拟压缩性方法在非定常球形Couette—Taylor流模拟中的应用

本文以拟压缩性法和物理时间／伪时间双重时间推进，数值求解非定常不可压缩流Ｎ－Ｓ方程。拟压缩性英是对伪时间的导数项，在每一物理时间层，进行对伪时间的推进使拟压缩性项趋于零，从而使连续方程得到满足。用Ｌｏｗｅｒ－Ｕｐｐｅｒ ＳｙｍｍｅｔｒｉｃＧａｕｓｓ－Ｓｅｉｄｅｌ格式求解用所得的方程。针对前人ＬＵ－ＳＧＳ格式未计及陷式物理粘性，在计算中低Ｒｅ数流动时容易发散或造成收敛率低的问题，利用简化的隐式粘性     

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。     

基于大涡模拟的非对称机翼尾流场湍流流动分析

该文以人工可压缩方法求解不可压缩Navier-Stokes方程,采用具有壁面自适应的WALE亚格子应力模型,开发了基于非结构网格的大涡模拟求解器,其中控制方程的对流项、粘性耗散项分别以三阶MUSCL格式和沿网格结点中心的方向导数法进行离散,数值离散得到的非线性方程组采用无矩阵运算的全隐式LU-SGS方法分步迭代求解。文中以具有钝体尾缘的非对称机翼为对象,实现了机翼周围非定常流动的大涡模拟。通过与实验结果的对比,表明所开发的流场求解器能够应用于复杂流动中的湍流结构的大涡模拟和湍流特征量分析。     

用密度函数法对自由表面进行数值模拟

本文从二维非定常N-S方程出发，提出了一种处理自由表面问题的数值方法。引入密度函数法(density-function method)追踪自由表面，在密度函数的传输方程中采用TVD格式达到了二阶精度。对均匀来流中的非定常不可压方柱绕流进行了数值模拟。数值结果成功地捕捉了自由表面波动以及漩涡的生成、分离的时间发展历程。同时验证了本方法的有效性。     

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。     

数值求解不可压Navier-Stokes方程的隐式算法

本文提出了一个求解二维不可压Navier-Stokes方程的隐式算法。这种方法隐式联立地处理了控制方程,和一般的迭代算法相比它具有更好的稳定性和收敛性。二维Poissuill流动的数值解和分析解是非常一致的,S形流道内分离流的计算结果和实验结果相比也是令人满意的。     

均匀来流中振动圆柱层迹涡结构的数值研究

本文从涡量流函数形式的Ｎ－Ｓ方程出发，对于不同的振动频率，振幅首次数值研究了均匀来流中沿任意方向振动的圆柱粘性绕流的涡脱泻现象。文中着重探讨了近迹复杂的涡结构及其非定常演经过程，不仅能够再现实验研究中所发现的一些重要的流动现象，同时还进一步预示了某些新的流场结构，使数值计算起到与实验研究相辅相成的作用。     

二维非定常不可压涡量-速度Navier-Stokes方程组的高精度紧致差分格式

提出了数值求解二维非定常不可压涡量-速度变量Navier-Stokes方程组的一种高精度全隐式紧致差分格式,其空间为四阶精度,时间为二阶精度,并且是无条件稳定的。为了验证本文方法的精确性和可靠性,进行了数值实验,数值实验结果与精确解或文献中的结果吻合得很好。     

含源项非定常对流扩散方程的高精度紧致隐式差分方法

提出了数值求解含源项非定常对流扩散方程的一种高精度紧致隐式差分方法，其空间为四阶精度，时间为二阶精度。由于每一时间层上只用到了三个网格点，所以差分方程为三对角型的，可采用追赶法进行求解。数值实验结果验证了本文方法的精确性和可靠性。     

绕流流场无穷远处流函数边值条件的数值研究

利用流函数－涡量方程求解二维不可压缩低雷诺数绕圆柱流动，在与其它学者计算结果一致的情况下，本文数值研究了无穷远处流函数边值对圆柱定常绕流、圆柱起动流动以及非定常周期性卡门涡街形成的影响。本文计算了各种条件下绕圆柱的阻力系数、流函数涡量分布以及扰动流函数等。计算结果显示，对于定常绕流及圆柱起动流动，几种无穷无流函数边值条件求得的结果基本一致。对于非定常周期性圆柱绕流，不同的无穷远流函数边值条件对计算     

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.     

一维河网非恒定流及悬沙数学模型的节点控制方法

本文的一维河网非恒定流及悬沙数学模型，是根据以一维圣维南方程组，悬沙非平衡输运方程及水位、含沙量节点控制法而建立。首先，利用单一河流有限差分方程组转换形式和节点处质量、能量守恒性，写出所有节点的水位控制方程组。求解此不规则稀疏矩阵方程组得到得有节点的水位，再由单一河流非恒定流的求解方法可获得所有单一河流的断面水位和流量。基于水注的节点水位控制法，本文提出了节点悬沙控制法。假设节点处冲刷或淤积较小，所有节点的含沙量控制方程组可通过输沙量守恒方程用矩阵形式写出。求解此不规则稀疏矩阵方程组，得到所有节点处的含沙量。所有单一河流断面处的含沙量通过单一河流悬沙输运的求解方法获得。本文介绍的模型适用于各种河网类型。作为检验，该模型成功地应用于珠江三角洲流域河网水流及悬沙的数值计算。     

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…     

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.     

NUMERICAL SOLUTION OF 2-D INCOMPRESSIBLE VISCOUS FLOW WITH HIGH ORDER COMPACT SCHEME USING DOMAIN DECOMPOSITION AND MATCHED METHOD

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｅｒｅｈａｖｅｂｅｅｎｓｔｉｌｌｒａｒｅｐｒｏｇｒａｍｓｆｏｒｃｏｍｐｌｅｘｆｌｏｗｓｉｍｕｌａｔｉｏｎｗｉｔｈＤｏｍａｉｎＤｅｃｏｍｐｏｓｉｔｉｏｎＭｅｔｈｏｄ(ＤＤＭ ) ,ｗｈｉｃｈｔｈｏｕｇｈｗａｓｂｒｉｅｆｌｙｒｅｐｏｒｔｅｄｂｙＺｈｕＺｉｑｉａｎｇ[1] .ＴｈｅｇｅｎｅｒａｌｆｌｏｗｃａｌｃｕｌａｔｉｏｎｓｏｆｔｗａｒｅｓｓｕｃｈａｓＣＦＸ 4 ,Ｐｈｏｅｎｉｃｓａｒｅａｌｓｏｌａｃｋｏｆｔｈｅｆｕｎｃｔｉｏｎｏｎｔｈｉｓａｓｐｅｃｔ.Ｆｏｒｔｈｅｓａｋｅｏｆｐ…     

STRUCTURES OF CONFINED VORTEX BREAKDOWN IN CONSTANT DIAMETER PIPE FLOW

Numerical solutions of three-dimensional, incompressible and unsteady Navier-Stokes equations for constant diameter swirling pipe flows are used to study vortex breakdown, including the detailed flow structures in the bubble domain and the “tail” behind the bubble during the vortex breakdown, and a comparison is made between the numerical solutions and the experimental results.     

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。     

NUMERICAL SIMULATIONS OF HIGHLY NONLINEAR STEADY AND UNSTEADY FREE SURFACE FLOWS

A numerical simulation model based on an open source Computational Fluid Dynamics (CFD) package-Open Field Operation and Manipulation (OpenFOAM) has been developed to study highly nonlinear steady and unsteady free surface flows. A two-fluid formulation is used in this model and the free surface is captured using the classical Volume Of Fluid (VOF) method. The incompressible Euler/Navier-Stokes equations are solved using a finite volume method on unstructured polyhedral cells. Both steady and unsteady free surface flows are simulated, which include: (1) a submerged NACA0012 2-D hydrofoil moving at a constant speed, (2) the Wigley hull moving at a constant speed, (3) numerical wave tank, (4) green water overtopping a fixed 2-D deck, (5) green water impact on a fixed 3-D body without or with a vertical wall on the deck. The numerical results obtained have been compared with the experimental measurements and other CFD results, and the agreements are satisfactory. The present numerical model can thus be used to simulate highly nonlinear steady and unsteady free surface flows.