Fourier series and integral equation method for the exterior Stokes problem

The exterior Stokes problem between two parallel planes that are separated by a prismatic cylinder is extended to the interior of the prism by requiring the continuity of the velocity across the lateral faces. The well‐posedness of the exterior–interior problem is proved in suitable weighted Sobolev spaces. The solution is represented by Fourier series in the z‐variable. The Fourier coefficients, solutions of auxiliary two‐dimensional exterior–interior problems, are analyzed by viewing them as boundary integral equations of potential theory and global regularity of the densities, is established in weighted Sobolev spaces of traces. A boundary element method, with suitably refined mesh size, is implemented for the numerical treatment of the Fourier coefficients. This provides optimal convergent semi‐ and fully‐discrete spectral methods of Fourier–Galerkin type. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Comments on ‘Simplex space–time meshes in finite element simulations’

Some comments are provided on the citations offered in a recent paper (M. Behr, Int. J. Numer. Meth. Fluids 2008; 57 :1421–1434) that describes space–time finite element computations of advection of ‘Gaussian hills’, including computations with mesh refinement in the time direction. Copyright © 2008 John Wiley & Sons, Ltd.     

A multiblock/multilevel mesh refinement procedure for CFD computations

A multiblock/multilevel algorithm with local refinement for general two‐ and three‐dimensional fluid flow is presented. The patched‐based local refinement procedure is presented in detail and algorithmic implementations are also presented. The multiblock implementation is essentially block‐unstructured, i.e. each block having its own local curvilinear co‐ordinate system. Refined grid patches can be put anywhere in the computational domain and can extend across block boundaries. To simplify the implementation, while still maintaining sufficient generality, the refinement is restricted to a refinement of the grid successively halving the grid size within a selected patch. The multiblock approach is implemented within the framework of the well‐known SIMPLE solution strategy. Computational experiments showing the effect of using the multilevel solution procedure are presented for a sample elliptic problem and a few benchmark problems of computational fluid dynamics (CFD). Copyright © 2001 John Wiley & Sons, Ltd.     

电饭锅自动控温电路的设计和安装

本文紧紧抓住学生对“自动控温”这一普通现象的好奇 ,积极引导学生去探索和研究 ,使学生在掌握“自动控温”原理的基础上 ,按照自己的意愿和设想来设计一个电路并能动手组装和检验。     

An adaptive cut‐cell method for environmental fluid mechanics

In this work we present a numerical method for solving the incompressible Navier–Stokes equations in an environmental fluid mechanics context. The method is designed for the study of environmental flows that are multiscale, incompressible, variable‐density, and within arbitrarily complex and possibly anisotropic domains. The method is new because in this context we couple the embedded‐boundary (or cut‐cell) method for complex geometry with block‐structured adaptive mesh refinement (AMR) while maintaining conservation and second‐order accuracy. The accurate simulation of variable‐density fluids necessitates special care in formulating projection methods. This variable‐density formulation is well known for incompressible flows in unit‐aspect ratio domains, without AMR, and without complex geometry, but here we carefully present a new method that addresses the intersection of these issues. The methodology is based on a second‐order‐accurate projection method with high‐order‐accurate Godunov finite‐differencing, including slope limiting and a stable differencing of the nonlinear convection terms. The finite‐volume AMR discretizations are based on two‐way flux matching at refinement boundaries to obtain a conservative method that is second‐order accurate in solution error. The control volumes are formed by the intersection of the irregular embedded boundary with Cartesian grid cells. Unlike typical discretization methods, these control volumes naturally fit within parallelizable, disjoint‐block data structures, and permit dynamic AMR coarsening and refinement as the simulation progresses. We present two‐ and three‐dimensional numerical examples to illustrate the accuracy of the method. Copyright © 2008 John Wiley & Sons, Ltd.     

A semi-automatic method for measuring interferometry fringes: prototype design and first results

A device for automatically obtaining the information contained in holographic interferometry fringes is proposed. The method may be applied to any kind of interferometric fringes. Accuracy has been demonstrated by contrasting the results obtained with our prototype system and those with the single-beam speckle interferometry technique for the measurement of displacements in a plane. The results show good correlation between the two series of measurements.     

On a graded mesh method for a class of weakly singular Volterra integral equations

In this paper a class of weakly singular Volterra integral equations with an infinite set of solutions is investigated. Among the set of solutions only one particular solution is smooth and all others are singular at the origin. The numerical solution of this class of equations has been a difficult topic to analyze and has received much previous investigation. The aim of this paper is to improve the convergence rates by a graded mesh method. The convergence rates are proved and a variety of numerical examples are provided to support the theoretical findings.     

Shape controlled interpolatory ternary subdivision

Ternary subdivision schemes compare favorably with their binary analogues because they are able to generate limit functions with the same (or higher) smoothness but smaller support.In this work we consider the two issues of local tension control and conics reproduction in univariate interpolating ternary refinements. We show that both these features can be included in a unique interpolating 4-point subdivision method by means of non-stationary insertion rules that do not affect the improved smoothness and locality of ternary schemes. This is realized by exploiting local shape parameters associated with the initial polyline edges.     

Structural,magnetic and optical properties of diluted magnetic semiconductor (DMS) phase of Ni modified CuO nanoparticles

Control on the size of copper oxide (CuO) in the nano range is a highly motivating approach to study its multifunctional nature. The present investigation reports a sol-gel derived Ni doped CuO nanoparticles (Cu_1-xNi_xO). Rietveld refinement of the XRD spectra confirms the formation of single monoclinic phase of Cu_1-xNi_xO nanoparticles having crystallite size within the range of 19–21 nm. Raman spectra show the presence of characteristics Raman active modes and vibrational bands in the Cu_1-xNi_xO samples that corroborate the monoclinic phase of the samples as revealed by refinement of XRD data. The estimated band gap of pure CuO is found to be ∼1.43 eV, which decreases with the increase of dopant concentration into CuO matrix. This result is in line with estimated crystallite size. Magnetization curves confirm the weak ferromagnetic nature of Cu_1-xNi_xO nanoparticles which reveal the DMS phase. This weak magnetic nature may be induced in the samples due to the exchange interaction between the localized magnetic d-spins of Ni ions and carriers (holes or electrons) from the valence band of pristine CuO lattice. Replacement of Cu⁺² by Ni⁺² ions into the host CuO lattice induces the magnetization. The quantified value of squareness ratio (S < 0.5) confirms the inter-grain magnetic interactions in the Cu_1-xNi_xO nanoparticles which is also the reason of weak induced magnetization.