A projection method for solving incompressible viscous flows on domains with moving boundaries

In this paper, a projection method is presented for solving the flow problems in domains with moving boundaries. In order to track the movement of the domain boundaries, arbitrary‐Lagrangian–Eulerian (ALE) co‐ordinates are used. The unsteady incompressible Navier–Stokes equations on the ALE co‐ordinates are solved by using a projection method developed in this paper. This projection method is based on the Bell's Godunov‐projection method. However, substantial changes are made so that this algorithm is capable of solving the ALE form of incompressible Navier–Stokes equations. Multi‐block structured grids are used to discretize the flow domains. The grid velocity is not explicitly computed; instead the volume change is used to account for the effect of grid movement. A new method is also proposed to compute the freestream capturing metrics so that the geometric conservation law (GCL) can be satisfied exactly in this algorithm. This projection method is also parallelized so that the state of the art high performance computers can be used to match the computation cost associated with the moving grid calculations. Several test cases are solved to verify the performance of this moving‐grid projection method. Copyright © 2004 John Wiley Sons, Ltd.     

Application of coset representations to the construction of symmetry adapted functions

Summary A coset representation (G(/G _i )), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG _i , is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G _i ) orbit belongs to theG _i site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.     

The application of laser reflective tomography in near-field measurements of ultrasonic transducers

With Laser Reflective Tomography（LRT）,the near fields of ultrasonic transducers were measured and analyzed.The principle of LRT measurement of ultrasonic field distribution was introduced and an experimental system was set up.Acoustic pressure of a multiple element piston transducer was measured by using of a laser vibrometer.Its distribution in amplitude and phase was obtained.The acoustic pressure in the same region was measured with a needle hydrophone to validate the LRT method.Furthermore,through reconstruction of acoustic fields,it indicated that LRT method is suitable for predicting the distribution on transducers＇surface and conditions of active elements.     

A CSP and tabulation-based adaptive chemistry model

We demonstrate the feasibility of a new strategy for the construction of an adaptive chemistry model that is based on an explicit integrator stabilized by an approximation of the Computational Singular Perturbation (CSP)-slow-manifold projector. We examine the effectiveness and accuracy of this technique first using a model problem with variable stiffness. We assess the effect of using an approximation of the CSP-slow-manifold by either reusing the CSP vectors calculated in previous steps or from a pre-built tabulation. We find that while accuracy is preserved, the associated CPU cost was reduced substantially by this method. We used two ignition simulations – hydrogen–air and heptane–air mixtures – to demonstrate the feasibility of using the new method to handle realistic kinetic mechanisms. We test the effect of utilizing an approximation of the CSP-slow-manifold and find that its use preserves the order of the explicit integrator, produces no degradation in accuracy, and results in a scheme that is competitive with traditional implicit integration. Further analysis on the performance data demonstrates that the tabulation of the CSP-slow-manifold provides an increasing level of efficiency as the size of the mechanism increases. From the software engineering perspective, all the machinery developed is Common Component Architecture compliant, giving the software a distinct advantage in the ease of maintainability and flexibility in its utilization. Extension of this algorithm is underway to implement an automated tabulation of the CSP-slow-manifold for a detailed chemical kinetic system either off-line, or on-line with a reactive flow simulation code.     

Generalized projection and approximation of fixed points of nonself maps

Let K be a nonempty closed convex proper subset of a real uniformly convex and uniformly smooth Banach space E; T:K→E be an asymptotically weakly suppressive, asymptotically weakly contractive or asymptotically nonextensive map with F(T){xK: Tx=x}≠. Using the notion of generalized projection, iterative methods for approximating fixed points of T are studied. Convergence theorems with estimates of convergence rates are proved. Furthermore, the stability of the methods with respect to perturbations of the operators and with respect to perturbations of the constraint sets are also established.     

完全Rees矩阵半群的分解及性质

用等价关系Q^~出了完全Rees矩阵半群的一种分解．而且得到了它的每个Q^~一类的表示．     

Galerkin Approximations for the Linear Parabolic Equation with the Third Boundary Condition

We solve a linear parabolic equation in ^d , d 1, with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the -method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.     

Bound on <Emphasis Type="Italic">m</Emphasis>-restricted Edge Connectivity

An m-restricted edge cut is an edge cut that separates a connected graph into a disconnected one with no components having order less than m. m-restrict edge connectivity λm is the cardinality of a minimum m-restricted edge cut. Let G be a connected k-regular graph of order at least 2m that contains m-restricted edge cuts and X be a subgraph of G. Let θ(X) denote the number of edges with one end in X and the other not in X and ξm=min{θ(X) ;X is a connected vertex-induced subgraph of order m}.It is proved in this paper that if G has girth at least m/2 2,then λm≤ξm.The upper bound of λm is sharp.     

基于组合权重的系统评价模型

提出了基于组合权重的系统评价新模型 ( CWSE) ,即 :直接根据评价指标样本数据集 ,用基于加速遗传算法的投影寻踪方法确定各评价指标的分类权重 ,用基于加速遗传算法的层次分析法确定各评价指标的排序权重 ,用加速遗传算法对各评价指标的分类权重和排序权重进行综合得到组合权重 ,然后以这些组合权重与各评价对象相应评价指标的标准化值进行加权平均 ,得到系统评价的综合指标值 ,据此可对各评价对象进行分类排序 .用 CW SE模型评价中国 30个区域 1995年开发度的结果表明 ,根据开发度的强弱可把这些区域分成 3个强开发区域、6个较强开发区域、10个中等开发区域和 11个弱开发区域 ;CWSE模型简便、通用 ,计算结果较为客观和稳定 ,为系统工程理论和实践提供了新的研究方法 .     

Remarks on a Noble''''s Theorem

Noble proved the following Theorem: If A (?) X with a nonisolated point and B (?) Y, then A × B is bounded in X×Y if and only if the projection map π : X × Y → X is a z-map with respect to A × B and A, A is bounded in X and B is bounded in Y. In this note, we give two examples showing the necessary and sufficient conditions of Noble's theorem are not right.