Pressure projection stabilized finite element method for Stokes problem with nonlinear slip boundary conditions

In this paper, we consider the pressure projection stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality problem of the second kind with the Stokes operator. The H¹ and L² error estimates for the velocity and the L² error estimate for the pressure are obtained. Finally, the numerical results are displayed to verify the theoretical analysis.     

The Trefftz method using fundamental solutions for biharmonic equations

In this paper, the Trefftz method of fundamental solution (FS), called the method of fundamental solution (MFS), is used for biharmonic equations. The bounds of errors are derived for the MFS with Almansi’s fundamental solutions (denoted as the MAFS) in bounded simply connected domains. The exponential and polynomial convergence rates are obtained from highly and finitely smooth solutions, respectively. The stability analysis of the MAFS is also made for circular domains. Numerical experiments are carried out for both smooth and singularity problems. The numerical results coincide with the theoretical analysis made. When the particular solutions satisfying the biharmonic equation can be found, the method of particular solutions (MPS) is always superior to the MFS and the MAFS, based on numerical examples. However, if such singular particular solutions near the singular points do not exist, the local refinement of collocation nodes and the greedy adaptive techniques can be used for seeking better source points. Based on the computed results, the MFS using the greedy adaptive techniques may provide more accurate solutions for singularity problems. Moreover, the numerical solutions by the MAFS with Almansi’s FS are slightly better in accuracy and stability than those by the traditional MFS. Hence, the MAFS with the AFS is recommended for biharmonic equations due to its simplicity.     

Scaling laws for gas-solid riser flow through two-fluid model simulation

Scale up of gas-solid circulating fluidized bed (CFB) risers poses many challenges to researchers.In this paper,CFD investigation of hydrodynamic scaling laws for gas-solid riser flow was attempted on the basis of two-fluid model simulations,in particular,the recently developed empirical scaling law of Qi,Zhu,and Huang (2008).A 3D computational model with periodic boundaries was used to perform numerical experiments and to study the effect of various system and operating parameters in hydrodynamic scaling o...     

A sufficient condition for asymptotically well behaved property of convex polynomials

In this paper, we employ an asymptotic assumption to show that the maximum of finitely many convex polynomials is an asymptotically well behaved function. We also give two examples to illustrate our main result. As an application, we reproduce some known results appeared recently in the literature.     

A Finite Element Algorithm for Nematic Liquid Crystal Flow Based on the Gauge-Uzawa Method

In this paper,we present a finite element algorithm for the time-dependent nematic liquid crystal flow based on the Gauge-Uzawa method.This algorithm combines the Gauge and Uzawa methods within a finite element variational formulation,which is a fully discrete projection type algorithm,whereas many projection methods have been studied without space discretization.Besides,error estimates for velocity and molecular orientation of the nematic liquid crystal flow are shown.Finally,numerical results are given to show that the presented algorithm is reliable and confirm the theoretical analysis.     

电视摄象机测量误差探讨

本文简述了用电视摄象机进行工业尺寸测量的微分法与拟合法的基本原理,同时详细的讨论了各自所能达到的精度极限。本文用实验验证了理论计算的结果,最后对二维工件测量时,如何根据工件的不同形状与位置以及光学系统的特点,提出了在测量时工件的放置应该注意的问题以及对工件拐角处如何进行处理的方法。     

Comments on the editorial "On quality of a measurement result"

A recent editorial reviewed several definitions of quality. The limitations of these definitions are discussed here, with a simple suggestion to define quality as meeting a specified error rate whereby the required elements for an error rate are listed. Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

Design of a Hybrid Fiber-Optic Network Using 3-D Optical Code Sequences

We present the design of a 3-dimensional (3-D) noncoherent optical hybrid network. We also report the design of a new family of 3-D codes for fiber optic hybrid networks. We show that the hybrid network allows for shorter bit times and a higher number of users, given a set chip rate, compared to previously conceived networks. These newly designed hybrid single-pulse-per-row (HSPR) codes have very low autocorrelation side-lobes and very small cross-correlation peaks. We compare the performance of our hybrid model using our codes with the Optical Orthogonal Codes (OOCs) and Temporal/Spatial (T/S) codes and show that the new network can support a greater number of users and higher data rates than those using OOCs and T/S codes.     

Robust Mean-Squared Error Estimation of Multiple Signals in Linear Systems Affected by Model and Noise Uncertainties

This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in which the second order statistics of the noise vectors (i.e., their covariance matrices) are also subjected to uncertainty. We seek a robust mean-squared error estimator immuned against both sources of uncertainty. We show that the optimal robust mean-squared error estimator has a special form represented by an elementary block circulant matrix, and moreover when the uncertainty sets are ellipsoidal-like, the problem of finding the optimal estimator matrix can be reduced to solving an explicit semidefinite programming problem, whose size is independent of N. The research was partially supported by BSF grant #2002038     

A global approach to error estimation and physical diagnostics in multidimensional computational fluid dynamics

An approach for simultaneously assessing numerical accuracy and extracting physical information from multidimensional calculations of complex (engineering) flows is proposed and demonstrated. The method is based on global balance equations, i.e. volume-integrated partial differential equations for primary or derived physical quantities of interest. Balances can be applied to the full computational domain or to any subdomain down to the single-cell level. Applications to in-cylinder flows in reciprocating engines are used for illustration. It is demonstrated that comparison of the relative magnitude of the terms in the balances provides insight into the physics of the flow being computed. Moreover, for quantities that are not conserved at the cell or control volume level in the construction of the numerical scheme, the imbalance allows a direct assessment of numerical accuracy in a single run using a single mesh. The mean kinetic energy imbalance is shown to be a particularly sensitive indicator of numerical accuracy. This simple and powerful diagnostic approach can be implemented for finite-difference, finite-volume or finite-element methods.