无网格方法中的背景积分方案及单颗粒下降过程的数值模拟

在用无网格方法对有边界移动的气固两相流动进行数值模拟时发现,如果采用背景积分网格对求解域进行积分,将会产生压力场的数值振荡,使计算结果失真.详细分析了产生这种数值振荡的原因,提出了解决方案,并计算了一个颗粒在管道内的下降过程.计算结果表明,提出的解决方案能有效地降低压力场的数值振荡,从而使无网格方法能应用于气固两相流动的直接数值模拟.     

126Ce的EC/β＋衰变

利用187 MeV的40Ca离子轰击同位素靶92Mo,由熔合蒸发反应生成目标核126Ce。藉助氦喷嘴快速带传输系统和X-X-t与X-γ-t符合测量,首次建立了126Ce的EC/β＋衰变纲图。建议了可能属于126Ce一个高自旋同核异能态的衰变,其β衰变后布居在与126La的高自旋同核异能态相关的低位能级区,测定的半衰期是57（9）s。也建议了可能属于126Ce基态的衰变,其β衰变后布居在与126La的低自旋同核异能态相关的低位能级区,它的半衰期被测定为12（4）s。但偶-偶核126Ce存在高自旋同核异能态的物理原因还有待进一步探究。     

Synthesis and polymerization of fluorinated monomers bearing a reactive lateral group. XII. Copolymerization of vinylidene fluoride with 2,3,3‐trifluoroprop‐2‐enol

An improved synthesis of 2,3,3‐trifluoroprop‐2‐enol (FA1) and its copolymerization in solution with vinylidene fluoride (VDF, or 1,1‐difluoroethylene) initiated by tert‐butyl peroxypivalate are presented. A new synthesis of FA1, with NaH and lithium diisopropylamine as bases, from 2,2,3,3‐tetrafluoropropanol is described. A series of nine copolymerization reactions were investigated from initial [VDF]₀/[FA1]₀ molar ratios of 9.1/90.9 to 94.2/5.8. The copolymer compositions were calculated via ¹⁹F NMR spectroscopy. From the Tidwell–Mortimer method, the reactivity ratios of both comonomers were determined (r_FA1 = 0.11 ± 0.22 and r_VDF = 0.83 ± 0.77 at 50°C), and they showed an azeotropic point. Alfrey and Price's Q and e values of FA1 were calculated to be 0.0178 (from Q_VDF = 0.008), 0.039 (from Q_VDF = 0.015), and 0.275 (from Q_VDF = 0.036) and 2.74 (vs e_VDF = 1.20), 2.04 (vs e_VDF = 0.50), and 1.94 (vs e_VDF = 0.4), respectively, and they indicated that FA1 is an electron‐accepting monomer. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3634–3643, 2002     

管内均相湍流燃烧加速的数值模拟

通过均相流体模型、湍流k 模型和EBU(EddyBreak Up) Arrhenius燃烧模型 ,选用Simple格式对管中戊烷和空气的燃烧实例进行了数值求解。其结果反映了燃烧导致的爆炸过程中管内流场各参数的变化规律 ,揭示了管内燃烧、流动、湍流之间的正反馈耦合关系 ,并与实验结果和相关数值结果基本相符。     

NUMERICAL ANALYSIS OF CRANK-NICOLSON SCHEME FOR THE ALLEN-CAHN EQUATION

We consider numerical methods to solve the Allen-Cahn equation using the second-order Crank-Nicolson scheme in time and the second-order central difference approach in space.The existence of the finite difference solution is proved with the help of Browder fixed point theorem.The difference scheme is showed to be unconditionally convergent in L∞ norm by constructing an auxiliary Lipschitz continuous function.Based on this result,it is demonstrated that the difference scheme preserves the maximum principle without any restrictions on spatial step size and temporal step size.The numerical experiments also verify the reliability of the method.     

An operator splitting algorithm for the three-dimensional advection–diffusion equation

Operator splitting algorithms are frequently used for solving the advection–diffusion equation, especially to deal with advection dominated transport problems. In this paper an operator splitting algorithm for the three-dimensional advection–diffusion equation is presented. The algorithm represents a second-order-accurate adaptation of the Holly and Preissmann scheme for three-dimensional problems. The governing equation is split into an advection equation and a diffusion equation, and they are solved by a backward method of characteristics and a finite element method, respectively. The Hermite interpolation function is used for interpolation of concentration in the advection step. The spatial gradients of concentration in the Hermite interpolation are obtained by solving equations for concentration gradients in the advection step. To make the composite algorithm efficient, only three equations for first-order concentration derivatives are solved in the diffusion step of computation. The higher-order spatial concentration gradients, necessary to advance the solution in a computational cycle, are obtained by numerical differentiations based on the available information. The simulation characteristics and accuracy of the proposed algorithm are demonstrated by several advection dominated transport problems. © 1998 John Wiley & Sons, Ltd.     

THE PARALLEL BLOCK ADAPTIVE MULTIGRID METHOD FOR THE IMPLICIT SOLUTION OF THE EULER EQUATIONS

A method capable of solving very fast and robust complex non-linear systems of equations is presented. The block adaptive multigrid (BAM) method combines mesh adaptive techniques with multigrid and domain decomposition methods. The overall method is based on the FAS multigrid, but instead of using global grids, locally enriched subgrids are also employed in regions where excessive solution errors are encountered. The final mesh is a composite grid with uniform rectangular subgrids of various mesh densities. The regions where finer grid resolution is necessary are detected using an estimation of the solution error by comparing solutions between grid levels. Furthermore, an alternative domain decomposition strategy has been developed to take advantage of parallel computing machines. The proposed method has been applied to an implicit upwind Euler code (EuFlex) for the solution of complex transonic flows around aerofoils. The efficiency and robustness of the BAM method are demonstrated for two popular inviscid test cases. Up to 19-fold acceleration with respect to the single-grid solution has been achieved, but a further twofold speed-up is possible on four-processor parallel computers.     

基于理想关联度的不确定多属性决策方法

针对只有部分属性权重信息且属性值以区间数形式给出的不确定多属性决策问题,提出了一种逼近理想关联度的决策分析方法。首先改进了文[4]给出的区间数决策矩阵的规范化方法;然后提出了利用期望-方差区间数排序方法求解理想最优方案;最后依据关联系数矩阵给出了属性权重信息不完全的区间数多属性决策问题的求解方法,其核心是求解线型规划得到属性权重,进而根据各个方案与理想最优方案的综合关联度大小进行排序。特别地,给出了属性权重完全未知的简洁方法,文后的实例验证了方法的可行性和有效性。     

Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems

Many applied problems are described by differential algebraic systems. Complex Rosenbrock schemes are proposed for the numerical integration of differential algebraic systems by the ?-embedding method. The method is proved to converge quadratically. The scheme is shown to be applicable even to superstiff systems. The method makes it possible to perform computations with a guaranteed accuracy. An equation is derived that describes the leading term of the error in the method as a function of time. An algorithm extending the method to systems of differential equations for complex-valued functions is proposed. Examples of numerical computations are given.     

The Neumann stability of high-order symmetric schemes for convection-diffusion problems

We find a series of sufficient conditions for the Neumann stability of the leapfrog-Euler scheme of arbitrary even order in the spatial coordinates for the three-dimensional convection-diffusion equation.