二维潮波模式底摩擦效应参数化方案同化研究

基于伴随同化方法对二维潮波模式底摩擦效应的线性与非线性参数化方案进行了比较研究。采用拉格朗日乘子法推导了底摩擦效应两种参数化方案的伴随表达式,并借助孪生实验对所述方法的参数反演能力进行了验证.通过同化高度计资料和验潮站资料,分别使用线性和非线性参数化方案,以及常数底摩擦系数与空间分布底摩擦系数设置的两两组合,对模拟结果进行了比较和分析。经过同化,模拟结果与观测数据的差异均有了明显下降。结果表明,如果将底摩擦系数设置为全区常数,则非线性参数化方案的模拟结果远优于线性方案;然而,在空间分布设置下,两者模拟得到的水位场与潮流场仅有细微差别,并尝试从底摩擦引起的能量耗散角度对其原因进行了分析。     

渤、黄海的底摩擦系数

利用伴随法，根据32个验潮站的水位观测资料来优化渤、黄海的底摩擦系数．所作的一系列数值模拟实验表明；利用伴随方法优化渤、黄海的底摩擦系数能够有效地减少数值模拟结果与观测结果的差异．     

一种基于“移去-恢复”理论的重力数据格网化方法

为提升重力数据格网化精度,从频谱组合角度出发,提出了一种基于"移去-恢复"理论的重力数据格网化方法。计算过程中结合地形数据将传统的数学拟合转化为顾及地球物理场信息的物理拟合。这一过程可被简化为"计算-移去-推估-恢复"四步:首先利用高分地形数据计算出目标区域完全布格改正项并利用均衡理论计算出均衡改正;然后将目标区域离散重力数据中的地形相关高频项移除;继而利用频谱更加单一的均衡重力异常进行格网化;最后恢复格网化数据中的地形高频项,得到目标区域格网化的重力数据。实验结果表明,移去地形影响后的重力数据更加平滑,更有利数据格网化;实验区内"移去-恢复"方法精度相比于传统的Kriging格网化精度提升了27.5%,误差阈值更小,分布更加收敛;而且所提出方法构造的局部重力异常能表达出实验区重力场的更多细节特征。     

坐标点分布对三维坐标变换参数估计不确定度的影响（英文）

相机坐标系和目标坐标系中公共特征点的测量精度和相对几何分布对参数估计具有重要影响,直接影响视觉导航精度。由于坐标点的测量精度依赖于测量系统的精度,而公共点的分布选取更容易调整,因此仅讨论公共特征点相对几何分布对平移旋转参数估计精度的影响。首先,采用非线性模型和加权整体最小二乘算法求解变换参数,并采用蒙特卡罗方法归纳总结了不同的特征点分布对参数估计精度的影响。同时,为了工程化应用,将坐标点分布的分散度进行量化作为其权重,提出一种重构协因数矩阵的方法。最后,基于实际测量数据的对比试验表明,在没有先验知识的情况下,所提出的方法可以改善参数的估计精度,即变换参数的后验标准差至少减小6.7%。     

全附体潜艇粘性流场的RANS模拟及场量和涡量的校验分析

采用相同拓扑结构和相近网格质量的4套网格和5种湍流模型,对全附体Suboff潜艇粘性流场进行RANS模拟,分析了网格密度、节点空间分布规律和湍流模型对计算精度的影响,详细校验了其力积分量、速度场量和涡量特征。结果表明:网格密度最大的G4网格(140万)计算精度最高,总阻力较实验值误差为0.723%,其采用SST湍流模型时最优。计算得到的压力系数和剪切应力系数分布均与实验值吻合很好;桨盘面速度等值线分布计算精度与文献相当,轴向相对速度0.9以上的计算半径稍大于实验值,其余半径与实验吻合较好;桨盘面上0.25倍半径处速度分量沿周向分布计算精度较文献高,轴向分量与实验值吻合较好,径向分量峰值稍小于实验值,但峰值所处周向位置与实验值一致。成功捕捉到了附体端面绕流诱导对旋涡、附体叶根截面下游处项链形涡对、尾翼端面尾缘上方附着涡蹄、附体马蹄涡系、尾翼截面通道流体挤压作用诱导涡以及桨盘面涡量汇集的潜艇涡量场特征,且围壳端面绕流诱导对旋涡沿流动方向持续稳定,不影响桨盘面涡量场,均与文献中由大涡模拟模拟得到的定性结论一致。研究表明,在网格密度较大、节点分布合理、网格质量较高、湍流模型选取适当和壁面函数使用有效的条件下,RANS模拟潜艇粘性流场的场量和涡量特征同样具有很高的计算精度,能够在工程应用中有力支撑新型艇型设计与性能分析。     

龙口垂向二维流场数值模拟

根据物理实验的具体条件,应用基于RANS方程和VOF方法对堰流垂向二维流动进行了数值模拟.计算结果复演了堰流的四种典型流态,并与实验结果中水位、流速分布以及最大流速沿程分布相比较,表明数值模拟方法是可行的.以长江口青草沙水库主龙口施工过程为背景,在给定上下游不同水位差的情况下,对龙口垂向二维流动进行了数值模拟.给出了龙口大流速区的位置,比较了在不同龙口底槛高程的情况下龙口局部流场的变化特征.     

逆压梯度边界层未分离情况下的湍流模式适用性研究Turbulence model applicability for boundary layer flow with adverse pressure gradient in attached case

边界层逆压梯度作用下的流动是许多工程中的一个基础问题,由于逆压梯度作用,流动形态复杂,使得数值模拟有很大的难度。基于雷诺平均纳维‐斯托克斯RANS（Reynolds Averaged Navier‐Stokes）方程对二维平板逆压梯度边界层作数值计算研究,选取6种代表性的湍流模式,得到局部摩擦系数的数值解,与实验值比较,发现k‐ω模式具有很好的精度。基于该湍流模式,给出了湍动能分布,该结果有助于认识逆压梯度边界层流动的复杂特征。     

超声速流动中非线性EASM湍流模式应用研究

针对超声速复杂流动区域精确模拟的需要,发展了基于k-ω可压缩修正形式的非线性显式代数雷诺应力模式(EASM),提高了该模式对超声速复杂流动的数值模拟精度。通过对二维超声速凹槽和三维双椭球的数值计算表明,与SA和SST常规线性涡黏性湍流模式比较,非线性的EASM模式对大分离以及剪切层流动结构的刻画能力更精细,对剪切层再附区的压力及摩擦系数分布模拟更加精确;EASM模式能够准确地模拟二次激波引起的压强和热流分布情况。     

逆压梯度边界层未分离情况下的湍流模式适用性研究

边界层逆压梯度作用下的流动是许多工程中的一个基础问题,由于逆压梯度作用,流动形态复杂,使得数值模拟有很大的难度。基于雷诺平均纳维-斯托克斯RANS(Reynolds Averaged Navier-Stokes)方程对二维平板逆压梯度边界层作数值计算研究,选取6种代表性的湍流模式,得到局部摩擦系数的数值解,与实验值比较,发现k-ω模式具有很好的精度。基于该湍流模式,给出了湍动能分布,该结果有助于认识逆压梯度边界层流动的复杂特征。     

超声速流动中非线性EASM湍流模式应用研究

针对超声速复杂流动区域精确模拟的需要,发展了基于k-ω可压缩修正形式的非线性显式代数雷诺应力模式（EASM）,提高了该模式对超声速复杂流动的数值模拟精度。通过对二维超声速凹槽和三维双椭球的数值计算表明,与SA和SST常规线性涡黏性湍流模式比较,非线性的EASM模式对大分离以及剪切层流动结构的刻画能力更精细,对剪切层再附区的压力及摩擦系数分布模拟更加精确;EASM模式能够准确地模拟二次激波引起的压强和热流分布情况。     

Parameter estimation for a three‐dimensional numerical barotropic tidal model with adjoint method

The parameters of a three‐dimensional (3‐D) barotropic tidal model are estimated using the adjoint method. The mode splitting technique is employed in both forward and adjoint models. In the external mode, the alternating direction implicit method is used to discretize the two‐dimensional depth‐averaged equations and a semi‐implicit scheme is used for the 3‐D internal mode computations. In this model the bottom friction is expressed in terms of bottom velocity which is different from the previous works. Besides, the bottom friction coefficients (BFCs) are supposed to be spatially varying, i.e. the BFC at some grid points are selected as the independent BFC, while the BFC at the other grid points can be obtained through linear interpolation with these independent BFCs. On the basis of the simulation of M₂ tide in the Bohai and North Yellow Seas (BNYS), twin experiments are carried out to invert the prescribed distributions of model parameters. The parameters inverted are the Fourier coefficients of open boundary conditions (OBCs), the BFC and the vertical eddy viscosity profiles. In these twin experiments, the real topography of BNYS is installed. The ‘observations’ are produced by the tidal model and recorded at the position of TOPEX/Poseidon altimeter data, tidal gauge data and current data. The experiments discuss the influence of initial guesses, model errors and data number. The inversion has obtained satisfactory results and the prescribed distributions have been successfully inverted. The results indicate that the inversion of BFC is more sensitive to data error than that of OBC and the vertical eddy viscosity profiles. Copyright © 2007 John Wiley & Sons, Ltd.     

Modeling Three-Dimensional Groundwater Flows by the Body-Fitted Coordinate (BFC) Method: I. Stationary Boundary Problems

Based on the body-fitted coordinate (BFC) method, a three-dimensional finite difference computer code, BFC3DGW, was developed to simulate groundwater flow problems. Methodology and solution procedures of the BFC method for simulating groundwater flows, particularly when the flow domain is stationary as in the case of confined aquifers, are described. The code was verified by comparing numerical results with analytical solutions for well-flow problems in an isosceles right-triangular aquifer. An example simulation is made to demonstrate capability of the code for solving flow problems in anisotropic aquifers where directions of anisotropy change continuously. The method differs from the conventional finite difference method (FDM) in the ability to use a flexible, nonorthogonal, and body-fitted grid. The main advantages of the method are the convenience of grid generation, the simplified implementation of boundary conditions, and the capability to construct a generalized computer code which can be consistently applied to problem domains of any shape.     

Modeling Three-Dimensional Groundwater Flows by the Body-Fitted Coordinate (BFC) Method: II. Free and Moving Boundary Problems

This paper presents a methodology and solution procedure of the time-dependent body-fitted coordinate (BFC) method for the analysis of transient, three-dimensional groundwater flow problems characterized by free and moving boundaries. The technique consists of numerical grid generation, time-dependent body-fitted coordinate transformation, and application of the finite difference method (FDM) to the transformed partial differential equations. Based on the time-dependent BFC method, a three-dimensional finite-difference computer code, BFC3DGW, was developed and used to solve two unconfined flow problems. The code was verified by comparing numerical results with analytical solutions for a steady-state seepage problem. In order to demonstrate capability of the method in dealing with flow problems with irregular and moving boundary surfaces, an unconfined well-flow problem was solved by the developed code. Difficulties associated with the free and moving irregular boundary have been successfully overcome by employing this method.     

On the nonlinear stability of a truncated shallow spherical shell under A uniformly distributed load

A problem of practical interest for nonlinear axisymmetrical stability of a clamped truncated shallow spherical shell with a nondeformable rigid body under a uniformly distributed load is studied in this paper. By using modified iteration method, some important analytic results are obtained and the corresponding numerical results are given in figures. This paper was read at The Third East China Symposium on Solid Mechanics, Jiuhuashan, October, 1986. Fomerly at University of Science and Technology of China, Hefei.     

2-D solution for free vibrations of parabolic shells using generalized differential quadrature method

The Generalized Differential Quadrature (GDQ) procedure is developed for the free vibration analysis of complete parabolic shells of revolution and parabolic shell panels. The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic. The governing equations of motion, written in terms of internal resultants, are expressed as functions of five kinematic parameters, by using the constitutive and kinematic relationships. The solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell. The discretization of the system by means of the Differential Quadrature (DQ) technique leads to a standard linear eigenvalue problem, where two independent variables are involved. The results are obtained taking the meridional and circumferential co-ordinates into account, without using the Fourier modal expansion methodology. Several examples of parabolic shell elements are presented to illustrate the validity and the accuracy of GDQ method. Numerical solutions are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Femap/Nastran, Straus, Pro/Mechanica. Very good agreement is observed. Furthermore, the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good. The accuracy of the method is sensitive to the number of sampling points used, to their distribution and to the boundary conditions. Different typologies of non-uniform grid point distributions are considered. The effect of the distribution choice of sampling points on the accuracy of GDQ solution is investigated. New numerical results are presented.     

Generalization of physical component boundary fitted co-ordinate (PCBFC) method for the analysis of free-surface flow

This paper presents a systematic and theoretically consistent approach for the analysis of free-surface flow, making use of a number of established ideas such as physical component, boundary-fitted co-ordinate (BFC) and Lagrangian front tracking. The approach extends, theoretically as well as numerically, the use of physical component to general non-orthogonal moving grids and provides a numerically stable BFC method with little labour of free-surface positioning, grid generation and grid renewal. The approach conserves mass even at the free surface and allows time step of the order of the Coulant number. The main body of the present paper starts with the definition of analytical space and Riemannian geometry intrinsic to the physical component by applying to it the theorems of differential geometry and manifold theory. Then the governing equations of flow and free surface for the physical component are defined in the general 3D form with the notation of the new Riemannian geometry. Numerical procedures and the fully discrete equations are also presented for the benefit of potential users. Finally, several 2D examples demonstrate the basic performance of the present method by showing the computability of complex free-surface motion.     

Evolution of single elliptic vortex rings

The evolution of single elliptic vortex rings for initial aspect ratio (AR)=2,4,6 has been studied. The incompressible Navier-Stokes equations are solved by a dealiased pseudo-spectral method with 64³ grid points in a periodic cube. We find that there are three kinds of vortex motion asAR increases and bifurcation occurs at certainAR. The processes of advection, interaction and decay of vortex ring are discussed. Numerical results coincide with experiments and other authors' numerical simulation. The project is supported by National Natural Science Foundation of China and Doctoral Program of Institution of Higher Education     

Solution of shallow water equations for complex flow domains via boundary-fitted co-ordinates

Many problems of applied oceanography and environmental science demand the solution of the momentum, mass and energy equations on physical domains having curving coastlines. Finite-difference calculations representing the boundary as a step function may give inaccurate results near the coastline where simulation results are of greatest interest for numerous applications. This suggests the use of methods which are capable of handling the problem of boundary curvature. This paper presents computational results for the shallow water equations on a circular ring of constant depth, employing the concept of boundary fitted grids (BFG) for an accurate representation of the boundary. All calculations are performed on a rectangle in the transformed plane using a mesh with square grid spacing. Comparisons of the simulations of transient normal mode oscillations and analytic solutions are shown, demonstrating that this technique yields accurate results in situations (provided that there is a reasonable choice of grid) involving a curved boundary. The software developed allows application to any two-dimensional area, regardless of the complexity of the geometry. Simulation runs were made with two co-ordinate systems. For the first system, the grid point distribution was obtained from polar co-ordinates. For the second one, grid point positions were calculated numerically, solving Poisson's equation. It was found that small variations in the metric coefficients do not deteriorate the accuracy of the simulation results. Moreover, comparisons of surface elevation and velocity components at grid points near the inner and outer radii obtained from an x?y Cartesian grid model with the BFG simulation were made. The former model produced inacccuracies at grid points near boundaries, and, owing to the large number of mesh points used to yield the necessary fine resolution, the computation time was found to be a factor of three higher.     

三维非均匀不稳定渗流方程的二维不均匀粗化算法

在无源汇条件下,根据流过某一个横截面的流体流量等于流过这一横截面内所有精细网格的流体流量之和这一特点提出了粗化网格等效渗透率的计算方法。在粗化区内,利用直接解法求解二维渗流方程,再用这些解合成粗化网格的三维合成解,并由合成解计算粗化网格的等效渗透率。根据精度的要求采用了不均匀网格粗化,在流体流速大的区域采用精细网格。利用所得等效渗透率计算了粗化网格的某三维非均匀不稳定渗流场的压降解,结果表明三维非均匀不稳定渗流方程的二维不均匀粗化解非常逼近采用精细网格的解,但计算的速度比采用精细网格提高了80倍。