混凝土板裂纹扩展的态型近场动力学模拟

构建考虑混凝土拉压异性和宏观断裂特征的混凝土类材料非局部态型近场动力学本构模型,并通过引入动态松弛、系统失衡判断和力边界等效等算法,构建适于分析混凝土类材料和结构变形破坏过程的态型近场动力学数值模拟体系.通过分组模拟和定量计算,分析算法的收敛性、计算精度和效率等问题;在此基础上开展含不同角度中心裂纹混凝土板的破坏模拟.     

数值求解优化问题在活动轮廓模型上的应用

针对活动轮廓模型图像分割过程中迭代次数多,分割速度慢的问题,提出一种高阶的数值求解方法。分析活动轮廓模型中基于全局信息的CV模型,以及基于局部信息的LBF模型,LIF模型。使用二阶、三阶Runge-Kutta方法,原始Euler方法对模型进行数值求解实验对比分析。并对LBF模型中平滑项系数,时间步长的选取进行讨论。通过对非同质图像、同质图像的实验结果分析表明,所采用的数值方法能够有效地提高数值收敛精度、减少迭代次数、计算效率高。对不同系数和时间步长,数值方法也能表现出较好的稳定性。     

基于时间分解求解时间依赖问题的并行算法研究

基于Lions等建立的Parareal模型,提出了改进的时间分解并行算法,并给出收敛性证明．采用主从模式构造了通用的MPI算法流程,通过分析算法的并行加速比给出了最佳的粗细网格步长之比．在集群系统下分别对热传导方程和对流扩散方程进行并行计算,证明了算法无论对线性还是非线性的问题均具有良好的适应性和扩展性．数值模拟结果表明:时间分解并行算法仅需极少的迭代次数即能取得很高的计算精度,且具有较好的并行加速比和并行效率．     

非线性San Venant方程组数值稳定性分析

分析了非线性San Venant方程组的解的特性,并在统一考虑阻力项的影响的基础上,分析了用Pressmainn格式求解非线性San Venant方程组的数值稳定性和收敛性.研究了φ和θ不同取值情况下,差分方程数值解的收敛情况与相对时间步长（Δt）/（Δx）和相对波长L/（Δx）的关系.指出数值解总是存在衰减和弥散现象,在实际模拟过程中,应合理选择φ和θ值,以兼顾数值衰减幅度和模拟速度.     

基于结合扩展精度技术的基本解方法的非线性功能梯度材料热传导问题求解

采用基本解方法结合扩展精度技术和Kirchhoff变换求解功能梯度材料的二维热传导问题.在求解瞬态热传导问题时运用Laplace变换处理时间变量,将时域问题转化为频域问题求解;采用基本解方法计算得到高精度的频域数值解,再分别采用Stehfest和Talbot这2种数值Laplace逆变换恢复原瞬态热传导问题的计算结果.通过3个非线性功能梯度材料的稳态和瞬态热传导基准算例,分析结合扩展精度技术的基本解方法的计算精度与扩展精度位数、边界布点数和虚拟边界参数三者之间的关系.比较Stehfest和Talbot这2种数值Laplace逆变换算法的优劣.采用结合扩展精度技术的基本解方法数值研究热传导系数随位置剧烈变化的功能梯度材料热传导行为.数值结果表明该方法具有求解精度高、适用性好等特点,能高效模拟非线性功能梯度材料的二维稳态与瞬态热传导行为.     

一个松弛非单调线搜索法

对于无约束优化问题,我们用松弛技术改进了一般非单调线搜索准则,建立了相应的求解算法,并证明了算法的整体收敛性.部分数值实验结果表明,这个松弛非单调算法有效.     

高精度自适应hp-FEM在电法测井数值模拟中的应用*

介绍了电法测井数值模拟的建模方法并提出一种新型的自适应高阶有限元方法(hp-FEM)用于求解各向异性地层中的电场问题。电场数值模型在相同的误差精度下,从计算时间和计算自由度的角度对h-FEM、p-FEM和hp-FEM进行了计算比较。数值结果表明,在各向同性和各向异性模式下,该自适应hp-FEM的性能(指数速率收敛)明显优于h-FEM和p-FEM。探讨了算法的收敛性,提出的hp-FEM可以改进现有的正演模拟方法,提高分析的正确性和工作效率,对于减小研究周期有重要的应用价值。     

连续时间 Hopfield网络模型数值实现分析

讨论使用Euler方法和梯形方法在数值求解连续时间的Hopfield网络模型时,离散时间步长的选择和迭代停止条件问题.利用凸函数的定义研究了能量函数下降的条件,根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件.分析连续时间Hopfield网络模型的收敛性证明,提出了一个广义的连续时间Hopfield网络模型.对于常用的Euler方法和梯形方法数值求数值实现连续时间Hopfield网络,讨论了离散时间步长的选择.由于梯形方法为隐式方法,分析了它的迭代求算法的停止条件.根据连续时间Hopfield网络的特点,提出改进的迭代算法,并对其进行了分析.数值实验的结果表明,较大的离散时间步长不仅加速了数值实现,而且有利于提高优化性能.     

近组分模型中主变量的选取问题研究

近组分模型有两种主变量选取方法,分别是选取自然变量作为主变量的方法和选取总属性变量作为主变量的方法。比较了这两种方法在数学模型和数值求解流程方面的差异,分析了在计算精度和计算效率方面产生的异同。二氧化碳驱概念模型的模拟结果表明,油气两相都存在时,虽然两种方法在一维驱替和二维驱替中的计算精度是一样的,但是选取自然变量作为主变量的方法不仅允许的最大时间步长更大,而且在相同时间步下运行速度更快。在相同时间步下,选取自然变量作为主变量的方法在二维驱替中提速效果有所降低。     

自适应策略下Heavy-Ball型动量法的最优个体收敛速率

同时使用自适应步长和动量两种优化技巧的AMSGrad在收敛性分析方面存在比自适应步长算法增加一个对数因子的问题.为了解决该问题,文中在非光滑凸情形下,巧妙选取动量和步长参数,证明自适应策略下Heavy-Ball型动量法具有最优的个体收敛速率,说明自适应策略下Heavy-Ball型动量法兼具动量的加速特性和自适应步长对超参数的低依赖性.求解l₁范数约束下的Hinge损失问题,验证理论分析的正确性.     

Dynamic simulation of natural circulation steam generators with the use of finite-volume-algorithms – A comparison of four algorithms

The paper reports the results of a comparison of the four finite-volume-algorithms SIMPLE, SIMPLEC, SIMPLER and PISO. The analysis has been done to explore and compare the suitability of the algorithms for the dynamic simulation of natural circulation steam generators based on a so called tube-header-model. The suitability of the algorithms was tested with the results of two simulation examples – a heat recovery steam generator with a horizontal tube bank (Fig. 3a) and a two-drum steam generator with a vertical tube bank (Fig. 3b). The calculations are done at low system pressure and under hot start-up conditions for the boilers. The results of the computations demonstrate that the SIMPLER algorithm should be preferred for dynamic simulations which are based on the tube-header-model. The algorithm shows a high stability, an extended field of variability of the under-relaxation factors as well as small required under-relaxation. The strong dependence of the calculation time on the number of control volumes is the only unfavourable characteristic of the SIMPLER algorithm.     

Comparison of finite-volume numerical methods with staggered and colocated grids

The paper presents a detailed comparison of two finite-volume solution methods for two-dimensional incompressible fluid flows, one with staggered and the other with colocated numerical grids. The staggered method is well-known and well-established, and it is used here as a standard against which the relatively new colocated approach is compared. Three test cases were considered, employing orthogonal rectilinear grids: lid driven cavity flow, backward facing step flow and flow through a pipe with sudden contraction. The results of the computations demonstrate that the convergence rate, dependency on under-relaxation parameters, computational effort and accuracy are almost identical for both solution methods. The colocated method converges faster in some cases, and has advantages when extensions such as multigrid techniques and non-orthogonal grids are considered.     

Higher-Order Gauss–Lobatto Integration for Non-Linear Hyperbolic Equations

Least-squares spectral elements are capable of solving non-linear hyperbolic equations, in which discontinuities develop in finite time. In recent publications [De Maerschalck, B., 2003, http://www.aero.lr.tudelft.nl/∼bart; De Maerschalck, B., and Gerritsma, M. I., 2003, AIAA; De Maerschalck, B., and Gerritsma, M. I., 2005, Num. Algorithms, 38(1–3); 173–196], it was noted that the ability to obtain the correct solution depends on the type of linearization, Picard’s method or Newton linearization. In addition, severe under-relaxation was necessary to reach a converged solution. In this paper the use of higher-order Gauss–Lobatto integration will be addressed. When a sufficiently fine GL-grid is used to approximate the integrals involved, the discrepancies between the various linearization methods are considerably reduced and under-relaxation is no longer necessary     

城市轨道交通客流需求分析模型及计算机仿真

针对传统“四阶段法”交通需求分析集聚特征显著、系统环境适应性差等问题以及城市交通系统很难进行实体仿真的缺陷,提出了一种基于城市综合公交统筹和TransCAD仿真的城市轨道交通客流分析模型。该模型基于“四阶段法”基本步骤,在第一阶段中,考虑了不同人口类别的出行强度和空间分布特征,给出了一种基于人口分类和出行目的的发生吸引模型;在交通分布中,引入K-因子和综合行程费用修正重力分布模型;在交通方式划分和分配中,结合合理系统结构边界和出行时间价值,对城市轨道交通客流分配进行精细配流。实验表明：通过对城市人口进行分类,考虑城市交通系统结构和各交通方式的出行广义费用可大大提高客流分析的精度和鲁棒性。     

颗粒离散元法中阻尼系数、刚度系数和 时步的选取方法

为解决颗粒离散元法(Distinct Element Method,DEM)中阻尼系数等参数选取困难的问题,对岩体工程中的DEM与颗粒DEM进行区分,着重讨论颗粒DEM中阻尼系数、刚度系数和时步等参数的选取方法.这些计算参数的合理选取对保证模拟的真实性具有重要意义.     

作战模拟方法的水面舰艇反导作战效能评估

在对抗仿真的基础上研究了水面舰艇对来袭导弹的作战效能.在分析水面舰艇反导作战过程的基础上,结合水面舰艇反导的特点,提出了基于攻防对抗仿真的反导作战效能评估一般可采用的四个环节.并采用自顶向下的分析方法,建立了水面舰艇反导作战效能评估的指标体系.还对反导作战效能评估方法和仿真模型的建立、仿真平台设计等进行了研究.最后以两艘水面舰艇对抗为例评估了水面舰艇的反导作战效能.结果表明该方法合理可行.     

过程仿真培训成绩的自动评定及其实现(I)——仿真培训成绩的评分方法

根据过程仿真培训的特点,提出了一套综合的过程仿真培训系统自动评分方法。该方法将操作工培训成绩分为：操作质量分、操作步骤分、事故处理分和教师印象分;并给出了相应成绩的计算方法。实际表明,该评分方法合理,能合理地反映操作工操作的实际情况     

混凝土浇筑过程中温度场和应力场仿真分析

在混凝土浇筑过程中,其弹性模量随时间变化.这一独特现象给混凝土结构的残余热应力应变的理论求解带来极大困难.即使使用有限元法对混凝土进行热力耦合分析,也必须解决材料弹性模量徐变的问题.采用分时间段方法对弹性模量的时变特性进行等效近似处理,在一个时间段内近似认为弹性模量为一个稳定值,并在各个时间段对混凝土进行热力耦合计算.每一时间段仿真分析时读取上个时间段的结果作为初始条件.最后提取整个龄期各测试点处的仿真温度数据,并与实测温度数据进行对比,验证温度场仿真方法的正确性.     

Navier-Stokes calculations with a coupled strongly implicit method—I: Finite-difference solutions

Stone's unconditionally stable, strongly implicit numerical method is extended to the 2 x 2 coupled vorticity-stream function form of the Navier-Stokes equations. The solution algorithm allows for complete coupling of the boundary conditions. Solution for arbitrary large time steps, and for cell Reynolds numbers much greater than two have been obtained. The method converges quite rapidly without adding artificial viscosity or the necessity for under-relaxation. This technique is used here to solve for a variety of internal and external flow problems. Moderate to large Reynolds numbers are considered for both separated and unseparated flows. The procedure is extended to higher-order splines in Part 2 of this study.     

On the simulation of nonlinear bidimensional spiking neuron models

Bidimensional spiking models are garnering a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons and are used particularly for large network simulations. These models describe the dynamics of the membrane potential by a nonlinear differential equation that blows up in finite time, coupled to a second equation for adaptation. Spikes are emitted when the membrane potential blows up or reaches a cutoff θ. The precise simulation of the spike times and of the adaptation variable is critical, for it governs the spike pattern produced and is hard to compute accurately because of the exploding nature of the system at the spike times. We thoroughly study the precision of fixed time-step integration schemes for this type of model and demonstrate that these methods produce systematic errors that are unbounded, as the cutoff value is increased, in the evaluation of the two crucial quantities: the spike time and the value of the adaptation variable at this time. Precise evaluation of these quantities therefore involves very small time steps and long simulation times. In order to achieve a fixed absolute precision in a reasonable computational time, we propose here a new algorithm to simulate these systems based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane, and compare this algorithm with fixed time-step Euler scheme and other more accurate simulation algorithms.