求解二维扩散方程的有限近似解法

提出求解二维扩散方程的新方法——有限近似解法7点格式，对非规则区域定常扩散方程和规则区域非定常扩散方程的计算与精确解比较，表明这一方法较有限分析法计算简单，计算精度高，并且可以适用于不规则边界区域的计算。最后计算了典型的坝基渗流流场，计算结果与实验结果吻合较好。     

摄动有限差分 (PFD) 方法的数值计算

本文利用数值摄动的思想发展了对流扩散(CD)方程的摄动有限差分(PFD)[2]格式,局部线化可获得摄动准确解(PENS)格式。把格式中的指数函数按网格雷诺数的幂级数展开,能够给出PENS格式的各阶近似,即各阶PFD格式。本文构造了一维CD方程的PENS及二阶PFD格式以及二维CD方程的二阶PFD格式,并利用二阶精度的PFD格式计算了一维CD方程、方腔流动和前、后台阶绕流流动等算例。计算给出了准确度较高的数值结果。     

基于修正Roe格式的有限体积法求解二维浅水方程

应用迎风有限体积法,对具有复杂地形的二维浅水方程进行数值模拟.基于非结构化网格,采用Roe格式的近似Riemann解计算非粘性界面通量.底坡源项采用简单的斜底模型离散,从而保证了地形的离散精度.为了保证该计算格式的压力项和底坡源项的和谐性,对经典的Roe格式计算数值通量中的静水压力项进行了修正,并证明了修正后的Roe格式具备和谐性.通过与超临界流倾斜水跃和有激波混合流算例理论解结果比较,验证了该模型具有良好的间断捕捉能力、计算稳定性和守恒性.     

三维对流扩散方程的混合有限分析解

本文应用线性微分方程的算子迭加原理，将二维对流扩散方程的有限分析法交替方向用于三维对流扩散方程，从而得到较三维有限分析法简单实用的混合有限分析法，接着用数学分析法证明了该方法的稳定性和收剑性，并用指定强迫解方法对方程离散格式和程序设制等做了验证。最后计算了三维紊动射流，计算结果与实验资料一致，表明用混合有限分析法计算三维对流扩散问题是可行的。     

基于自适应网格的二维水动力模型

为准确地模拟流域洪水传播和淹没情况,基于自适应网格技术,以有限体积法为离散格式构建数值模型.模型以二维浅水方程为控制方程,采用HLL格式近似黎曼解计算界面通量,采用WAF格式对计算的通量进行加权修正,保证时间和空间上的二阶精度,并使其满足TVD条件,减小数值振荡.底坡源项采用水深差分重构,摩阻源项采用半隐式格式,保证数...     

基于自适应网格的急流条件下污染物输运高效高精度模拟

为了高效准确模拟急流条件下突发水污染事件中污染物的输运规律,基于自适应网格技术构建了Godunov格式有限体积模型。模型利用自适应结构网格离散二维浅水控制方程,对水位梯度或污染物浓度梯度较大的区域进行精细网格划分,同时细化干湿边界区域网格。模型采用MUSCL-Hancock方法求解二维浅水控制方程,使模型具有时空二阶精度;利用HLLC格式近似Riemann解计算界面通量,对界面两侧的Riemann变量进行非负重构和局部底部高程修正以确保模型计算的和谐性和稳定性。算例验证表明:自适应网格技术可以自动识别水位梯度或污染物浓度梯度较大的区域以及干湿边界区域并细化该区域网格,保证模型模拟精度的基础上,提升模型模拟效率;该模型能够准确高效地模拟急流条件下污染物的输运过程,适用于突发水污染事件的评估、预警和应急管理。     

基于Roe格式黎曼近似解的二维FVM模型

提出一种基于黎曼近似解Godunov格式的二维FVM模型求解口门区二维通航水力特性,并采用Roe格式计算界面通量。采用水面坡度代表源项中压力项的作用,有利于复杂地形条件计算的稳定性;通过对斜底单元干湿特性的合理划分,确保计算单元的水量和动量平衡及数值计算精度。利用该模型计算分析了衢江梯级塔底枢纽上下游口门区及引航段发电及泄洪条件下的通航水力特性,结果表明Roe格式的有限体积方法计算复杂地形条件下的水流流场稳定性好、计算精度高,为合理制定衢江梯级枢纽调度规则提供数据支持。     

大名泛区洪水演进数值模拟

利用结构化网格的有限体积法,建立了二维浅水方程的高精度、低计算负荷的数值计算模型。对结构化网格的处理采用一种自适应网格加密方法,提出四叉树的网格构造,以提高网格对地形和水力变化的敏感度。推导出一种具有激波捕捉能力的二维浅水方程的守恒形式,采用单元中心式有限体积离散。方程的离散采用Godunov格式,利用近似Riemann解求解界面通量,并介绍和采用了具有二阶精度的HLLC算法。对在此基础上,建立大名泛区二维洪水演进模型,获取了不同时段的淹没范围栅格图像、不同时刻淹没水深、洪泛区的蓄水量变化过程以及泛区内点的水力要素信息,为泛区的防洪规划和实时洪水预报提供理论参考。     

运用有限单元法计算短波折射和绕射的综合作用

<正> 提要:本文提出了一种计算短波折射和绕射综合作用的二维有限单元数值模型。求解的波动方程适用于底坡缓和海域里的小振幅表面重力波的传播。本文提出了一种有效的计算格式,这种格式能够求解需要大量计算格点的实际问题。本文还将有限单元法计算的结果跟解析解、二维数值解、三维数值解、以及水力学模型的实测资料进行了比较。     

基于近似黎曼求解器的三维浅水方程组求解方法

将求解平面二维浅水方程组的Godunov型有限体积法扩展至求解三维浅水方程组,建立具有激波捕捉特性的三维数学模型,将扩大三维浅水方程数学模型的应用范围。模型中湍流封闭采用非线性K-ε模型,水平方向数值通量采用HLLC近似黎曼求解器计算。为改善数值格式稳定性,垂向扩散项采用隐式离散,且在局部小水深处将三维模型退化为水深平均平面二维模型,所开发的模型在形式上具有时、空二阶精度。随后采用水跃、干河床溃坝洪水演进等算例对模型进行检验,结果表明:该模型具有较好的稳定性,能保证静水平衡,在间断解处能给出高分辨率的数值解,并具有较好的干湿边界模拟能力。     

2D numerical modeling of grain-sorting processes and grain size distributions

A depth-averaged finite difference two-dimensional hydrodynamic-morphological and sediment transport model is presented in the orthogonal curvilinear grid system. The sediment submodel considers the influence of selective sorting by modifying the sediment transport capacity and incorporates a simple simulation method to describe changes in the grain size distribution of the bed surface by solving the governing equation for sediment mass conservation. The 2D numerical model was applied to the experiment on downstream fining. The model simulation results and the measurements are in acceptable agreement. The result illustrates the capability of the two-dimensional model to predict the sediment wedge evolution and grain sorting process.     

FINITE PROXIMATE METHOD FOR CONVECTION-DIFFUSION EQUATION

A finite proximate method was presented to solve the convection-diffusion equation in curvilinear grids. The method has characteristics of automatic upwind effect and the good stability. It was verified through exact solution and other calculation results of two-dimensional dam-break flow in a frictionless, horizontal channel. The calculation results are in good agreement with the exact solution and other calculation results, which show that the finite proximate method can be applied to solve the convection-diffusion equation directly not only in the rectangular grids, but also in the curvilinear grids.     

纯隐格式的混合有限分析法在广雅桥水流数值模拟中的应用

分别建立柳州市柳江河道大范围河段和拟建广雅桥局部范围曲线坐标系下的二维水流数学模型,并采用纯隐格式的混合有限分析法来离散和求解该数学模型,将常用的干湿网格判别标准与冻结法结合起来模拟计算河道中的浅滩。所建立的大范围柳州市柳江河道二维水动力数学模型计算成果一方面用于验证,另一方面为广雅桥局部二维水动力数学模型提供初始和边界条件。结果表明,广雅桥的建设对局部河道的壅水和水流流态存在一定的影响,同时也证实了纯隐格式的混合有限分析法在工程实际应用中的准确性和有效性。     

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.     

NUMERICAL SOLUTION FOR TIDAL FLOW IN OPENING CHANNEL USING COMBINED MACCORMACK-FINITE ANALYSIS METHOD

A new numerical scheme for solving the tidal flow in an opening channel using the advective-diffusion shallow-water equations as the governing equations is proposed based on the combination of the MacCormack and the finite analysis methods. In the present scheme, the finite analysis method is used to discretize the momentum equation and the MacCormack technique is used to discretize the continuity equation in a single grid system. The matrix of the discretized momentum equation is characterized by predominantly main diagonal elements, which ensures favorable convergence and stability for the numerical simulation by the combined method. To verify the present method, hydraulics simulation is carried out for a section down mainstream of the Huangpu River. The computational results agree with the measured data. By use of orthogonal curvilinear coordinate system, the methods can be easily extended to the numerical simulation of the tidal flow in a tortuous channel.     

A spacetime discontinuous Galerkin method for the two-dimensional unsteady convection-dispersion problems

The unsteady two-dimensional convection-diffusion (CD) equation, which is the governing equation of the unsteady two-dimensional convection-dispersion problem, as the water contamination problems, has a mixed hyperbolic-parabolic character. When the equation has a strong mixed hyperbolic character, the exact solution is nonsmooth. In this case, the conventional numerical methods give approximate solutions which either oscillate or smear out the sharp front of the exact solution. The spacetime discontinuous Galerkin method (STDGM) is an extention of the space discontinuous Galerkin method (SDGM), applying the discontinuity in the time direction, as well as in space. Both these methods are respective modifications of the standard Galerkin finite element method (SGM). In this paper, the STDGM is applied to solve the CD equation, when the Péclet number has extremely high values, which means a strong mixed hyperbolic character. With this method, three artificial diffusion terms are introduced by modifying the test functions of the finite element method. These functions include the discontinuity int, x andy axis. The results obtained from the analytical solution of the problem are used for testing the numerical solution, applying both the space-discontinuous Galerkin method (SDGM) and the STDGM and are presented in diagrams, from which useful observations, comparisons and conclusions can be drawn.     

潮汐河流排污口设置对水质的影响

以扬州市青山污水处理厂长江排污口的设置为例,根据潮汐河流的水动力、污染物输移特征,采用正交曲线网格离散计算区域,采用有限体积法离散控制方程,建立了非稳态平面二维水动力、水质数学模型,采用90%保证率下的枯水设计径流量与大潮、小潮典型潮位过程的组合作为设计水文条件,模拟分析了典型水文条件下,污水排放对纳污水体水环境的影响...     

NUMERICAL SIMULATION OF 2-D TIDAL FLOW AND WATER QUALITY UNDER THE CURVILINEAR COORDINATES

This paper presents a numerical method to simulate the 2-D tidal flow and water quality under the curvilinear coordinates. In order to overcome the computational difficulties in natural rivers, such as the complicated boundary figures, the great disparity between length and width of computational domain, etc. , boundary-fitted grid is used, the irregular domain in physical plane is transformed into a rectangular domain in transformed plane, and the depth-averaged momentum equations and mass equation are rewritten and discretized based on the finite volume techniques in curvilinear coordinates. Practical application of the method is illustrated by an example for the Dachangzhen Section of the Yangtze River. A fair agreement between the values measured and computed demonstrates the validity of the method developed.