A Monte Carlo Algorithm for Immiscible Two-Phase Flow in Porous Media

We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that tracks the motion of the fluid interfaces. The Monte Carlo algorithm is based on the configuration probability, where a configuration is defined by the positions of all fluid interfaces. We show that the configuration probability is proportional to the inverse of the flow rate. Using a two-dimensional network, advancing the interfaces using time integration, the computational time scales as the linear system size to the fourth power, whereas the Monte Carlo computational time scales as the linear size to the second power. We discuss the strengths and the weaknesses of the algorithm.     

卫星在轨道平面内的可达范围研究

对在初始轨道上施加平面内幅值固定的脉冲后卫星的可达范围进行了研究. 考虑脉冲幅值较小、生成轨道均为椭圆的情况. 根据平面曲线族包络线的定义,针对不同任务的需求,考虑脉冲施加点固定而方向任意、脉冲施加点任意而方向固定、脉冲施加点和方向均任意的3种情况,分别给出了确定可达范围边界的方法. 数值仿真表明: 所提出的方法能够确切描述卫星可达范围的边界,所得结论对初始椭圆轨道的偏心率没有限制,可以用于单颗卫星机动范围的评估和不同卫星间安全距离的设计.      

基于减基概念的凸集结构可靠性分析方法

针对椭球凸集参数域结构的可靠性分析问题,提出了一种基于减基概念的快速求解方法。首先,将椭球参数域进行坐标正交变换,获得标准的椭球域及其相应的矩形域,在矩形域采样且通过坐标逆向变换获得原椭球参数域的样本参数点集,并以此构建结构的减基空间及其相应的减基算法;随后,在标准椭球域产生均匀的等概率抽样点,并通过坐标逆向变换和相应的减基算法进行蒙特卡洛减基模拟来分析结构的可靠度及其可靠域。由于是在低维的逼近空间中进行椭球参数域结构的位移向量解分析,故而较之有限元法能够获得较高的计算效率。算例测试验证了本文方法的有效性。     

SPACECRAFT EVASION STRATEGY USING ACTIVE MANEUVERS BASED ON MANEUVERING-TARGET ACCELERATION ESTIMATION 1)

随着空间操控技术的发展, 航天器在轨安全问题日益受到重视.具有主动机动能力的航天器对目标航天器的自主接近严重威胁航天器的在轨安全.航天器近距离追逃博弈时,相对位置、速度、加速度等状态获取是追逃双方博弈策略形成的基础.本文在追逃双方信息获取不完全的情况下,提出了基于机动目标滤波估计与最大化视线偏转率的主动规避逃脱策略.追逃双方航天器基于当前统计模型滤波算法获得对方的相对位置、速度、加速度等导航信息.追踪航天器采用比例导引律自主接近逃逸航天器.逃逸航天器计算相对于追踪航天器的视线方向及视线偏转率,采用基于最大化视线偏转率的主动规避策略进行逃脱.对不同规避策略及不同工况进行仿真分析, 结果表明:逃逸航天器的机动能力达到追踪航天器的60%以上时,所提出的规避策略可有效规避追踪航天器的自主接近;规避策略对观测设备的测量精度和工作频率不敏感;规避效果与规避策略的响应时间有关, 逃逸航天器收到预警信息越早, 规避效果越好.     

基于机动目标滤波估计的航天器主动规避策略

随着空间操控技术的发展,航天器在轨安全问题日益受到重视.具有主动机动能力的航天器对目标航天器的自主接近严重威胁航天器的在轨安全.航天器近距离追逃博弈时,相对位置、速度、加速度等状态获取是追逃双方博弈策略形成的基础.本文在追逃双方信息获取不完全的情况下,提出了基于机动目标滤波估计与最大化视线偏转率的主动规避逃脱策略.追逃双方航天器基于当前统计模型滤波算法获得对方的相对位置、速度、加速度等导航信息.追踪航天器采用比例导引律自主接近逃逸航天器.逃逸航天器计算相对于追踪航天器的视线方向及视线偏转率,采用基于最大化视线偏转率的主动规避策略进行逃脱.对不同规避策略及不同工况进行仿真分析,结果表明:逃逸航天器的机动能力达到追踪航天器的60%以上时,所提出的规避策略可有效规避追踪航天器的自主接近;规避策略对观测设备的测量精度和工作频率不敏感;规避效果与规避策略的响应时间有关,逃逸航天器收到预警信息越早,规避效果越好.     

Modeling wall effects in a micro-scale shock tube using hybrid MD–DSMC algorithm

Wall effects in a micro-scale shock tube are investigated using the Direct Simulation Monte Carlo method as well as a hybrid Molecular Dynamics–Direct Simulation Monte Carlo algorithm. In the Direct Simulation Monte Carlo simulations, the Cercignani–Lampis–Lord model of gas–surface interactions is employed to incorporate the wall effects, and it is shown that the shock attenuation is significantly affected by the choice of the values of tangential momentum accommodation coefficient. A loosely coupled Molecular Dynamics–Direct Simulation Monte Carlo approach is then employed to demonstrate incomplete accommodation in micro-scale shock tube flows. This approach uses fixed values of the accommodation coefficients in the gas–surface interaction model, with their values determined from a separate dynamically similar Molecular Dynamics simulation. Finally, a completely coupled Molecular Dynamics–Direct Simulation Monte Carlo algorithm is used, wherein the bulk of the flow is modeled using Direct Simulation Monte Carlo, while the interaction of gas molecules with the shock tube walls is modeled using Molecular Dynamics. The two regions are separate and coupled both ways using buffer zones and a bootstrap coupling algorithm that accounts for the mismatch of the number of molecules in both regions. It is shown that the hybrid method captures the effect of local properties that cannot be captured using a single value of accommodation coefficient for the entire domain.     

非线性函数的混沌优化方法比较研究

已有的混沌优化方法几乎都是利用Logistic映射作为混沌序列发生器，而Logistic映射产生的混沌序列的概率密度函数服从两头多、中间少的切比雪夫型分布，不利于搜索的效率和能力。为此，首先根据Logistie映射混沌轨道点密度函数的特点，建立改进的混沌-BFGS混合优化算法。之后，考虑到Kent映射混沌轨道点密度为均匀分布，建立了基于Kent映射的混沌-BFGS混合优化算法。然后对五种混合优化方法——不加改进的和改进的基于Logistic映射的混沌-BFGS法，基于Kent映射的混沌-BFGS法，Monte Carlo试验-BFGS法，网格-BFGS法进行了研究，分别对3个低维和2个高维非线性复杂测试函数进行优化计算，对它们的全局优化计算效率和寻优能力做了比较，并探讨了混合优化方法全局优化性能差异的原因。结果表明，混沌优化方法是与Monte Carlo方法类似的一种随机性试验优化方法。而且，这类优化方法的计算性能至少与以下因素有关：混沌／随机序列的统计性质，优化问题全局最优点位置。     

最优轨迹规划方法及其平动点航天器编队均衡耗能重构应用

由于均衡耗能航天器编队能够提高整体航天器编队服役时间,针对平动点航天器编队重构的均衡耗能最优轨迹规划问题,提出一种以状态、协态和控制三类变量插值为核心的求解非线性最优控制问题的新方法。基于连续时间表达的非线性最优控制问题通过变分原理转化为非线性方程组的求解,并进一步推导非线性方程组显示格式的Jacobi矩阵提高非线性方程组的计算效率。本文方法既满足最优控制理论的一阶必要条件又具有较大的收敛域;同时,不需要对协态初值准确猜测,避免了大规模非线性规划问题的求解。通过对中心航天器位置固定和无中心航天器两种情况的数值模拟,结果表明,本文方法对航天器编队重构轨迹规划问题能够达到均衡耗能的目标,具有一定的应用价值。     

Random response of integrable Duhem hysteretic systems under non-white excitation

In this study, an integrable Duhem hysteresis model is derived from the mathematical Duhem operator. This model can represent a wide category of hysteretic systems. The stochastic averaging method of energy envelope is then adapted for response analysis of the integrable Duhem hysteretic system subjected to non-white random excitation. Using the integrability of the proposed model, potential energy and dissipated energy of the hysteretic system can be represented in an integration form so that the hysteretic restoring force is separable into conservative and dissipative parts. Based on the equivalence of dissipated energy, a non-hysteretic non-linear system is obtained to substitute the original system, and the averaged Itô stochastic differential equation of total energy is derived with the drift and diffusion coefficients being expressed as Fourier series expansions in space averaging. The stationary probability density of total energy and response statistics are obtained by solving the Fokker–Planck–Kolmogorov (FPK) equation associated with the Itô equation. Verification is given by comparing the computational results with Monte Carlo simulations.     

FV/MC混合算法求解轴对称钝体后湍流流场

介绍一种有限容积／Monte Carlo结合求解湍流流场的相容的混合算法．有限容积法求解Reynolds平均的动量方程和能量方程，Monte Carlo方法求解模化的脉动速度—频率—标量联合的PDF方程．将该算法发展到无结构网格，探讨了在无结构网格中实现两种方法的耦合，包括颗粒定位，颗粒场和平均场之间数据交换等问题．并以二维轴对称钝体后湍流流场作为算例，比较了计算结果与实验结果．     

Variance‐reduced Monte Carlo solutions of the Boltzmann equation for low‐speed gas flows: A discontinuous Galerkin formulation

We present and discuss an efficient, high‐order numerical solution method for solving the Boltzmann equation for low‐speed dilute gas flows. The method's major ingredient is a new Monte Carlo technique for evaluating the weak form of the collision integral necessary for the discontinuous Galerkin formulation used here. The Monte Carlo technique extends the variance reduction ideas first presented in Baker and Hadjiconstantinou (Phys. Fluids 2005; 17 , art. no. 051703) and makes evaluation of the weak form of the collision integral not only tractable but also very efficient. The variance reduction, achieved by evaluating only the deviation from equilibrium, results in very low statistical uncertainty and the ability to capture arbitrarily small deviations from equilibrium (e.g. low‐flow speed) at a computational cost that is independent of the magnitude of this deviation. As a result, for low‐signal flows the proposed method holds a significant computational advantage compared with traditional particle methods such as direct simulation Monte Carlo (DSMC). Copyright © 2008 John Wiley & Sons, Ltd.     

A stochastic approach to capture crystal plasticity

A stochastic crystal plasticity model is proposed and applied within the rate-independent regime. As opposed to conventional deterministic algorithms wherein multiple slip systems are activated and redundant constraints may exist, the new Monte Carlo plasticity (MCP) paradigm is based on a stochastic chain of singly activated slip systems and thus avoids the possible ill-condition associated with multi-slip algorithms. The choice of the activated slip system is made at each Monte Carlo (MC) step based on the Metropolis algorithm. The MCP model is implemented within a Material Point Method (MPM) as a constitutive model to capture the elasto-plastic behavior of polycrystalline materials. A comparison with a commonly used singular value decomposition (SVD) algorithm indicates that MCP offers superior computational efficiency while maintaining comparable accuracy.     

Optimal nonlinear feedback control of spacecraft rendezvous with finite low thrust between libration orbits

This paper presents the nonlinear closed-loop feedback control strategy for the spacecraft rendezvous problem with finite low thrust between libration orbits in the Sun–Earth system. The model of spacecraft rendezvous takes the perturbations in initial states, the actuator saturation limits, the measurement errors, and the external disturbance forces into consideration from an engineering point of view. The proposed nonlinear closed-loop feedback control strategy is not analytically explicit; rather, it is implemented by a rapid re-computation of the open-loop optimal control at each update instant. To guarantee the computational efficiency, a novel numerical algorithm for solving the open-loop optimal control is given. With the aid of the quasilinearization method, the open-loop optimal control problem is replaced successfully by a series of sparse symmetrical linear equations coupled with linear complementary problem, and the computational efficiency can be significantly increased. The numerical simulations of spacecraft rendezvous problems in the paper well demonstrate the robustness, high precision, and dominant real-time merits of the proposed closed-loop feedback control strategy.     

Methods for calculating tracer distribution in multiphase plug flow systems

A novel continuous time and space Monte Carlo simulation technique is presented for solving equations describing tracer distribution in multiphase inhomogeneous plug-flow systems. Comparison is made with the commonly employed method of characteristics. This comparison indicates that the method of characteristics is unreliable for systems with spacially varying parameters. Further, results indicate that the suggested Monte Carlo technique is more efficient in the use of computer time than the method of characteristics. Examples are given.     

湍流燃烧中的概率密度函数方法

用求解速度和化学热力学参数联合概率密度函数(pdf)输运方程的方法,计算湍流燃烧问题时,湍流输运和化学反应等过程可以精确计算,无须模拟。它还可以提供比统计矩模型方法更多的信息,因此是一个很有潜力的方法。本文给出了湍流燃烧概率密度函数的输运方程,扼要地介绍了目前应用较多的随机过程模型,以及求解概率密度函数方程的Monte Carlo算法。最后引用两个例子说明概率密度函数方法的优越性。      

A direct probabilistic approach to solve state equations for nonlinear systems under random excitation

In this paper, a direct probabilistic approach (DPA) is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random process. The proposed method has the advantage of obtaining the response’s moments directly from the initial conditions and statistical characteristics of the corresponding external exci-tations. First, the response’s moment equations are directly derived based on a DPA, which is completely independent of the It?/filtering approach since no specific assumptions regarding the correlation structure of excitation are made. By solving them under Gaussian closure, the response’s moments can be obtained. Subsequently, a multiscale algo-rithm for the numerical solution of moment equations is exploited to improve computational efficiency and avoid much wall-clock time. Finally, a comparison of the results with Monte Carlo (MC) simulation gives good agreement. Furthermore, the advantage of the multiscale algorithm in terms of efficiency is also demonstrated by an engineering example.     

Apparent emissivity of an absorbing-emitting-scattering semitransparent slab with variable spatial refractive index

A backward Monte Carlo curved ray-tracing method is developed to analyze the apparent emissivity of one-dimensional absorbing-emitting-scattering semitransparent slab with variable spatial refractive index. An isothermal semitransparent slab with linear variable spatial refractive index is taken as an example to examine the accuracy of the proposed method. The directional apparent emissivity is determined by the proposed method and compared with the data in references, and the effects of the single scattering albedo and the scattering phase function on the directional apparent emissivity are analyzed. The results show that the backward Monte Carlo curved ray-tracing method has a good accuracy in solving the apparent emissivity of semitransparent slab with variable spatial refractive index, and converges more quickly than the forward Monte Carlo method. The effect of single scattering albedo is significant and the influence of the scattering phase function is similar to that of the slab with constant refractive index.     

航空重力匹配定位方法

为了在重力特征显著区域内实现航空重力匹配定位,定义了匹配区重力场模糊度指标作为匹配结果可信度的度量指标,提出了一种基于Monte Carlo方法的重力匹配算法。由于航空重力仪的测量值中包含各种误差因素,使用常用的相关匹配算法估计出的匹配位置往往不是飞行器的真实位置,而是随机分布于真实位置周围。根据这个特点,将地形匹配中的均方差算法(MSD)和Monte Carlo方法结合,形成一种新的重力匹配方法。该方法根据惯性导航系统指示位置从重力图上提取参考重力数据,将重力测量数据进行若干次随机干扰后和参考重力数据使用MSD算法进行匹配,得到若干个匹配位置,取其均值作为最终匹配位置。仿真结果表明,算法在重力场特征显著区域内匹配效果优于常用的相关分析算法。     

AN ARBITRARILY MIXED EXPLICIT-IMPLICIT ASYNCHRONOUS INTEGRATION ALGORITHM BASED ON UNIFORM DISCRETIZATION FORMAT

动力学问题的有限元分析需要在每一时步求解系统信息,相对于静力学问题,其计算量要大得多.因而,提高计算效率,节省计算工作量是动力学求解方法研究的主要内容.该文针对大型复杂动力学系统的高效求解问题,提出了一种基于Newmark离散格式的显式、隐式任意混合异步算法,根据整体系统不同局部的物理力学特性和求解精度要求,在空间域及时间域内对动力学系统方程进行多尺度求解.该方法根据显式、隐式算法固有的信息传递机制,采取动态的可变边界处理方法,避免了异步边界上的误差积累;并通过对整体系统能量平衡的校验,动态地确定和修正仿真计算时步,可以有效地预防不稳定性的产生和发展.数值算例表明：该算法能在保持较高的计算精度的同时,极大地降低计算资源消耗,因而具有一定的实用价值.     

统一格式的显式与隐式任意混合异步算法

动力学问题的有限元分析需要在每一时步求解系统信息,相对于静力学问题,其计算量要大得多.因而,提高计算效率,节省计算工作量是动力学求解方法研究的主要内容.该文针对大型复杂动力学系统的高效求解问题,提出了一种基于Newmark离散格式的显式、隐式任意混合异步算法,根据整体系统不同局部的物理力学特性和求解精度要求,在空间域及时间域内对动力学系统方程进行多尺度求解.该方法根据显式、隐式算法固有的信息传递机制,采取动态的可变边界处理方法,避免了异步边界上的误差积累;并通过对整体系统能量平衡的校验,动态地确定和修正仿真计算时步,可以有效地预防不稳定性的产生和发展.数值算例表明:该算法能在保持较高的计算精度的同时,极大地降低计算资源消耗,因而具有一定的实用价值.