On the use of fuzzy inference techniques in assessment models: part I—theoretical properties

An assessment model is a mathematical model that produces a measuring index, either in the form of a numerical score or a category to a situation/object, with respect to the subject of measure. From the numerical score, decision can be made and action can be taken. To allow valid and useful comparisons among various situations/objects according to their associated numerical scores to be made, the monotone output property and the output resolution property are essential in fuzzy inference-based assessment problems. We investigate the conditions for a fuzzy assessment model to fulfill the monotone output property using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to its input. This derivative should be greater than the minimum resolution required. From the derivative, we suggest improvements to the output resolution property by refining the fuzzy production rules.     

Evaluation of adaptive mesh refinement and coarsening for the computation of compressible flows on unstructured meshes

The compressible gas flows of interest to aerospace applications often involve situations where shock and expansion waves are present. Decreasing the characteristic dimension of the computational cells in the vicinity of shock waves improves the quality of the computed flows. This reduction in size may be accomplished by the use of mesh adaption procedures. In this paper an analysis is presented of an adaptive mesh scheme developed for an unstructured mesh finite volume upwind computer code. This scheme is tailored to refine or coarsen the computational mesh where gradients of the flow properties are respectively high or low. The refinement and coarsening procedures are applied to the classical gas dynamic problems of the stabilization of shock waves by solid bodies. In particular, situations where oblique shock waves interact with an expansion fan and where bow shocks arise around solid bodies are considered. The effectiveness of the scheme in reducing the computational time, while increasing the solution accuracy, is assessed. It is shown that the refinement procedure alone leads to a number of computational cells which is 20% larger than when alternate passes of refinement and coarsening are used. Accordingly, a reduction of computational time of the same order of magnitude is obtained. Copyright © 2005 John Wiley & Sons, Ltd.     

Sliding mesh algorithm for CFD analysis of helicopter rotor–fuselage aerodynamics

The study of rotor–fuselage interactional aerodynamics is central to the design and performance analysis of helicopters. However, regardless of its significance, rotor–fuselage aerodynamics has so far been addressed by very few authors. This is mainly due to the difficulties associated with both experimental and computational techniques when such complex configurations, rich in flow physics, are considered. In view of the above, the objective of this study is to develop computational tools suitable for rotor–fuselage engineering analysis based on computational fluid dynamics (CFD). To account for the relative motion between the fuselage and the rotor blades, the concept of sliding meshes is introduced. A sliding surface forms a boundary between a CFD mesh around the fuselage and a rotor‐fixed CFD mesh which rotates to account for the movement of the rotor. The sliding surface allows communication between meshes. Meshes adjacent to the sliding surface do not necessarily have matching nodes or even the same number of cell faces. This poses a problem of interpolation, which should not introduce numerical artefacts in the solution and should have minimal effects on the overall solution quality. As an additional objective, the employed sliding mesh algorithms should have small CPU overhead. The sliding mesh methods developed for this work are demonstrated for both simple and complex cases with emphasis placed on the presentation of the inner workings of the developed algorithms. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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.     

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.