散心柱面胞格爆轰演化数值研究

采用有限体积方法,在自适应非结构网格上求解二维含化学反应Euler方程,数值研究了柱面胞格爆轰波演化现象．化学反应计算采用单步可逆总包反应模型．数值结果演示了散心柱面胞格爆轰波演化过程中胞格结构的分裂现象,获得了与实验结果定性一致的结果．胞格结构的分裂演化在点火区近场和远场显示了不同的特点,其中爆轰波传播过程中波阵面当地曲率的变化是控制胞格分裂演化行为的关键因素．数值结果也显示胞格结构的分裂现象来自于爆轰波前锋结构中横波的自组织行为,即沿爆轰波波面传播的小扰动发展成为横波的过程,这种现象与胞格爆轰波的不稳定性密切相关．     

混合层无粘稳定性分析的Legendre级数解

基于泛函分析中的不动点理论,采用不动点方法首次获得混合层无粘线性稳定性方程的显式Legendre级数解,该级数解在整个无界流动区域内一致有效．现有基于传统摄动法得到的无界流动区域一致有效解仅适用于长波扰动和中性扰动两种特殊情况,而使用不动点方法可以得到所有不稳定扰动波数的特征解．另外,在不动点方法框架下,扰动相速度和扰动增长率可根据方程的可解性条件来唯一确定．为了验证该方法的有效性,将该方法和现有文献中的数值计算结果相比较,对比结果表明该方法具有精度高、收敛快等优点．     

解算子与右端数据均有扰动的半正定算子方程的动态系统方法

本文研究了求解算子与右端数据均有扰动的第一类半正定算子方程的动态系统方法．证明了相应的动态系统Cauchy问题的整体解存在且收敛于原算子方程的解．此外,给出了解Cauchy问题的迭代方法并证明了方法的收敛性．     

基于改进粒子群算法V型非传统布局仓库通道优化设计

V型仓储布局是一种典型的非传统布局方式,针对V型布局主通道设计的问题,将主通道抽象为若干个点连接而成的折线通道,每条拣货通道按物动量大小对仓库进行分区,采用更加符合实际的存取货物作业的概率不相等的非完全随机存储策略,建立最小化平均拣货距离的仓库主通道设计数学优化模型。其次,设计了基于极值扰动算子的改进粒子群优化算法(EDO-PSO)进行算法求解,利用极值扰动算子解决易陷入局部最优问题,采用并行深度搜索策略,提高算法性能,并用Benchmark函数与其他改进PSO算法对比验证算法性能。最后,结合具体实验数据仿真分析,计算结果表明,该方法在相同货位分配策略下,能有效缩短总拣货距离,验证了方法的有效性。     

一维可压缩Euler方程组的两个模型

作者考察了一维可压缩Euler方程组的两个模型.利用特征分解和Gronwall不等式,首先得到具有几何结构且绝热指数γ=3的一维可压缩Euler方程组L~∞模的一致有界性.进一步,考虑当绝热指数γ=-1时,一维非等熵可压缩Euler方程组的Cauchy问题.在适当的假设下,得到该系统的整体经典解.     

固体平板上超薄水膜去湿润过程的分子动力学模拟

运用分子动力学模拟研究固体表面超薄水膜的失稳和破裂过程．结果表明薄膜中小扰动将失稳,并在初始阶段线性增长．但固体和液体的相互作用对扰动的初期增长影响较小．最小厚度的下降导致薄膜发生破裂．此后破裂边缘以一定的动态接触角后退．与宏观理论预测一致,边缘半径随时间的变化与时间平方根成正比．若固液相互作用较强,将引起破裂时间延迟,动态接触角减小,固体表面附近的液体密度增加．     

无界区域上基于自然边界归化的一种重叠型区域分解法及其离散化

1．引言由于科学技术的迅猛发展，人们遇到许多大规模科学和工程计算问题．随着并行计算机的出现和应用，并行技术越来越得到人们的重视和研究．区域分解法成为并行计算和处理这类问题的主要方法之一．但是，对于无界区域上的椭圆边值问题，因进行区域分解后至少有一个区域仍为无界区域，故仅应用通常的区域分解算法求解是不够的．由于边界归化是处理无界区域问题的有效手段，通常采用边界元和有限元耦合的方法求解此类问题IZ，6。8。121．或片什适当的人工边界并在此边界上加近似边界条件，再在有限区域应用有限元方法求解【人习．近年来…     

波动方程的差分反演模型

为了反演波动方程的系数函数,利用差分离散及扰动假设,推导出一个适合迭代的数值模型．解决了以往方法中正反演模型数值精度不一致问题,以及由此带来的一系列问题．经数值模拟计算说明,该方法是可行的和有效的．     

索结构的静力分析

根据柔索应变与位移的非线性几何关系以及自重作用与温度影响下的平衡方程,采用Euler描述的坐标系统精确地求得了各点的位移和张力的一般解．由索结构静力问题建立的非线性代数方程组应用改进的Powell混合算法编制的高精度DNEQNF程序直接进行求解A·D2在例题中计算了由3根索被一竖直弹簧支撑在一起的索结构,并与其他学者用不同方法得到的结果进行对比．     

自适应多重网格法的应用

本文运用自应并行多重网格法求解了轴向大扰动,径向小扰动的跨音速方程。其计算结果表明该方法能够大大提高计算效率。     

Speedup estimates for some variants of the parallel implementations of the branch-and-bound method

The efficiency of parallel implementations of the branch-and-bound method in discrete optimization problems is considered. A theoretical analysis and comparison of two parallel implementations of this method is performed. A mathematical model of the computation process is constructed and used to obtain estimates of the maximum possible speedup. Examples of problems in which none of these two parallel implementations can speed up the computations are considered.     

求解刚性常微分方程的并行广义Rosenbrock方法

本文构造了求解刚性常微分方程的并行广义Rosenbrock方法（PEROWs），分析了方法的收敛性和数值稳定性。通过用Powell方法优化方法的稳定域，构造了二级四阶并行格式PEROW4，并证明该方法是A－稳定的。新方法比同级的并行Rosenbrock方法MPROW3及PRM3均高一阶，因而在计算精度上处于优势。此外，PEROW4能使得各处理机上的负载基本均衡，从而达到非常理想的加速比和并行效率。     

Parallel Multi-Stage & Multi-Step Method in ODEs

In this paper, the theory of parallel multi-stage and multi-step method is discussed, which is a form of combining Runge-Kutta method with linear multi-step method that can be used for parallel computation.     

Eulerian Simulation of Gas‐Solid Particle Flow by BDIM

The numerical scheme based on the boundary domain integral method (BDIM) for the numerical simulation of twophase two‐component flows is presented. A program is being developed to model the hydrodynamics of fluidized bed systems by using the Eulerian approach in terms of velocity‐vorticity variables formulation. With the vorticity vector both phases motion computation scheme is partitioned into its kinematic and kinetic aspect. Influence of the drag coefficient on the two‐phase two‐component flow field is studied on the two‐phase gas‐solid particles vertical channel flow.     

Parallel iterative methods using factorized preconditioning matrices for solving elliptic equations on triangular grids

Parallel analogs of the variants of the incomplete Cholesky-conjugate gradient method and the modified incomplete Cholesky-conjugate gradient method for solving elliptic equations on uniform triangular and unstructured triangular grids on parallel computer systems with the MIMD architecture are considered. The construction of parallel methods is based on the use of various variants of ordering the grid points depending on the decomposition of the computation domain. Results of the theoretic and experimental studies of the convergence rate of these methods are presented. The solution of model problems on a moderate number processors is used to examine the efficiency of the proposed parallel methods.     

Combination method for parallel computation in ODE

In this paper, a 4th order parallel computation method with four processes for solving ODEs is discussed. This method is the Runge-Kutta method combined with a linear multistep method, which overcomes the difficulties of the 4th order parallel Runge-Kutta method discussed in [1]. The concept of critical speedup for parallel methods is also defined, and speedups of some methods are analyzed by using this concept.     

An Eulerian‐Lagrangian control volume scheme for two‐dimensional unsteady advection‐diffusion problems

We develop a mass conservative Eulerian‐Lagrangian control volume scheme (ELCVS) for the solution of the transient advection‐diffusion equations in two space dimensions. This method uses finite volume test functions over the space‐time domain defined by the characteristics within the framework of the class of Eulerian‐Lagrangian localized adjoint characteristic methods (ELLAM). It, therefore, maintains the advantages of characteristic methods in general, and of this class in particular, which include global mass conservation as well as a natural treatment of all types of boundary conditions. However, it differs from other methods in that class in the treatment of the mass storage integrals at the previous time step defined on deformed Lagrangian regions. This treatment is especially attractive for orthogonal rectangular Eulerian grids composed of block elements. In the algorithm, each deformed region is approximated by an eight‐node region with sides drawn parallel to the Eulerian grid, which significantly simplifies the integration compared with the approach used in finite volume ELLAM methods, based on backward tracking, while retaining local mass conservation at no additional expenses in terms of accuracy or CPU consumption. This is verified by numerical tests which show that ELCVS performs as well as standard finite volume ELLAM methods, which have previously been shown to outperform many other well‐received classes of numerical methods for the equations considered. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012     

A computationally efficient Kalman smoother for the evaluation of the CH4 budget in Europe

Two data assimilation methods of the Kalman filtering approach are applied to the evaluation of the methane (CH₄) distribution in the atmosphere of Europe. The long term historical observation data of CH₄ concentration are integrated with the dynamical Eulerian dispersion model (EUROS). In each proposed method a specific algorithm is employed to avoid the heavy computation burden and huge storage requirement of the conventional Kalman filter for large scale systems. Moreover, a smoother algorithm is developed to identify the emission input. The feasibility of proposed data assimilation methods is verified by the application results.     

Eulerian and even-face ribbon graph minors

In this paper, we introduce Eulerian and even-face ribbon graph minors. These minors preserve Eulerian and even-face properties of ribbon graphs, respectively. We then characterize Eulerian, even-face, plane Eulerian and plane even-face ribbon graphs using these minors.     

An improved GPBi-CG algorithm suitable for distributed parallel computing

An improved generalized product-type bi-conjugate gradient (GPBi-CG) method (IGPBi-CG method, in brief) for solving large sparse linear systems with unsymmetrical coefficient matrices is proposed for distributed parallel environments. The method reduces three global synchronization points to two by reconstructing GPBi-CG method and the communication time required for the inner product can be efficiently overlapped with useful computation. The cost is only slightly increased computation time, which can be ignored compared with the reduction of communication time. Performance and isoefficiency analysis show that the IGPBi-CG method has better parallelism and scalability than the GPBi-CG method. Numerical experiments show that the scalability can be improved by a factor greater than 1.5 and the improvement in parallel communication performance approaches 33.3˙%.