耦合时间精度对模拟飞行器自由运动特性的影响

将亚迭代技术引入流体动力学和刚体动力学方程的耦合求解,获得细长三角翼极限环运动的规律.探讨耦合时间精度对飞行器非定常运动特性的影响,细长三角冀的大迎角自由滚运动最终形成极限环振荡的周期性自维持运动,不同攻角自由滚振幅阶跃式的变化特点较好地吻合了自由滚试验的规律.对于多系统耦合问题,亚迭代耦合求解(耦合时间精度为二阶)对物理时间步长的依赖性不明显;而存在一阶时间滞后的解耦推进方法的数值结果强烈地依赖于物理时间步长选取,稍大的时间步长将导致非物理的数值结果.     

随机选取法和多波近似在一维浅水方程大时间步长格式中的应用

利用黎曼精确解和行波法相结合,在一维浅水方程中实现大时间步长(Large Time Step,LTS)格式,并采用多波近似解决稀疏波断裂的问题,采用随机选取法(Random Choice Method,RCM)解决非线性方程使用LTS格式出现的震荡问题.一系列数值试验发现,通过多波近似和随机选取法对大时间步长格式的改进,提高了计算效率,减小了震荡,取得了很好的计算效果.     

定时间步长变坐标步长差分求解单相Stefan问题

对单相Stefan问题提出了一种定时间步长、变坐标步长的差分求解方法.在固定时间步长内,以计算得到的移动界面位置作为网格节点的坐标,前后界面位置之差为空间步长,逐步地自动形成网格的划分,计算这些节点处的温度,从而获得下一时刻的移动界面的位置.     

混沌系统中可预报性的研究

针对简化的气候模式、Rossler吸引子和超混沌系统,进一步阐明了不确定原理,在数值求解时由于计算机固有精度而引起的舍入误差,造成对解的不确定性,存在最优步长和最大有效计算时间.运用自忆性原理,导出了各混沌系统的自忆性方程,取最优步长时,其预报性能有明显的改善 关键词： 自忆性 不确定原理 最优步长     

磁场与流场耦合问题中Newton-Laphson方法的收敛性分析(英文)

针对磁场与流场耦合问题的数值分析,提出并证明求解离散化过程所得到的非线性方程组牛顿-拉夫逊方法的-类局部收敛性条件.这-条件不仅给出了时间步长与空间步长、拟压缩因子等之间的关系,而且为数值求解磁场与流场耦合问题的牛顿-拉夫逊方法收敛性提供了理论依据.数值算例表明时间步长的实际取值要比理论值偏大.     

二维三温热传导方程求解中的非线性迭代初值选取

由于二维三温热传导方程具有很强的非线性特性,因此采用全隐格式对该方程离散后,所得非线性代数方程组的求解将变得非常困难.针对二维三温热传导方程离散所得非线性代数方程组的迭代求解,提出了一种有效的选取初值的方法.对两种不同性质的介质进行数值实验,结果表明,所设计的初值选取方法不仅大大提高了计算效率,而且能够降低非线性解法器对时间步长的影响.     

二维三温流体力学计算中时间步长的自动控制

研究了二维三温流体力学计算中时间步长的控制问题,提出了控制时间步长的多种约束条件:既考虑了显式流体力学离散方程的CFL(Courant-Friedrichs-Lewy)条件,又考虑了隐式三温能量方程温度的相对变化,还考虑了Lagrange网格密度(或体积)的相对变化以及三温能量方程的迭代次数等.在计算过程中这些约束条件可以随时自动地改变时间步长,以最经济和合理的时间步长完成计算.最后给出了数值实验结果.     

LJ团簇和H2O团簇的局域优化计算

将传统分子动力学方法中时间积分步长定义成粒子的最大加速度、最大速度和变化的最大允许空间步长的函数,并给出了空间步长的确定方法.作为对这个算法有效性的检验,计算了较小Lennard-Jones团簇和H₂O团簇的稳定结构,发现了新的(H₂O)₁₃的最小能结构.     

混沌系统的时间延迟同步误差分析

对Pecora和Carroll的混沌自同步方案的延迟同步误差进行了研究.在计算机上对Lorenz混沌系统伪装的延迟同步误差进行了模拟:给定系统参数,对应不同延迟时间,得出了均方误差与采样步长的关系曲线;给定系统参数和延迟时间,对应不同采样步长,得到了混沌时间序列的误差曲线;给定采样步长,对应不同的系统参数,获得了混沌时间序列的尺度效应和均方误差与采样步长的关系曲线.提出了减小延迟同步误差的一些方法,得到一些对混沌同步和混沌控制应用有意义的结果. 关键词： 混沌同步 时间同步 误差分析     

守恒律方程组的大时间步长叠波格式

大时间步长叠波格式最初思想为LeVeque提出的大时间步长Godunov格式,通过叠加间断分解发出的强波来构造数值格式.原方法只给出了间断强波的穿越叠加方法,文章对其进行了完善,并推广到多维.针对膨胀波提出了一种网格单元分解法可以自动满足熵条件,避免出现非物理解.给出了格式的具体计算公式,并用单个守恒律方程、一维/多维Euler方程组进行了数值计算.计算结果表明,新格式除了可以采用大时间步长的优点外,在一定范围内随CFL数增加其耗散反而更低,因而对激波接触间断膨胀波的分辨率更高.     

ALE计算中基于声速分布的网格优化技术

基于声速分布,提出一种拉氏流体力学计算中大变形网格优化的数值技术.该方法不但可以优化网格的几何形状且可以提高拉氏流体计算的时间步长.介绍基于声速分布的网格松弛泛函、修正梯度流方程的推导、离散和求解方法,启动/终止网格优化过程的条件,及基于这种网格优化方法的ALE算法.给出Rayleigh-Taylor不稳定性问题等数值算例,用以证明该方法的有效性.     

Unconditionally convergent nonlinear solver for hyperbolic conservation laws with S-shaped flux functions

This paper addresses the convergence properties of implicit numerical solution algorithms for nonlinear hyperbolic transport problems. It is shown that the Newton–Raphson (NR) method converges for any time step size, if the flux function is convex, concave, or linear, which is, in general, the case for CFD problems. In some problems, e.g., multiphase flow in porous media, the nonlinear flux function is S-shaped (not uniformly convex or concave); as a result, a standard NR iteration can diverge for large time steps, even if an implicit discretization scheme is used to solve the nonlinear system of equations. In practice, when such convergence difficulties are encountered, the current time step is cut, previous iterations are discarded, a smaller time step size is tried, and the NR process is repeated. The criteria for time step cutting and selection are usually based on heuristics that limit the allowable change in the solution over a time step and/or NR iteration. Here, we propose a simple modification to the NR iteration scheme for conservation laws with S-shaped flux functions that converges for any time step size. The new scheme allows one to choose the time step size based on accuracy consideration only without worrying about the convergence behavior of the nonlinear solver. The proposed method can be implemented in an existing simulator, e.g., for CO₂ sequestration or reservoir flow modeling, quite easily. The numerical analysis is confirmed with simulation studies using various test cases of nonlinear multiphase transport in porous media. The analysis and numerical experiments demonstrate that the modified scheme allows for the use of arbitrarily large time steps for this class of problems.     

水珠滴落的最小二乘粒子有限元方法模拟

提出了一种最小二乘粒子有限元方法,用其模拟了二维水珠滴落水面并飞溅散开的过程.该法基于拉格朗日描述,在每个时间步上使用扩展的Delaunay划分更新计算网格,并应用α形方法识别自由面形状;用最小二乘有限元方法离散流体运动的Navier-Stokes方程,并推导了一种自适应时间步长方案以提高计算效率和鲁棒性;引入网格拉伸技术修正减小流体质量误差.对水滴飞溅进行仿真,得到了与商用软件Flow-3d比较符合的结果,且具有更清晰锐利的自由面. 关键词： 滴落 网格划分 α形')" href="#">α形 最小二乘有限元     

基于LU-SGS的非结构弹簧网格迭代算法

针对运动间断拟合中需频繁更新网格点位置的特点,提出一种基于LU-SGS(lower-upper symmetricGauss-Seidel)迭代方法的非结构弹簧网格运动算法.根据弹簧网格原理构建与网格拓扑关系相对应的稀疏系数矩阵,将LU-SGS思想成功引入动网格迭代算法,并辅以合理的网格运动管理策略,实现动网格的快速迭代.研究表明,在非结构网格下,LU-SGS算法可以满足运动间断拟合的需求,在流场隐式时间推进时,仍能保证获得稳定解;与传统的SOR方法相比,计算时耗减少20%以上.     

复杂高阶对象的预测PID控制

针对复杂高阶对象提出了一种基于数值最优模型降阶方法,并基于这种降阶模型设计了预测PID控制器,将此控制器应用于原始模型能够得到很好地控制效果。数值最优模型降阶算法使高阶对象能近似为一阶加时滞对象或二阶加时滞对象,通过模型阶跃响应和Bode图对比,降阶模型曲线很好地逼近原始模型曲线。预测PID对大时滞对象有着很好地控制效果,模型降阶使得预测PID很好地控制复杂高阶对象,且其结构简单,可调参数少的特点。     

Time and frequency response of structures with frequency dependent,non-proportional linear damping

A method to compute the non-stationary time and frequency response of structures with a frequency-dependent non-proportional linear damping, called the resonance modes method, is presented in this paper. It consists of two main steps. The first step aims at spotting the structure resonance modes, which are the solutions of the matrix nonlinear eigenvalue problem obtained using the finite element method in the complex plane. This step requires a complex eigensolver and an iterative scheme, a perturbation technique or a combination of both. The second step uses the computed resonance modes and an analytical expression of the inverse Laplace transform to deduce the time or frequency response of structures to general excitations. The response of an aluminum plate damped with an elastomer treatment to a point-force excitation, computed with the classical modal approach, the direct solution and the presented method shows its precision and efficiency. An acoustic power computation finally validates the implementation of a fast variant, based on the perturbation technique, for vibroacoustic applications.     

An unconditionally stable fully conservative semi-Lagrangian method

Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had.     

Combined digital filtering of harmonic content of phase-shift keyed signals in the problem of estimation of the time delay

We propose a two-step method for digital filtering of phase-shift keyed signals filtering in the problem of determination of the time delay during the multichannel propagation. The first step is realized as an information-optimal linear filter with complex coefficients, while the second step, as a quadratic filter based on the minimum-variance criterion. The e.ciency of the proposed method is demonstrated for short PSK signals with various carrier frequencies against the background of additive and multiplicative noise. The developed algorithm can easily be implemented in real time on the basis of a digital signal processor. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 3, pp. 255–264, March 2007.     

注蒸汽井筒沿程热物性参数及热损失新算法

基于干度的定义,对传统蒸汽干度方程进行改进,计算井筒热损失速率时,既按深度分段又按注汽时间分段,并采用Hasan等提出的两相流漂移流动模型计算井筒压力降.结果表明:改进后的模型用新算法的计算结果与现场实测值吻合很好,比传统的Beggs-Brill算法更准确.另外,在相同井深处,随着注汽时间的延长,蒸汽压力、温度和干度几乎不变,但是热损失速率逐渐降低.新算法为准确计算井筒热损失提供了参考.     

非定常输运问题适应于消息传递并行编程环境的香农熵计算方法

在多计算步的非定常输运问题的蒙特卡罗模拟中,为自动调整每一步的样本数以获得较高的计算效率,可以有多种准则.一种可选的方法是在每一步每隔若干样本监测一次系统中未死亡粒子属性分布对应的香农熵的收敛情况以决定何时停止追加样本,此种方法需要在每一步频繁计算香农熵值.由于在MPI消息传递并行编程环境下香农熵的经典计算方法必须广播大量的数据,导致每一步的计算时间随香农熵计算频率的提高而快速增大,这显然是不能满足实际需求的.本文提出了一种适应于消息传递并行编程环境的香农熵计算新方法,该方法计算得到的香农熵值并不等价于经典方法,但二者之间的差别会随着样本数的增加而趋于零.新方法的最大优势是高频计算香农熵值的时间代价大为降低,为最终实现基于香农熵收敛判断的每步样本数的自动调整奠定了必要的基础.