Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.

A new complex variable meshless method for transient heat conduction problems

In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.

NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.

Improved Particle Swarm Optimization for Solving Transient Nonlinear Inverse Heat Conduction Problem in Complex Structure

Accurately solving transient nonlinear inverse heat conduction problems in complex structures is of great importance to provide key parameters for modeling coupled heat transfer process and the structure’s optimization design.The finite element method in ABAQUS is employed to solve the direct transient nonlinear heat conduction problem.Improved particle swarm optimization(PSO)method is developed and used to solve the transient nonlinear inverse problem.To investigate the inverse performances,some numerical tests are provided.Boundary conditions at inaccessible surfaces of a scramjet combustor with the regenerative cooling system are inversely identified.The results show that the new methodology can accurately and efficiently determine the boundary conditions in the scramjet combustor with the regenerative cooling system.By solving the transient nonlinear inverse problem,the improved particle swarm optimization for solving the transient nonlinear inverse heat conduction problem in a complex structure is verified.

A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems

On the basis of the complex variable moving least-square （CVMLS） approximation, a complex variable meshless local Petrov-Galerkin （CVMLPG） method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional （2D） problem is formed with a one-dimensional （1D） basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method （FEM）. This comparison illustrates the accuracy as well as the capability of the CVMLPG method.

Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions

Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are derived using a time-domain Green’s function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.

An analytical solution for one-dimension transient solute transport

The mechanism of transport of chemicals in soil is an important research topic of environmental science and engineering, and some models and methods for a variety of solute transport problems have been done. However. most of previous works are usually for a soil column of infinite dimension. Starting from the one-dimension transient solute transport equation and its boundary and initial condition for a solute transport problem of soil column of finite length, this work has successfully applied a variable transformation to simplify the partial differential equation of solute transport problem. And an analytical serial solution for the simplified equation is then established by the so-called separated variable method and the superposition method. Compared with numerical methods such as finite different method and finite element method, this analytical solution is more accurate and of higher computation efficiency. In addition, the solution procedure presented could be extended for applications such as quality analysis, design of physical experimentation, or parameter estimation and measurement of solute transport problems.

New nonconforming finite element method for solving transient Naiver-Stokes equations

For transient Naiver-Stokes problems, a stabilized nonconforming finite element method is presented, focusing on two pairs inf-sup unstable finite element spaces, i.e., pNC/pNC triangular and pNQ/pNQ quadrilateral finite element spaces. The semi- and full-discrete schemes of the stabilized method are studied based on the pressure projection and a variational multi-scale method. It has some attractive features： avoiding higher-order derivatives and edge-based data structures, adding a discrete velocity term only on the fine scale, being effective for high Reynolds number fluid flows, and avoiding increased computation cost. For the full-discrete scheme, it has second-order estimations of time and is unconditionally stable. The presented numerical results agree well with the theoretical results.

A meshless model for transient heat conduction analyses of 3D axisymmetric functionally graded solids

A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.

基于动态模态分解-自适应变步长油浸式电力变压器绕组瞬态温升快速计算方法

为了改善当前油浸式电力变压器绕组瞬态温升计算过慢的问题,该文结合动态模态分解法和自适应变步长法提出了一种动态模态分解(DMD)-自适应变步长(ATS)快速计算方法。首先,该方法引入了动态模态分解算法,利用动态系统中前若干时步提取得到的变化特征,近似拟合其后一段时间内的系统变化,并通过选取主模态降低计算时间。其次,为了提高DMD算法性能,进一步提出结合ATS方法,通过自适应调整计算步长,提高瞬态计算效率;为了验证算法的计算精度和效率,建立了八分区分匝绕组数值传热模型并在此基础上将该文所提算法与仿真软件Fluent的计算结果进行对比,结果表明,在计算精度方面,二者结果几乎一致,计算误差最大不超过0.3 K;对于计算效率,该文算法的总计算时间为5.99 s,仅为Fluent总计算时间的1/89,且算法时间步数仅为Fluent的4.7%。最后,为了验证DMD-ATS算法的工程实用性,基于产品级油浸式电力变压器绕组结构搭建温升实验平台,并将所提算法计算结果与实验结果进行对比,结果表明所提算法在各测量线饼的误差均处在可接受的范围内,最大误差仅为4.57 K,且包含预处理时间在内的计算时间仅为69.14 s,计算时步仅需17步,较当前主流的计算方法效率有明显提高。综合算法的精度和效率,充分说明所提算法具有一定工程价值。

A Hybrid TCNN Optimization Approach for the Capacity Vehicle Routing Problem

A novel approximation algorithm was proposed for the problem of finding the minimum total cost of all routes in Capacity Vehicle Routing Problem (CVRP). CVRP can be partitioned into three parts: the selection of vehicles among the available vehicles, the initial routing of the selected fleet and the routing optimization. Fuzzy C-means (FCM) can group the customers with close Euclidean distance into the same vehicle according to the principle of similar feature partition. Transiently chaotic neural network (TCNN) combines local search and global search, possessing high search efficiency. It will solve the routes to near optimality. A simple tabu search (TS) procedure can improve the routes to more optimality. The computations on benchmark problems and comparisons with other results in literatures show that the proposed algorithm is a viable and effective approach for CVRP.

基于子循环自适应串行交错时间匹配算法的油浸式变压器绕组瞬态温升计算

针对传统算法存在的步长调整及耦合点选择问题,该文提出基于子循环自适应串行交错(SCAS)的时间匹配算法。首先,在步长调整方面,通过加入自适应(ATS)-启发式(HTS)混合变步长算法,解决步长无法实时调整的问题;然后,针对耦合点选择问题,该文在传统常规串行交错(CSS)时间匹配算法及现有改进方案子循环常规串行交错(SCSS)的基础上,提出SCAS时间匹配算法,采用自适应方案确定计算时间窗及预定耦合点,并引入指数平滑法对其精度进行保证;最后,该文基于110 kV油浸式电力变压器建立二维瞬态单分区分匝绕组模型,并将所提算法与其他传统方法进行对比分析。结果表明:在精度方面,与传统CSS算法相比SCAS算法的流场及温度场最大平均相对误差均不超过0.45%,在可接受误差范围内;在效率方面,SCAS算法总体计算效率较CSS算法提高了近20倍。同时,为了说明所提算法的工程价值,该文搭建基于110 kV变压器绕组模型的温升实验平台,将SCAS时间匹配算法应用于该模型中,实验结果表明:在精度方面,SCAS算法与实验达到稳态时最大绝对误差为2.7 K;在计算效率上,本文所提算法的计算效率较传统算法提升约46倍,计算步数约为传统的1/47,减少了计算冗余。

Deflection of transient thermoelastic circular plate by Marchi-Zgrablich and Laplace integral transform technique

This paper deals with the determination of temperature distribution and thermal deflection function of a thin circular plate with the stated conditions. The transient heat conduction equation is solved by using Marchi-Zgrablich transform and Laplace transform simultaneously and the results of temperature distribution and thermal deflection function are obtained in terms of infinite series of Bessel function and it is solved for special case by using Mathcad 2007 software and represented graphically by using Microsoft excel 2007.

基于POD-αATS的油浸变压器瞬态温升降阶自适应变步长计算方法

针对油浸式电力变压器瞬态温升计算效率过低的问题,该文提出本征正交分解-αATS(proper orthogonal decomposition-adaptive time stepping based onαfactor,POD-αATS)降阶自适应变步长瞬态计算方法。首先,推导变压器绕组瞬态温升计算的有限元离散方程;其次,采用POD降阶算法改善传统瞬态计算中存在的条件数过大及方程阶数过高的问题;同时对于瞬态计算中的时间步长选择问题,提出适用于非线性问题的αATS变步长策略;然后,为验证方法的有效性,基于110 kV油浸式电力变压器绕组的基本结构建立二维八分区数值计算模型,同时将计算结果与基于110 kV绕组的温升实验结果进行对比。数值计算及实验结果表明,所提算法与全阶定步长算法在流场和温度场中的精度几乎相同,且流场计算效率提升约45倍,温度场计算效率提升约38倍,计算速度得到显著提高。这一点在温升实验中同样得到验证,说明该文所提算法的准确性、高效性及一定的工程实用性。

稳态及瞬态中子输运模型的JFNK求解方法研究

三维全堆芯pin-by-pin中子输运模型的高效加速方法是核反应堆高精度计算的重点和难点。本文有效融合课题组开发的并行多维离散纵坐标(S_(N))中子输运程序comeSn和Jacobian-Free Newton Krylov(JFNK)通用求解框架comeJFNK的高效并行特性、鲁棒性和强收敛性,开发了一套三维稳态及瞬态中子输运模型的JFNK并行求解程序comeSn_JFNK。为了提高计算效率,选择中子标通量密度(而非中子角通量密度)作为JFNK全局求解变量,并利用基于空间区域并行的KBA输运扫描方法和物理预处理方法,分别构建了稳态及瞬态模型的JFNK统一残差计算模型。计算结果表明,comeSn_JFNK相比于comeSn,计算效率具有显著优势,对于三维pin-by-pin稳态KAIST-3A算例,加速比为10倍以上;对于栅元均匀化的二维七群瞬态C5G7-TD2系列基准算例,加速比约为30倍。

针对样本类不平衡的深度残差网络电力系统暂态稳定评估方法

系统的量测数据可能受到噪声以及样本类分布不平衡问题的影响,导致基于数据驱动的暂态稳定评估模型性能下降。提出一种针对样本类不平衡的的深度残差网络电力系统暂态稳定评估方法。首先,利用改进过采样技术为滤除噪声的少数类样本构造所需的新样本,改善样本类不平衡问题,并减少噪声的影响;然后,基于深度残差网络构建电力系统暂态稳定评估模型,解决梯度消失导致的模型性能退化问题,提高模型的鲁棒性和准确性;最后,在新英格兰10机39节点和47机140节点系统上的仿真结果表明,所提方法能减小噪声干扰、降低不平衡数据集所带来的影响和减少计算复杂度。

基于最优路径跳变的网络移动目标防御技术

移动目标防御(MTD,moving target defense)是一种改变网络攻防对抗格局的技术,路径跳变则是该领域的研究热点之一。针对现有路径跳变技术,由于路径选取存在盲目性,跳变实施缺乏约束性,难以在保证网络性能的同时最大化防御收益等问题,提出基于最优路径跳变的网络移动目标防御技术。通过可满足性模理论形式化规约路径跳变所需满足的约束,以防止路径跳变引起的瞬态问题;通过基于安全容量矩阵的最优路径跳变生成方法选取最优跳变路径和跳变周期组合,以实现防御收益的最大化。理论与实验分析了该技术抵御被动监听攻击的成本和收益,证明其在保证网络性能的同时实现了跳变收益的最大化。

基于瞬变流反问题分析的输水管道泄漏检测方法

对基于瞬变流反问题分析(ITA)的管道泄漏检测方法进行了研究。将管道泄漏检测问题转化为优化问题,建立以泄漏位置和泄漏面积为决策变量、以实测压力和计算压力的平方差之和最小为目标函数的优化模型,采用遗传算法(GA)求解,在适应度值的计算过程中,对瞬变流正问题的计算采用一维Vardy-Brown模型。通过模型试验,验证该泄漏检测方法的可行性,并对其主要影响因素进行分析。结果表明,检测结果的准确度受水锤波传播速度的影响较大。

瞬变电磁法正反演问题研究进展

对瞬变电磁法的方法发展概况和仪器研制状况做出了综述性评价.对瞬变电磁法正反演问题的研究成果进行了系统总结.目前的数值模拟正演方法主要有一维滤波系数法,三维积分方程法,二维,三维有限差分法,2.5维有限元法等,主要的反演方法有:一维浮动薄板解释法,人机对话自动反演法,烟圈理论解释法,神经网络反演法,成像类反演等,论述了瞬变电磁法各种计算方法的特点.瞬变电磁法的正反演发展趋势主要是研究三维正反演的计算方法和目标体成像系统.

有压瞬变流限压控制反问题的最优控制理论解法

以简单管系统为研究对象,建立了有压瞬变流限压控制反问题的最优控制数学模型.采用δ-摄动法并经过空间离散,将由拟线性偏微分方程控制的有压瞬变流系统转化为时间连续线性系统,从而使有压瞬变流限压控制反问题能应用时间连续系统最优控制理论来求解.