ｙ（ａ）＝ａ，ｙ（ｂ）＝β（２）的边值问题，所得天的数值解是无振荡的（即使网络Ｐｅｃｌｅｔ数高达１００以上），具有二阶精度。文中对常系数、变系数、非线性及守恒型等各种情况，用六个典型例子给予经验，结果表明，修正积分因子方法用来求     

气液活塞泵数值计算的修正特征线法

本文研究了气液活塞泵的运动机理，提出了一种用于定常振荡流数值计算的“修正特征线法”.在常规特征线法的基础上，通过将“时间修正因子”引入运动方程，不仅统一了变波速多介质段计算节点的特征线斜率，保证计算在矩形网格上进行，而且还在一定程度上提高了计算速度.文章推导了修正特征线法的特征型微分方程及差分方程：针对单介质管路和多介质管路分别提出了不同的处理方法；并在最后给出了气液活塞泵定常振荡流计算实例，与试验结果的对比一方面验证了“修正特征线法”计算变波速多介质段定常振荡流问题的优越性，另一方面也提出该方法在精度分析和敛散性方面尚需进一步研究.     

承压含水层中抽水井附近非达西流的近似解析解

本文将线性化方法和Laplace变换相结合研究承压含水层中单一抽水井附近的非达西流问题,得到了水位降深在抽水后期和抽水稳定阶段的近似解析解,并对抽水后期近似解析解的适用性进行了讨论.通过Stehfest数值Laplace逆变换得到了任意时刻任意位置水位降深的半解析解,并采用数值解对线性化方法所得到的近似解进行了验证.研究结果表明:在抽水后期,水位降深随着Izbash定律中的两个常数的增大而减小;在抽水后期,水位降深近似为时间的幂函数,在抽水稳定阶段,水位降深可以近似为距离的幂函数;在抽水后期,线性化方法所得到近似解与数值解吻合很好,而在抽水初期线性化方法则存在一定误差,会低估水位降深.     

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。     

一维不恒定流泥沙数学模型研究

本文着重对求解一维不恒定流泥沙数学模型控制方程的数值解法进行了研究，结果表明，用线性化方法与非线性选代计算对圣维南方程进行求辑，二者计算结果的差异很小，但线性化方法可以节省大量的计算工作量，且可取较大的时同步长进行计算。对悬移质泥沙运动方程式，相临时层之同用差分法求解，在局—时层上球其分析解。不仅可以避免含抄量计算结果的不合理现象，而且计算量也较小。用丹江口水库下游的资料对模型进行了验证，计算结果与实测资料符合良好。验证计算同时表明，用不恒定流泥沙数学模型进行河床变形计算，计算时间不会比恒定流泥沙数学模型增加很多。     

基于N-S方程的波浪与可渗防波堤相互作用的数值模拟

采用N-S方程作为波浪场和孔隙流域的控制方程,应用有限差分方法对控制方程进行离散求解,采用VOF方法跟踪自由表面,反复迭代求解得到整个流域的压力场和速度场,并分析堤后渗透波高随入射波高、入射波周期的变化规律。最后结合波浪水槽物理模型试验验证本文所建立的数学模型,验证结果表明,此文所建立的数学模型可较好的模拟波浪与可渗防波堤的相互作用。     

一种稳定的移动粒子半隐式法

该文提出了一种稳定的移动粒子半隐式法(MPS)。分析了MPS方法求解封闭区域流动的有解条件、自由面流动中粒子以较大速度撞击壁面或液面时出现的不稳定现象。为了解决这些问题,提出了Navier-Stokes方程新的求解算法和自由面边界处理方法。改进后的MPS方法提高了计算的稳定性,采用该方法成功模拟了自由面流动的溃坝现象,从而验证了该方法的有效性。     

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.     

拖式吊舱螺旋桨定常性能理论计算

本文提出拖式吊舱螺旋桨(螺旋桨位于吊舱首部)定常水动力性能的势流理论计算方法。螺旋桨采用升力面理论涡格法、吊舱采用面元法分析计算，二者的相互干扰通过叠代计算来处理。考虑吊舱的影响，修改了尾涡模型。应用本方法，计算了拖式吊舱螺旋桨的定常性能，并与空泡水筒试验结果进行了比较，计算与试验吻合良好。     

A COUPLED THERMO-HYDRAULIC MODEL FOR STEAM FLOW IN PIPE NETWORKS

This article aims to establish a coupled thermo-hydraulic mathematical model for steam network by adopting a set of equations, i.e., the continuity equation, motion equation, energy equation, state equation and enthalpy equation and considering the interaction of hydraulic and thermal working conditions. The model is simplified according to steam flow features in pipe networks. The unsteady flow model is simplified to a steady one with considering engineering practice and the solution to the governing equations are obtained by using the standard fourth-order Runge-Kutta method. Many factors of steam flow are generally considered, such as condensability, change of state, friction and heat transfer in the model. It is concluded that coupled iteration can be employed in steam network thermo-hydraulic computation. The numerical results with the model are basically in accordance with practical operation data.     

绕圆柱非定常周期性涡旋脱落的数值模拟

利用非定常流函数涡量方程数值模拟圆柱突然起动尾流涡旋的形成及周期性脱落过程。对求解的流函数的一阶导数即速度项采用四阶精度的Hermitian公式，而方程的对流项则采用四阶精度的差分格式，并利用ADI方法迭代求解差分方程组。当雷诺数Re不大于40时，圆柱尾流为附体的两个对称涡，为定常解。当Re大于40后流动为非定常及非对称的，圆柱尾流呈现周期性涡旋交替脱落而形成著名的Karman涡街。选择Re=100为例，在初始条件未加任何扰动情况下，成功地模拟了圆柱非定常涡旋形成与脱落的完整过程（无量纲时间算到t=250及以上）。所计算的阻力系数与实验结果及其它数值方法的计算结果一致。约在t=200形成严格的Karman涡街。对涡量方程ADI求解方法的稳定性进行了分析。对流项采用四阶精度差分格式，若应用于定常问题，将极大提高数值求解的精度，若应用于非定常问题的求解，将对求解精度有所改善，其中时间空间两阶混合偏导数的处理是关键，有待进一步的数值实验。     

THE SLOP FLUX METHOD FOR NUMERICAL BALANCE IN USING ROE＇S APPROXIMATE RIEMANN SOLVER

Imbalance arises when the Roe’s method is directly applied in the shallow water simulation.The reasons are different for the continuity equation and the momentum equations.Based on the Roe’s method,a partial surface method is proposed for a perfect balance for the continuity equation.In order to generate a mathematically hyperbolic formulation,the momentum equations are split,which causes incompatibility in the calculation of the momentum equations.In this article a numerical approach named the Slop Flux Method(SFM)is proposed to balance the source terms and the flux gradient based on the finite volume method.The method is first applied to shallow water equations.The model is verified by analytical results of classical test cases with good agreement.Finally the method is applied to a steady flow simulation over a practical complicated topography and the result shows good balance and conservation.     

新抛物型缓底坡波动方程

应用变分原理导出修改抛物型缓底坡方程和扩展抛物型缓底坡方程。通过数值模拟方法数值求解具体地形上的波浪折射绕射，同Kirby抛物型缓坡方程的线性方程和非线性方程进行比较。结果表明新的抛物型缓底坡方程具有适用性。提供了一种模拟波浪折射绕射的新方法     

半自适应网格方法及其应用

本文发展了一种简单而有效的所谓半自适应网格方法，该方法的一个特点是所有的计算均在物理平面上完成。这种半自适应方法已被成功地应用于定常和非定常一维二维对流扩散方程初值问题的数值解，与存在精确解的结果比较表明，半自适应网格方法的结果具有很少的数值耗散，精度较好，与通常的差分方法比大约增加一倍多一点的计算时间，与变分或微分形式的自适应网格方法相比，大大减少了计算工作量。     

基于三维数值流形法的位移边界处理方法

针对三维数值流形法中罚函数法施加任意方向边界位移和多步加载误差累积问题,通过修正传统三维数值流形法控制方程中的位移边界部分,推导出含沿着某一方向施加边界位移条件和相应的分步加载情况的计算公式,以期扩大控制方程在位移边界处理上的适用范围和减少多步加载误差累积效应。选取2个典型算例进行数值模拟和对比分析,验证该方法的准确性。计算结果表明:文中方法的计算结果与解析解相吻合,修正公式适用于不同方向施加边界位移的情况,具有较强的适应性;考虑位移边界误差修正比不考虑误差修正的计算精度高;随分步加载步数的增多,不考虑位移边界误差修正的累积计算误差逐渐增大,考虑位移边界误差修正的则影响不大。     

波浪传播的数值模拟与物理模拟耦合模型

此文对于二维波浪的传播建立了数值模拟与物理模拟的耦合模型。模型中,数值模拟采用基于改进Boussinesq方程的三角形网格有限元模型,物理模拟采用推板式造波机。模型的求解采用空间五点的拉格朗日插值和时间的四阶Runge-Kutta格式。通过波浪模拟实验研究了耦合模型在不同波浪要素下的适应性。进一步针对于规则波和不规则波分别建立了实时修正由于造波机造波性能所引起的模拟误差的方法。波浪模拟实验结果表明,耦合边界附近数模结果与物模结果吻合很好,实时修正方法能很好修正由于造波机造波性能所引起的模拟误差,耦合模型和实时修正方法能有效建立起数模与物模的确定性联合。     

天然湖泊定常流场数值模拟的预处理方法

天然浅水湖泊流场主要是风应力作用而引起的。本文建立了模拟天然湖泊风生流的数学模型，提出了该模型的预处理方法，应用此方法采用交错网格法，对滇池定常风生流进行了数值模拟，结果表明该方法具有较好的稳定性及较快的收敛速度，对胡泊或各种浅水域风生流的数值具有重要的应用价值。     

Numerical solutions for two nonlinear wave equations

The split-step pseudo-spectral method is a useful method for solving nonlinear wave equations. However, it is not widely used because of the limitation of the periodic boundary condition. In this paper, the method is modified at its second step by avoiding transforming the wave height function into a frequency domain function. Thus, the periodic boundary condition is not required, and the new method is easy to implement. In order to validate its performance, the proposed method was used to solve the nonlinear parabolic mild-slope equation and the spatial modified nonlinear Schr dinger (MNLS) equation, which were used to model the wave propagation under different bathymetric conditions. Good agreement between the numerical and experimental results shows that the present method is effective and efficient in solving nonlinear wave equations.     

WAVE-CURRENT INTERACTIONS WITH THREE-DIMENSIONAL FLOATING BODIES

A Time-domain Higher-Order Boundary Element Method (THOBEM) is developed for simulating wave-current interactions with 3-D floating bodies. Through a Taylor series expansion and a perturbation procedure, the model is formulated to the first-order in the wave steepness and in the current velocity, respectively. The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem. Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching. An artificial damping layer is adopted to dissipate the scattering waves. Different from the other time-domain numerical models, which are often focused on the wave-current interaction with restrained bodies, the present model deals with a floating hemisphere. The numerical results of wave forces, wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods. The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry. In this work, the regular and focused wave combined with current interacting with a truss-spar platform is investigated.     

NUMERICAL SIMULATIONS OF A CENTERED CONDUCTING BODY ON NATURAL CONVECTION AND HEAT TRANSFER IN AN ENCLOSURE

1.INTRODUCTIONA heat-conducting body is located somewherewithinthe enclosure,thereby affecting the naturalconvection flowand heat transfer.Soit is veryi m-portant in theory and used widely in many engi-neering systems.For example in a metal castingprocess,a solid may be placedinthe mold to forma holeinthe casting,another examplein electronicpackages with windows or walls.Natural convection and heat transfer of a cen-tered conducting body in an enclosure are complexproblems in the fluid me…