基于最小二乘的N-S方程算子分裂有限元法

提出一种新的求解N S方程的有限元法,即基于最小二乘的N S方程算子分裂有限元法。该算法采用算子分裂法将N S方程分解成扩散项和对流项:扩散项时间离散采用向后差分格式,空间离散采用标准Galerkin有限元法;对流项时间离散采用向后差分格式,空间离散采用最小二乘有限元法。应用该算法对方腔流和后台阶流进行数值模拟,方腔流数值计算结果与标准解吻合很好;在后台阶流数值模拟中给出了不同雷诺数下的流场特征和速度对比曲线,所得计算结果与试验结果吻合较好,表明基于最小二乘的N S方程算子分裂有限元法具有较好的收敛性和较高的精度。     

数值求解非线性Burgers方程的有限分析混合格式

本文采用有限分析混合格式对非线性Burgers方程进行数值模拟,通过定常和非定常算例表明,在连续特征线法离散的非线性对流算子所生成的非均匀网格上,采用有限分析法耦合离散扩散算子,对处理大Re数和大Pe数问题行之有效,数值结果是令人满意的。     

交替方向的三维有限分析方法

本文在二维有限分析方法的基础上利用交替方向的原理,构造了三维有限分析方法的27点计算格式,该格式除了满足原有限分析方法的优点外,还具有节约内存及运算时间的特点。文中应用该方法计算了三维方腔流动及浮运沉井施工期的三维流场,计算结果与实验及实测结果符合较好。     

混合拉普拉斯变换有限单元法计算二维地下水溶质运移问题

在求解对流占优的地下水溶质运移问题时，常规数值方法会产生数值扩散和过量现象．本文将混合拉普拉斯变换有限单元法引入求解二维对流扩散问题，结果表明，这种新的计算方法能有效地消除数值扩散和过量现象，同时由于具有一步到位、局部求解的优点，因而特别适于大区域地下水污染的长期预报     

对流扩散方程逆控制的基函数算法

文中根据逆边界逆过程控制理论，将 Ｄ、 Ｆ、和 Ｐ、 Ｊ、 Ｈ 等人为求解热传导逆过程提出的基函数方法推广应用于水污染控制问题。文中建立了对流扩散逆边界逆过程混合控制的精确计算公式；并将基函数算法应用于洛河河段的水污染控制规划计算中，计算结果说明了该算法的有效性。本文将讨论在未来有限时间 Ｔ 内的水环境污染控制问题，在给定的终端水质标准条件下，将控制函数表达成有限维基函数的线性组合，这种算法能克服对流扩散动态控制计算中的严重病态问题。与现行的最优控制算法相比，它直接以对流扩散方程为基础进行求解，充分考虑了水体自净能力和社会经济的发展变化，物理概念明确。本算法对水环境动态精确控制进行了初步尝试。     

N—S方程SUPG有限元解法

SUPG是八十年代初期发展的一种先进的有限元算法,该法既具有迎风算法的长处,又抑制了迎风法造成的虚假扩散问题,具有较好的稳定性和精度,是一种很有前途的新算法。本文从非定常二维不可压Navier-Stokes方程组出发,选用流函数-涡做为方程变量,构造了SUPG有限元离散化变分方程组,并采用预估—多步校正算法解方程组,在具体算例的计算中,数值生成了卡门涡街现象。     

A NEW ARTIFICIAL DIFFUSION FACTOR IN THE STREAMLINE UPWIND/PETROV GALERKIN FORMULATION

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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     

MODIFIED INTEGRAL-FACTOR METHOD FOR STEADY CONVECTION-DIFFUSION EQUATIONS

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改进MCMC方法及其应用

概率反演中，马尔科夫链蒙特卡罗(Markov chain Monte Carlo, MCMC)是一类重要的后验概率进行抽样方法，但由于各种原因MCMC算法搜索往往会陷入局部最优解，从而限制了MCMC方法在具有非唯一解反问题中的应用。鉴于此，提出了一种基于Metropolis-Hastings算法的多链搜索的方法，该方法可以根据搜索结果实时调整链的个数，因而在搜索到尽可能多的解的同时节省了多链搜索的时间。最后将该算法应用于地下水污染源反问题的求解，计算结果表明改进后的算法对求解具有非唯一解反问题具有良好的效果。     

感潮河段盐水入侵的河口水质模型

盐潮入侵将严重影响内河水质。本文考虑强混合型河口潮汐的特点,采用同步不同格式对河口盐潮入侵问题的流场及浓度场进行数值计算。采用欧拉-拉格朗日混合解法将对流-扩散方程中的扩散项和对流项分裂求解,应用高精度时间序列插值的特征差分隐格式求解对流项,扩散项采用传统的有限差分法。在汊口处,将描述河网汊口水质变化的三维对流扩散方程在汊口控制体体积积分,变量间的插值分布采用Panankar提出的幂函数,得到新的汊口离散方程。计算与实测结果比较表明,本文提出的方法有效可行。     

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.     

数值流形法覆盖系统并行生成算法研究

计算效率低是当前制约数值流形法应用于大型实际工程模拟的瓶颈问题,并行计算作为一种加速计算技术,能有效地提高数值流形法的计算效率。在串行算法基础上,系统研究了基于分布式内存编程模式的数值流形法覆盖系统和流形单元并行生成算法。首先,在分析并行算法与串行算法不同点和难点的基础上,采用区域分解算法实现并行任务分配,并提出覆盖系统并行生成主要步骤。采用临时规则粗网格形成负载均衡的子区域,提出相应子区域生成算法。其次,在深入分析数值流形法数学覆盖、物理覆盖和流形单元之间关系基础上,探讨并行算法中子区域覆盖系统生成的关键技术,以及物理覆盖和流形单元编号规则。然后,针对并行算法提出了建立覆盖系统界面信息算法,为数值流形法并行计算过程中通讯和数据交换提供支持。最后,在覆盖系统并行生成算法基础上,采用C++面向对象编程技术开发了相应程序。2个算例结果验证了算法正确性和有效性,为后续并行模拟提供了前处理器。     

Multi-Objective Optimization of the Proposed Multi-Reservoir Operating Policy Using Improved NSPSO

Severe water shortage is unacceptable for water-supply reservoir operation. For avoiding single periods of catastrophic water shortage, this paper proposes a multi-reservoir operating policy for water supply by combining parametric rule with hedging rule. In this method, the roles of parametric rule and hedging rule can be played at the same time, which are reducing the number of decision variables and adopting an active reduction of water supply during droughts in advance. In order to maintain the diversity of the non-dominated solutions for multi-objective optimization problem and make them get closer to the optimal trade-off surfaces, the multi-population mechanism is incorporated into the non-dominated sorting particle swarm optimization (NSPSO) algorithm in this study to develop an improved NSPSO algorithm (I-NSPSO). The performance of the I-NSPSO on two benchmark test functions shows that it has a good ability in finding the Pareto optimal set. The water-supply multi-reservoir system located at Taize River basin in China is employed as a case study to verify the effect of the proposed operating policy and the efficiency of the I-NSPSO. The operation results indicate that the proposed operating policy is suitable to handle the multi-reservoir operation problem, especially for the periods of droughts. And the I-NSPSO also shows a good performance in multi-objective optimization of the proposed operating policy.     

感潮河段盐水入侵的水质模型

盐潮入侵严重影响内河水质。盐度的纵向分布受制于上游径流和海洋潮汐，其水动力学特性非常复杂。数值求解不恒定盐度入侵，主要困难在于对流占优时对纯对流算子的恰当处理，否则将会产生严重的数值耗散和伪振荡等非物理效应。考虑到强混合型河口潮汐的特点，本文采用同步不同格式对盐潮入侵问题的流场及浓度场进行了数值计算。采用欧拉—拉格朗日混合解法（ELM），将对流—扩散方程中的扩散项和对流项分裂求解，应用高精度时间序列插值的特征差分隐格式求解对流项，扩散项采用传统的有限差分法。在汊口处，将描述河网汊口水质变化的三维对流扩散方程在汊口控制体积积分，变量间的插值分布采用Panankar提出的幂函数，得到新的汊口离散方程。计算与实测结果比较表明，本文提出的方法有效可行。     

稳态对流-扩散方程参数反演的变分有限元法

通过误差平方和最小原则及正则化方法,将稳态对流扩散方程参数反问题转化为一个变分问题,通过拉格朗日乘子法和有限元离散,并利用Armijo型线性搜索和最速下降法得到了数值计算方法。数值解与精确解的比较表明了此算法的可行性和有效性。     

AN OPERATOR-SPLITTING ALGORITHM FOR ADVECTION-DIFFUSION-REACTION EQUATION

An operator-splitting algorithm for three-dimensional advection-diffusion-reactionequation is presented.The method of characteristics is adopted for the pure advection operator,the explicit difference scheme is used for diffusion,and a prediction-correction scheme is em-ployed for reaction.The condition for stability of the algorithm is analysed.Severall inear andnonlinear examples are illustrated to test the convergence and accuracy of the numerical proce-dure,and satisfactory agreements between computed and analytical solutions are achieved.Dueto its simplicity,stability,and validity for both one-and two-dimensional problems,the success-ful algorithm can be used to numerical simulations of viscous fluid flows,the transport of pollu-tants and sedimentations in reservoirs,lakes,rivers,estuaries and other environments,cooling-problems in heat or nuclear power plants,etc.     

改进的MCMC方法及其应用

概率反演中,马尔科夫链蒙特卡罗是一类重要的后验概率抽样方法,但由于该算法的搜索往往会陷入局部最优解,因而限制了其在具有非唯一解反问题中的应用。鉴于此,本文对基于Metropolis_Hastings算法的多链搜索的方法进行了改进,改进后的方法可以根据搜索结果实时调整链的个数,因而可以在搜索到尽可能多的解的同时节省了多链搜索的时间。最后将该算法应用于一个地下水污染源反问题的求解,计算结果表明改进后的算法对求解非唯一性反问题具有较好的效果。     

Application of Intelligent Water Drops Algorithm in Reservoir Operation

Optimum reservoir operation is a challenging problem in water resources systems. In this paper, Intelligent Water Drops (IWD) algorithm is applied in a reservoir operation problem. IWD is a population based algorithm and is initially proposed for solving combinatorial problems. The algorithm mimics the dynamics of river system and the behavior of water drops in the rivers. For this purpose data from Dez reservoir, located in southwestern Iran, has been used to examine the performance of the model. Moreover, due to similarities between IWD and the Ant Colony Optimization (ACO) algorithms, the results are compared with those of the ACO algorithm. Comparison of the results shows that while the IWD algorithm finds relatively better solutions, it is able to overcome the computational time consumption deficiencies inherited in the ACO methods. This is very important in large models with too many decision variables where run time becomes a limiting factor for optimization model applications.     

污水排放域优选共轭水质模型

本文专门针对区域规划中污水排放位置优化控制问题，应用逆问题求解理论，提出了一种新的显式共轭水质模型，该模型克服了传统方法的缺点，可应用于一、二维水流系统污水排放位置的确定。