A moving finite element method for the population balance equation

A moving finite element algorithm has been compared against the upwind-differencing and Smolarkiewicz methods for the population balance equation of multicomponent particle growth processes. Analytical solutions and an error function have been used to test the numerical methods. The moving finite elements technique is much more accurate than other methods for a wide range of parameters. Since this method uses moving grids, it is able to model very narrow particle size distributions. It is also shown that the method can be extended to solve condensational growth problems which include particle curvature and non-continuum mass transfer effects.     

Open boundary condition symposium benchmark solution: Stratified flow over a backward-facing step

This paper presents a detailed numerical solution to a simplified version of two-dimensional stratified flow over a backward-facing step with a Froude number of 16/9, a Reynolds number of 800 and a Prandtl number of 1—one of the Open Boundary Condition Symposium test problems. The steady state solution was derived by integrating the time-dependent Boussinesq equations forward in time using a semi-implicit finite-element-based model on a 38400-element mesh. In addition to presenting the results derived on this grid, the paper also presents the results of a Richardson extrapolation calculation for a set of ‘key’ parameters. It is hoped that this solution can be used as a baseline to compare the performance of the various techniques discussed at the Open Boundary Condition Symposium.     

Geometrically nonlinear analysis with a 4-node membrane element formulated by the quadrilateral area coordinate method

Recently, a 4-node quadrilateral membrane element AGQ6-I, has been successfully developed for analysis of linear plane problems. Since this model is formulated by the quadrilateral area coordinate method (QACM), a new natural coordinate system for developing quadrilateral finite element models, it is much less sensitive to mesh distortion than other 4-node isoparametric elements and free of various locking problems that arise from irregular mesh geometries. In order to extend these advantages of QACM to nonlinear applications, the total Lagrangian (TL) formulations of element AGQ6-I was established in this paper, which is also the first time that a plane QACM element being applied in the implicit geometrically nonlinear analysis. Numerical examples of geometrically nonlinear analysis show that the presented formulations can prevent loss of accuracy in severely distorted meshes, and therefore, are superior to those of other 4-node isoparametric elements. The efficiency of QACM for developing simple, effective and reliable serendipity plane membrane elements in geometrically nonlinear analysis is demonstrated clearly.     

Mode-coupling effects in the density dependence of the shear viscosities of dense argon and methane

We argue that the density dependence of the shear viscosities of dense argon at 174, 223, and 301 K and of dense methane at 298 K can be understood on the basis of the mode coupling theory for hard spheres, in particular near the fluid-solid phase transition.     

Extension of the Coherent Gradient Sensor (CGS) to the Combined Measurement of In-Plane and Out-of-Plane Displacement Field Gradients

The Coherent Gradient Sensor (CGS) is extended to the optical differentiation of specular, diffracted wave fronts leading to the combined measurement of in- and out-of-plane displacement field gradients. A derivation of the underlying optical interference principles is presented along with an analysis of the effective instrument sensitivity. In order to demonstrate the capabilities of the technique, experimental measurements of crack-tip deformation fields were conducted under various loading conditions corresponding to mode-I, mode-II, and mixed mode near-tip crack fields. The experimental procedures and results of these tests are presented as validation of the technique.     

Topology optimization of microfluidic mixers

This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering the layout of flow/non‐flow regions subject to a constraint on the pressure drop between inlet and outlet. For a square cross‐sectioned pipe the mixing is increased by 70% compared with a straight pipe at the cost of a 2.5 fold increase in pressure drop. Another example where only the bottom profile of the channel is a design domain results in intricate herring bone patterns that confirm findings from the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Frequency– and Time-domain BEM Analysis of Rigid Track on a Half-Space with Vibration Barriers

The rapid development of high-speed trains like the TGV or the ICE in recent years results in high dynamic loads causing vibrations which propagate from the train-track structure into the ground and further into nearby buildings. In this context it is important to develop rigid tracks with improved dynamic behaviour and to investigate possible means of vibration reduction. The boundary element method in frequency and time domain is used to simulate train-track structures subjected to dynamic loading and the reduction of vibrations which for instance can be achieved via a trench running parallel to the rigid track. In this context the non-causality error, which arises when the time-domain BEM algorithm is applied to mathematically concave domains, is discussed and the substructure method is proposed as a solution to this problem. A two-layered cylindrical elastic structure on a half-space with a trench is added as an example of a possible application.     

CVD全离散化的混合有限元解的数值模拟

在已有的对CVD化学方程半离散化和全离散化混合有限元解的存在性及其误差分析的基础上,对其全离散化混合有限元解进行了数值模拟,结果进一步表明了混合有限元解的高精度、易于计算的良好性质.     

Local Rings of Rings of Quotients

The aim of this paper is to characterize those elements in a semiprime ring R for which taking local rings at elements and rings of quotients are commuting operations. If Q denotes the maximal ring of left quotients of R, then this happens precisely for those elements if R which are von Neumann regular in Q. An intrinsic characterization of such elements is given. We derive as a consequence that the maximal left quotient ring of a prime ring with a nonzero PI-element is primitive and has nonzero socle. If we change Q to the Martindale symmetric ring of quotients, or to the maximal symmetric ring of quotients of R, we obtain similar results: an element a in R is von Neumann regular if and only if the ring of quotients of the local ring of R at a is isomorphic to the local ring of Q at a. Partially supported by the Ministerio de Educación y Ciencia and Fondos Feder, jointly, trough projects MTM2004-03845, MTM2007-61978 and MTM2004-06580-C02-02, MTM2007-60333, by the Junta de Andalucía, FQM-264, FQM336 and FQM02467 and by the Plan de Investigación del Principado de Asturias FICYT-IB05-017.     

Stokes问题各向异性网格Q2-P1混合元超收敛分析

讨论Stokes问题在各向异性冈格下的Q2-P1混合有限元方法，利用积分恒等式技巧得到了与传统方法相同的超逼近性质，同时基于插值后处理的技巧，构造了速度和压力的一对插值后处理算子，并且前者具有备向异性特征，从而导出了整体超收敛结果．