bluuebunny/crossref_metadata_2025 huggingface dataset:
Coupled discrete‐layer finite elements for laminated piezoelectric platess
Authors: Heyliger Paul , Ramirez Guillermo , Saravanos Dimitris
Published: August 2005

Finite element models based on discrete‐layer theories are presented for the coupled‐field analysis of laminated plates containing piezoelectric layers. The three displacements and the electrostatic potential are treated as unknowns in this formulation, which allows for piece‐wise approximations of the variables through the thickness of each layer. Two specific models are demonstrated in which the transverse displacement is either variable or constant, and the in‐plane displacements and potential take piece‐wise linear approximations through the thickness. The models are applied to example problems with applied surface tractions and specified surface potentials. Good agreement is found with exact solutions.
Comparison of explicit and implicit finite element methods in the quasistatic simulation of uniaxial tension
Authors: Hu Xiaoyu , Wagoner Robert H. , Daehn Glenn S. , Ghosh Somnath
Published: August 2005

On the basis of simple one‐dimensional finite element analyses, comparison in simulations of uniaxial tension using explicit dynamic and implicit static tonnulations has been made. Results show that for materials having a Hollomon‐type constitutive law with power‐law strain rate sensitivity, the explicit dynamic method can be employed for the quasistatic simulations of tensile tests only below the critical test velocities or critical normalized material densities. These critical values are determined numerically as a function of material parameters.
An improved FE expansion for micropolar localization analysis
Authors: Steinmann Paul
Published: August 2005

A mixed variational principle is presented for the geometrically linear micropolar continuum. Then a suitable discretization and its implementation are discussed, resulting in an improved element behaviour for micropolar localization analysis. The intriguing element performance is demonstrated for the case of localization within a compression problem.
Boundary characteristic orthogonal polynomials in numerical approximation
Authors: Singh Bani , Chakraverty S.
Published: August 2005

The paper describes a procedure to generate boundary characteristic orthogonal polynomials (BCOPs) over a domain in Rn. The method is based upon the Gram‐Schmidt process of orthogonalization. The orthogonal polynomial sequence (OPS) is generated from a set of linearly independent functions which satisfy the given boundary conditions. The procedure is illustrated by taking several examples in R2, the most important case from the application point of view. Extensive numerical work has been carried out for simple domains like the circle, square and isosceles right‐angled triangle. The following cases have been considered: (a) when the BCOPs vanish on the boundary; (b) when they and their normal derivatives vanish on the boundary; (c) when no conditions have been imposed on the boundary. The results for other geometries such as an ellipse, a parallelogram and an arbitrary triangle follow by some simple transformations. The procedure is also applicable to one‐dimensional problems and can be easily extended to R3.
Investigation of equilibrium states of viscoelastic circular plates by the deformation map technique
Authors: Drawshi Muhamad , Cederbaum Gabriel
Published: August 2005

The geometrically non‐linear response of a circular plate is investigated by means of a ‘deformation map’. The plate is subjected to static radial forces and bending moments, both uniformly distributed along the supported edges, in addition to a transverse load. The deformation map gives the complete picture for the investigated structure. The classical formulation of large deformation for the above‐mentioned problem goes back to Timoshenko (1940). To create a deformation map, it is necessary to convert the boundary value problem into an initial value problem (Cauchy's problem). The Runge‐Kutta (RK) method can then be used to solve numerically the equilibrium equations for the above‐mentioned circular plate. In the paper several kinds of transverse loading are considered and their influence on the plate response is examined. It is shown that in some cases the plate's behaviour is chaotic‐like (unpredictable), in the sense that various equilibrium states are possible for a certain given set of loads. Yet, it is shown that the viscoelasticity reduces the range of the possible equilibrium states, and thus stabilizes the system.
2D or 3D frictional contact algorithms and applications in a large deformation context
Authors: Feng Zhi‐Qiang
Published: August 2005

The paper is devoted to the analysis of two‐ or three‐dimensional contact problems with Coulomb friction and large deformation. The classical approach is based on two minimum principles or two variational inequalities: the first for unilateral contact and the second for friction. A coupled approach using only one principle or one inequality is presented. This new approach allows us to extend the notion of normality law to dissipative behaviours with a non‐associated flow rule, such as surface friction. Non‐differentiable contact potentials are regularized by means of the augmented Lagrangian method. Using the C++ language, an object‐oriented finite element database is created, which allows us to implement the contact and friction in an existing code in a very simple and neat way. Numerical examples are carried out in many difficult cases such as shock absorber and three‐dimensional contact. The numerical results prove that this approach is robust and efficient concerning numerical stability.
A robust implementation of Zienkiewicz and Zhu's local patch recovery method
Authors: Labbé P. , Garon A
Published: August 2005

While implementing Zienkiewicz and Zhu's superconvergent patch recovery method in our finite element solver, we came across two difficulties: rank deficiency of the local system to be solved, and ill‐conditioning. The first problem was solved by increasing the number of sampling points and the second by using LU decomposition with partial pivoting.
Hierarchic and mixed‐interpolated finite elements for Reissner–Mindlin problems
Authors: Scapolla T. , Della Croce L.
Published: August 2005

The focus of the present work is directed towards the construction of a family of special finite elements for the numerical solution of the Reissner–Mindlin plate problem. The model describes the deformation of a plate when transverse shear deformation is taken into account. The model is widely used for thin to moderately thick plates. Despite its simple formulation, the numerical approximation is not straightforward. When standard low‐order finite elements are used for the approximation the solution degenerates very rapidly for small thickness (locking phenomenon). To overcome such behaviour, non‐standard formulations of the problem are usually combined with low‐order finite elements to weaken or possibly eliminate the locking of the numerical solution.

In recent years high‐order finite elements have been introduced and successfully applied in several fields. Previously we have constructed a family of hierarchic high‐order finite elements to solve the Reissner–Mindlin problem in its plain formulation. The locking was strongly reduced but was still active for very thin plates. Meanwhile some mixed‐interpolated finite elements have been developed and shown to be locking free. In this paper we combine the two approaches, namely, the hierarchic high‐order elements and the mixed‐interpolated elements. The result is a family of special finite elements that exhibits both properties of convergence and robustness.
A laminate theory based on global–local superposition
Authors: Li Xiaoyu , Liu Dahsin
Published: August 2005

Combining a high‐order shear deformation theory and a layerwise theory, a laminate theory of zigzag type is presented. Like the high‐order shear deformation theories, the number of independent variables of the present theory is independent of layer number. The numerical efficiency is thus guaranteed. Similar to the layerwise theories, the in‐plane displacement components vary from layer to layer. Hence, the imposition of continuity conditions of interlaminar shear stresses on the laminate interfaces becomes possible. Consequently, the accuracy of displacement and stress components can be improved. Numerical studies on composite laminates made of alternate sequences based on 0° and 90° layers are performed. It can be concluded that the present theory gives accurate in‐plane displacement and stress for 6‐layer, 19‐layer and 32‐layer laminates. Its predictions on transverse displacement, transverse shear stress and transverse normal stress seem to be gradually improved as the number of alternate layers increases.
An accurate finite strip for analysing deep beams and shear walls
Authors: Cheung Y. K. , Kong J.
Published: August 2005

A new finite strip for the analysis of 2D elastic problems is presented. Displacement in each of the two in‐plane directions is interpolated by a set of computed shape functions in the longitudinal direction and, as usual, standard 1D Lagrangian shape functions in the transverse direction. Unlike all other finite strips, the unknown parameters of the present finite strip are represented by the physical displacement variables at nodal points. Furthermore, C0‐continuity is maintained across the boundaries between adjacent strips. Deep beams with geometric discontinuity can be treated in a standard finite element manner. Several numerical examples are given to demonstrate its accuracy in analysing deep beams and shear walls.
On the completeness of the multiple reciprocity series approximation
Authors: Power Henry
Published: August 2005

In the paper we apply the boundary element multiple reciprocity method to the Brinkman equation, showing that the technique yields an incomplete series representation of the corresponding fundamental solution, incompleteness that is due to a weakness in the way the method is usually applied. For the present case an additional integral relation is found that makes the series complete. Unfortunately, the relation is particular to this problem and cannot be generalized in a simple way. The result found in this work suggests that in multiple reciprocity it is necessary to have an extra relation in integral form to define the missing terms in the series representation. This extra relation has to yield zero contribution for cases when the multiple reciprocity method gives the complete series representation.
On the application of 2D potential theory to electrostatic simulation
Authors: Shi Fan , Ramesh Palghat , Mukherjee Subrata
Published: August 2005

Computing the charge density on the surfaces of conductors is fundamental to many electrostatic applications. Difficulties arise in two‐dimensional simulation due to the O(log|r|) potential. Fully understanding the 2D potential problem, and reasonably connecting the mathematical formulation with physical interpretation, are key to handling this difficulty properly. In the absence of these factors it is easy for one to propose an ill‐posed problem. In this paper, a complete investigation of potential theory, from 3D to 2D, is made for computing charge density on the surfaces of conductors. Various integral formulations are derived ‐ these are applicable in different situations. It is shown that, in general, the electrostatic potential need not be finite valued at infinity for 2D problems. Numerical examples for the 2D case are constructed to show that the formulations are consistent. Criteria for choosing the most appropriate formulation for a given problem are suggested.
Anti‐kinetochore staining for single laser, bivariate flow sorting of Indian muntjac chromosomes
Authors: Levy Howard P. , Schultz Roger A. , Ordóñez José V. , Cohen Maimon M.
Published: August 2005

Flow cytometric chromosome sorting typically relies upon dual‐laser, bivariate analysis after staining with two different base pair‐specific dyes for resolution of chromosomes with similar DNA content. The availability of FITC‐conjugated antibodies offers the possibility of singlelaser bivariate analysis when combined with propidium iodide (PI) DNA staining, but requires exploitable antigenic differences between chromosomes of interest. A technique was developed for indirect immunofluorescent anti‐kinetochore staining of Indian muntjac chromosomes in suspension. Primary antibody binding within permeabilized whole cells minimized centrifugation‐induced loss of chromosomal integrity. Subsequent FITC‐conjugated second antibody binding was not affected by concurrent PI‐counterstaining. Anti‐kinetochore staining facilitated resolution of chromosomes No. 2 and X, which formed a doublet peak upon univariate DNA content analysis, as well as recognition of the Y2 peak which was indistinguishable from debris by univariate analysis. The technique allowed greater than 90% purification of each Indian muntjac chromosome.
Single laser three color immunofluorescence staining procedures based on energy transfer between phycoerythrin and cyanine 5
Authors: Lansdorp Peter M. , Smith Cam , Safford Meredith , Terstappen Leon W. M. M. , Thomas Terry E.
Published: August 2005

Monoclonal antibodies specific for phycoerythrin (PE) were covalently labeled with the fluorescent dye cyanine 5 (Cy5). Excitation at 488 nm of immune complexes obtained by mixing Cy5‐anti‐PE with PE resulted in a 4‐fold reduction of PE fluorescence measured at 565 nm and an increase of fluorescence measured at 655 nm. The observed energy transfer between PE and Cy5‐anti‐PE was used to develop three color immunofluorescence staining procedures for flow cytometers equipped with an Argon laser tuned at 488nm. Mouse IgG1 monoclonal antibodies specific for cell surface antigens were cross‐linked with either unlabeled or Cy5 labeled mouse IgG1 anti‐PE using F(ab′)2 fragments of monoclonal rat anti‐mouse IgG1. PE was added to these immune complexes in sufficient amounts to saturate all PE binding sites. Cells were incubated with PE‐labeled and PE/Cy5‐labeled tetrameric antibody complexes together with FITC labeled antibodies and analyzed by flow cytometry. The emission from FITC, PE and PE/Cy5 could be readily separated and bright three color immunofluorescence staining of mononuclear cells from human peripheral blood and bone marrow was observed. The results of these experiments demonstrate that useful probes for single laser three color staining of cell surface antigens can be readily obtained by mixing of selected reagents. Compared to standard procedures for the covalent labeling of PE (tandem) molecules to antibodies, the non‐covalent procedures described in this report provide significant advantages in terms of the amount of reagents, time and equipment required to obtain suitable reagents for three color immunofluorescence staining.
Viral and cellular oncogene expression during progressive malignant transformation of SV40 transformed human fibroblasts
Authors: Goolsby Charles L. , Steiner Marianne , Nemeth Jeffrey
Published: August 2005

In vitro investigation of the multistep neoplastic progression which occurs during transformation of human cells has been hindered by resistance of human cells to both immortalization and tumorigenicity (Mut. Res. 199; 273, 1988). Previously our laboratory established a cell line, HSF4‐T12, by transfection of normal human foreskin fibroblasts with the plasmid pSV3‐neo which contains the early genes of simian virus 40 (SV40). A multi‐step progression in karyotypic alterations and transformed phenotype occurred resulting in a neoplastic cell line that was immortal, transformed, and tumorigenic. We have examined changes in the SV40 proteins, large T (T‐antigen) and small t (t‐antigen) antigens, and in the cellular protein, p53, during progressive transformation of these cells. Total viral protein expression relative to total cellular protein increased following immortalization of HSF4‐T12 as did the ratio of T‐antigen to t‐antigen. Interestingly, no significant change in DNA content accompanied immortalization. However, during the progressive in vitro transformation of HSF4‐T12 which occurred primarily post‐immortalization, DNA index increased to 1.6 but only small additional increases in T‐antigen expression were seen. No consistent or critical role for t‐antigen in development of the tumorigenic phenotype was found in this system.
Elevated serum urate concentration independently predicts poor outcome following stroke in patients with diabetes
Authors: Newman Edward J. , Rahman Fariel S. , Lees Kennedy R. , Weir Christopher J. , Walters Matthew R.
Published: August 2005

Background

Type 2 diabetes is a risk factor for stroke and confers increased risk of poor outcome and further vascular events following stroke. Hyperuricaemia occurs commonly in patients with type 2 diabetes, but its significance as a predictor of outcome following stroke is uncertain. We sought to investigate the prognostic significance of elevated serum urate concentration in diabetic subjects following stroke.

Methods

We studied a cohort of type 2 diabetes patients presenting to our unit with computed tomography‐confirmed acute stroke. Fasting blood samples were drawn within 24 h of admission for urate concentration and standard battery of biochemistry and hematological tests. Information on age, stroke type, prior hypertension, smoking status, resolution time of symptoms and National Institutes of Health Stroke Score was collated. The main outcome event was time to myocardial infarction, recurrent stroke or vascular death, as defined in the CAPRIE trial. Stepwise proportional hazards regression was used to estimate the effect of the above variables on event‐free survival following stroke.

Results

One hundred and forty patients were studied. Median follow‐up duration was 974 days (IQR 163 to 1830 days). Sixty‐four patients suffered an outcome event. Urate levels of greater than 0.42 mmol/L (p < 0.001) and an increasing NIHSS score (p < 0.001) independently predicted increased likelihood of suffering an event.

Conclusion

Elevated urate concentration is significantly and independently associated with increased risk of future vascular events in diabetic stroke patients. Further studies to elucidate the mechanism of this observation are required. Copyright © 2005 John Wiley & Sons, Ltd.
On conservative finite element formulations of the inviscid Boussinesq equations
Authors: Cliffe K. A.
Published: August 2005

The finite element discretization of the inviscid Boussinesq equations is studied with particular emphasis on the conservation properties of the discrete equations. Methods which conserve the total energy, total temperature and total temperature squared, or two of the above mentioned quantities, are presented. The effect of time discretization, and other numerical errors, on the conservation laws is considered. Finally, the theory is supported and illustrated by several numerical experiments.
A regular boundary element method for fluid flow
Authors: Patterson C. , Sheikh M. A.
Published: August 2005

The Boundary Element Method is now well established as a valid numerical technique for the solution of field problems, equal to the Finite Element Method in generality and surpassing it in computational efficiency in some cases.1 In this paper is presented a 'Regular Boundary Element Method' as applied to inviscid laminar fluid flow problems. It involves the formation of a system of regular integral equations obtained by moving the singularity outside the domain of the given problem. It is also shown that non‐conforming elements may be used whereby freedoms are not defined at the geometric nodes under the boundary element discretization. A linear element is developed here; higher order variants could easily be defined. Satisfactory numerical results have been obtained using the proposed regular method with both conventional (continuous across the boundary) and non‐conforming boundary elements for two‐dimensional inviscid laminar fluid flow problems having regular and singular solutions.
Numerical integration of the shallow water equations over a sloping shelf
Authors: Johns B.
Published: August 2005

A finite‐difference method is described for the numerical integration of the one‐dimensional shallow water equations over a sloping shelf that allows for a continuously moving shoreline. An application of the technique is made to the propagation of non‐breaking waves towards the shoreline. The results of the computation are compared with an evaluation based upon an exact analytical treatment of the non‐linear equations. Excellent agreement is found for both tsunami and tidal scale oscillations.
Surface tension driven flows in micro‐gravity conditions
Authors: Strani M. , Piva R.
Published: August 2005

The importance of convective flows generated by surface tension gradients, in comparison with the ones generated by other driving forces, has been investigated in connection with space technological applications involving fluid processes. A theoretical model of the boundary conditions at the interface, considered free and diffusive, has been derived in general tensor form to allow for the use of non orthogonal curvilinear co‐ordinates. For the study of flow fields contained in enclosures, these co‐ordinates are more suitable to fit all teh boundaries, in particular near the contact angle between the interface and the solid walls, thus giving more accurate numerical solutions.

A computational procedure to solve the complete set of bulk and surface equations is proposed and applied to a simplified two dimensional flow in a rectangular enclosure with a temperature gradient between the lateral walls. The numerical results show the importance of considering the interface to be deformable and diffusive for an accurate evaluation of the convective flow in the fluid bulk.
The application of the finite‐element method to meteorological simulations—a review
Authors: Staniforth A. N.
Published: August 2005

The application of the finite‐element method to the simulation of meterological fluid flow problems is reviewed. Early studies were aimed primarily at demonstrating the viability of the method for one‐ and two‐dimensional flows, whereas more recent studies have been aimed at demonstrating the efficiency and viability of the method for more complex three‐dimensional simulations. There has also been a shift towards exploiting such models to better understand and predict the underlying meteorological phenomena, rather than restricting attention to the development of the algorithms.
On the finite‐element calculation of turbulent flow using the k‐ϵ model
Authors: Smith R. M.
Published: August 2005

Although the finite‐element (FE) method has been successful in analysing complex laminar flows, a number of difficulties can arise when two‐equation turbulence models (e.g. the k‐ϵ model) are incorporated. This work describes a particular FE discretization of the k‐ϵ model and reports its performance in recirculating flow. Severe problems encountered in attempts to obtain convergence of the numerical scheme are isolated and analysed, and methods by which the problems can be overcome are suggested.

Insight gained in this work has enabled a practical turbulent flow FE code to be constructed which is robust and efficient. This code is the subject of a further paper.
A practical method of two‐equation turbulence modelling using finite elements
Authors: Smith R. M.
Published: August 2005

Incorporation of the k‐ϵ turbulence model into Galerkin finite‐element fluid‐flow codes (which, unlike upwind finite‐difference codes, have no artificial damping) can lead to severe iterative convergence difficulties. This paper introduces an alternative turbulence model (the q‐f model) and an associated finite‐element discretization method which are designed to overcome these problems. The new model forms the basis of a finite‐element fluid‐flow code which is robust and efficient. Furthermore, it is demonstrated on a practical example that the code can give good agreement with experiment on fairly coarse meshes.
A finite element method for the three‐dimensional non‐steady Navier‐Stokes equations
Authors: Mizukami A. , Tsuchiya M.
Published: August 2005

The algorithm for solving the three‐dimensional non‐steady Navier‐Stokes equations by the explicit forward Euler method is shown and the Galerkin finite element formulation is presented. As a numerical example, an entrace flow in a square duct is illustrated.
Numerical computations of critical flow over a weir
Authors: O'Carroll M. J. , Toro E. F.
Published: August 2005

Computing critical flows in hydraulics involves three problems in one: the internal flow problem, the location of the free surface and the determination of the critical flow rate. The subject can involve such difficulties as non‐uniqueness, non‐existence, ill‐conditioning and catastrophes.

This paper discusses the difficulties relating to computing critical flows over weirs. A new rapidly convergent method of determining the critical flow rate is presented and various results are shown using it with finite element discretization and with a new streamline shifting method. Numerical results are in good agreement with published data, both numerical and experimental.
Spline collocation approach to boundary value problems
Authors: Doctor H. D. , Bulsari A. B. , Kalthia N. L.
Published: August 2005

A well‐known Stokes problem is discussed by a cubic spline collocation method. Two consecutive cubic splines are obtained for the problem. The results by this method are compared with those of an orthogonal collocation method. The selection of the length of the subintervals of the range of the boundary value problem is also justified. The results obtained by these two methods are compared with the analytic solution. The methods involve simple algebra, and hence the calculations do not require the help of a computer. Necessary error analysis has been carried out.
Some explicit triangular finite element schemes for the Euler equations
Authors: Angrand Françoise , Dervieux Alain
Published: August 2005

Several explicit schemes are presented for triangular P0 and P1 finite elements. A first‐order accurate upwind P0 scheme is compared to a FLIC type method. A second‐order accurate Richtmyer scheme is constructed. Applications are given for the Euler system of conservation laws in the 2‐dimensional case.
On the interactions of surface waves with immersed structures
Authors: Bird H. W. K. , Shepherd R.
Published: August 2005

The fluid forces resulting from wave interaction with large submerged structures may be calculated using numerical procedures based on the solution of the associated boundary‐value problem. In this paper, the analysis of wave interaction with a fixed submerged object of arbitrary cross‐section and infinite length using a two‐dimensional boundary value formation based on linear diffraction theory is summarized. Subsequently, the application of the boundary element method to obtain a solution is presented. The numerical considerations are emphasized with particular reference to computational efficiency.

Numerical results are presented in the form of dimensionless wave force plots for various structural shapes. In the case of a bottom‐seated half cylinder, for which there exists a closed‐form solution, comparisons are made between results generated using both boundary element and equivalent finite element approaches. In the case of a submerged cylinder, comparisons are made between boundary element derived values and experimental results. The boundary element results compare well with both the closed‐form solution and the experimental values.
Prediction of periodic boundary layers
Authors: Menendez A. N. , Ramaprian B. R.
Published: August 2005

A relatively simple, yet efficient and accurate finite difference method is developed for the solution of the unsteady boundary layer equations for both laminar and turbulent flows. The numerical procedure is subjected to rigorous validation tests in the laminar case, comparing its predictions with exact analytical solutions, asymptotic solutions, and/or experimental results. Calculations of periodic laminar boundary layers are performed from low to very high oscillation frequencies, for small and large amplitudes, for zero as well as adverse time‐mean pressure gradients, and even in the presence of significant flow reversal. The numerical method is then applied to predict a relatively simple experimental periodic turbulent boundary layer, using two well‐known quasi‐steady closure models. The predictions are shown to be in good agreement with the measurements, thereby demonstrating the suitability of the present numerical scheme for handling periodic turbulent boundary layers. The method is thus a useful tool for the further development of turbulence models for more complex unsteady flows.
Diffraction of waves by semi‐infinite breakwater using finite and infinite elements
Authors: Bettess P. , Liang S. C. , Bettess J. A.
Published: August 2005

A finite and infinite element model is derived to predict wave patterns around a semi‐infinite breakwater in water of constant depth. Both circular and square meshes of elements are used. The wave theory used is that of Berkhoff. The appropriate boundary conditions for finite and infinite boundaries are described. The singularity in the velocity at the breakwater tip is modelled effectively using the technique of Henshell and Shaw originally developed in elasticity. The results agree well with the analytical solution. In addition the problem of waves incident upon a semi‐infinite breakwater and parabolic shoal, where both diffraction and refraction are present, is solved. There is no analytical solution for this case. The combination of finite and infinite elements is found to be an effective and accurate technique for such problems.
On some accurate finite‐difference methods for laminar flame calculations
Authors: Ramos J. I.
Published: August 2005

The ozone‐decomposition flame has been studied by means of fourth‐ and second‐order accurate schemes. The fourth‐order methods include a method of lines, a time‐linearization algorithm, and a majorant operatorsplitting technique. The second‐order schemes include two time‐linearization methods which use different temporal approximations. It is shown that the fourth‐order techniques yield comparable results to those obtained with very accurate finite element and adaptive grid finite‐difference algorithms. The results of the second‐order methods are in good agreement with second‐order explicit predictor‐corrector methods but predict a lower flame speed than that obtained by means of fourth‐order techniques. It is also shown that the temporal approximations are not as important as the spatial approximations in flame propagation problems characterized by the presence of several small time scales.
Efficient ADI and spline ADI methods for the steady‐state Navier‐Stokes equations
Authors: Napolitano Michele
Published: August 2005

The present paper provides an improved alternating direction implicit (ADI) technique as well as high‐order‐accurate spline ADI method for the numerical solution of steady two‐dimensional incompressible viscous flow problems. The vorticity‐stream function Navier‐Stokes equations are considered in a general curvilinear coordinate system, which maps an arbitrary two‐dimensional flow domain in the physical plane into a rectangle in the computational plane. The stream function equation is parabolized in time by means of a relaxation‐like time derivative and the steady state solution is obtained by a time‐marching ADI method requiring to solve only 2 × 2 block‐tridiagonal linear systems. The difference equations are written in incremental form; upwind differences are used for the incremental variables, for stability, whereas central differences approximate the non‐incremental terms, for accuracy, so that, at convergence, the solution is free of numerical viscosity and second‐order accurate. The high‐order‐accurate spline ADI technique proceeds in the same manner; in addition, at the end of each two‐sweep ADI cycle, the solution is corrected by means of a fifth‐order spline interpolating polynomial along each row and column of the computational grid, explicitly. The validity and the efficiency of the present methods are demonstrated by means of three test problems.
Pressure and time treatment for Chebyshev spectral solution of a Stokes problem
Authors: Deville M. , Kleiser L. , Montigny‐Rannou F.
Published: August 2005

To investigate the influences of time scheme, pressure treatment and initial conditions in incompressible fluid dynamics, a Stokes problem is solved numerically on a slab geometry within the framework of spectral approximation in space. Four algorithms are examined: splitting schemes, influence matrix method, penalty formulation and pseudo‐spectral space‐time technique. It is shown that splitting schemes are less accurate than the other processes. Furthermore, the initial field should respect a compatibility condition to avoid singularities at the initial time. If it is not possible to build such a compatible field, the numerical procedure has to present good damping properties at the first steps of the time integration.
Buoyancy effects on turbulent swirling flows
Authors: Takhar H. S. , Halim M. A.
Published: August 2005

A three‐parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time‐averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T′2. Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl.

The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results.
On the effect of flow direction on mixed convection from a horizontal cylinder
Authors: Badr H. M.
Published: August 2005

The influence of free stream direction on mixed (natural and forced) convective heat transfer from a circular cylinder is investigated. The cylinder, which has an isothermal surface, is placed with its axis horizontal and normal to the oncoming flow. The free stream direction varies between the vertically upward (parallel flow) and the vertically downward (contraflow) directions. The investigation is based on the time integration of the unsteady, two‐dimensional equations of motion and energy until reaching steady conditions. The study is limited to Reynolds numbers up to Re = 40 and Grashoff numbers of Gr = Re2. The results are compared with the available experimental data and the agreement is satisfactory.
Development and application of an adaptive finite element method to reaction‐diffusion equations
Authors: Ramos J. I.
Published: August 2005

An adaptive finite element method is developed and applied to study the ozone decomposition laminar flame. The method uses a semidiscrete, linear Galerkin approximation in which the size of the elements is controlled by an integral which minimizes the changes in mesh spacing. The sizes and locations of the elements are controlled by the location and magnitude of the largest temperature gradient. The numerical results obtained with this adaptive finite element method are compared with those obtained using fixed‐node finite‐difference schemes and an adaptive finite‐difference method. It is shown that the adaptive finite element method developed here using 36 elements can yield as accurate flame speeds as fourth‐order accurate, fixed‐node, finite‐difference methods when 272 collocation points are employed in the calculations.
Numerical calculation of equivalent moment of inertia for a fluid in a cylindrical container with partitions
Authors: Partom Ilya S.
Published: August 2005

A 3‐D numerical code was developed to solve the irrotational flow of an ideal fluid inside a moving cylindrical container with partitions. The problem is formulated in terms of two Poisson equations, the velocity equation and the pressure equation. These are expressed in terms of finite differences and solved by a procedure of line over relaxation. From the fluid pressure we computed the resultant moment on the container which was then expressed in terms of the equivalent moment of inertia. The code was checked against analytical results of Moiseyev and we found an agreement of 2–5 per cent even for a sparse mesh. We then demonstrated the capability of the code by computing the equivalent moment of inertia for various configurations with full and partial partitions.
Computation of high speed turbulent boundary‐layer flows using the k–ϵ turbulence model
Authors: Liakopoulos A.
Published: August 2005

The applicability of a finite element‐differential method to the computation of steady two‐dimensional low‐speed, transonic and supersonic turbulent boundary‐layer flows is investigated. The turbulence model chosen for the Reynolds shear stress and turbulent heat flux is the K‐ϵ two‐equation model. Calculations are extended up to the wall and the exact values of the dependent variables at the wall are used as boundary conditions. A number of transformations are carried out and the assumed solutions at a longitudinal station are represented by complete cubic spline functions. In essence, the method converts the governing partial differential equations into a system of ordinary differential equations by a weighted residuals method and invokes an ordinary differential equation solver for the numerical integration of the reduced initial‐value problem. The results of the computations reveal that the method is highly accurate and efficient. Furthermore, the accuracy and applicability of the k‐ϵ turbulence model are examined by comparing results of the computations with experimental data. The agreement is very good.
The addition of quasi‐three‐dimensional terms into a finite element method for transonic turbomachinery blade‐to‐blade flows
Authors: Cedar R. D. , Stow P.
Published: August 2005

This paper describes the extension of a purely two‐dimensional finite element method for the calculation of transonic turbomachinery blade‐to‐blade flows to include the quasi‐three‐dimensional terms. These terms account for the effect of variations in streamline radius, stream‐tube height and blade rotation.

By approximating the stream surface as a piecewise linear function, then using a local developed cone transformation on an element basis, the finite element equations are shown to remain of the same form as the two‐dimensional equations.

The numerical results presented demonstrate that the stream‐tube height, streamline radius and blade rotation terms must be included if the prediction of the Mach number distribution around a gas turbine blade is to be calculated correctly.
A finite element method for the solution of two‐dimensional transonic flows in cascades
Authors: Whitehead D. S. , Newton S. G.
Published: August 2005

Steady two‐dimensional transonic flow is calculated in cascades of compressor and turbine blades using a mesh of triangular finite elements. A velocity potential is used, the equations being solved by the Newton‐Raphson technique. The resulting computer program is fast, and is shown to give good accuracy. Shock waves are well represented, provided they are not too strong.
A numerical procedure for the generation of orthogonal body‐fitted co‐ordinate systems with direct determination of grid points on the boundary
Authors: Papantonis Dimitris E. , Athanassiadis Nicholas A.
Published: August 2005

The procedure proposed is based on the solution by finite difference means of a set of Laplace's equations, by the application of a relaxation method.

The curvilinear orthogonal grid so generated is fitted to a 2‐D physical domain with closed boundary and the contribution of the present work consists in the arbitrary choice of grid points on two adjacent boundaries, in order to achieve the desired density of grid points where the geometry of the boundaries varies rapidly.

The method proposed is rapid and stable. Some characteristic examples are finally presented.
A review of some finite element methods to solve the stationary Navier‐Stokes equations
Authors: Segal A.
Published: August 2005

In this paper the integrated solution approach, the penalty function approach and the solenoidal approach for the finite element solution of the stationary Navier‐Stokes equations are compared. It is shown that both the penalty function approach and the solenoidal approach compare favourably to the integrated solution method. For fine meshes the solenoidal approach appears to be the cheapest method.
Application of the DuFort‐Frankel and Saul'ev methods with time splitting to the formulation of a three dimensional hydrodynamic sea model
Authors: Davies Alan M.
Published: August 2005

A three dimensional hydrodynamic sea model of an arbitrary sea area is formulated using sigma co‐ordinates in the vertical. The solution of the equations using finite difference grids in the horizontal and the vertical is described.

Discretization of the vertical viscosity term in the hydrodynamic equations using the DuFort‐Frankel and Saul'ev methods is developed. Some numerical instabilities occur with the DuFort‐Frankel method which can be overcome by splitting the hydrodynamic equations into equations describing the mean flow and equations describing the deviations from it. The computational advantages of solving these equations with different time steps are discussed.

The accuracy and stability of the various methods is demonstrated for wind induced flow in a simple rectangular basin having dimensions representing the North Sea.
Application of the Dorodnitsyn finite element method to swirling boundary layer flow
Authors: Fletcher C. A. J.
Published: August 2005

The Dorodnitsyn finite element method for turbulent boundary layer flow with surface mass transfer is extended to include axisymmetric swirling internal boundary layer flow. Turbulence effects are represented by the two‐layer eddy viscosity model of Cebeci and Smith1 with extensions to allow for the effect of swirl. The method is applied to duct entry flow and a 10 degree included‐angle conical diffuser, and produces results in close agreement with experimental measurements with only 11 grid points across the boundary layer. The introduction of swirl (we/ue = 0.4) is found to have little effect on the axial skin friction in either a slightly favourable or adverse pressure gradient, but does cause an increase in the displacement area for an adverse pressure gradient. Surface mass transfer (blowing or suction) causes a substantial reduction (blowing) in axial skin friction and an increase in the displacement area. Both suction and the adverse pressure gradient have little influence on the circumferential velocity and shear stress components. Consequently in an adverse pressure gradient the flow direction adjacent to the wall is expected to approach the circumferential direction at some downstream location.
Conforming finite element computations applied to a spatially periodic, harmonic Navier‐Stokes problem
Authors: Borne Lionel , Chambon René , Auriault Jean‐Louis
Published: August 2005

In this paper computations in the two dimensional case of a harmonic Navier‐Stokes problem with periodic boundary conditions are presented. This study of an incompressible viscous fluid leads to a non‐symmetric linear problem (very low Reynolds number). Moreover unknown functions have complex values (monochromatic dynamic behaviour). Numerical treatment of the incompressibility condition is a generalization of the classical treatment of Stokes problem. A mixed formulation, where discrete pressure plays the role of Lagrange multipliers is used (Uzawa algorithm).

Two conforming finite element methods are tested on different meshes. The second one uses a classical refinement in the shape function: the so‐called bulb function. All computational tests show that the use of a bulb function on each element gives better results than refinement in the mesh without introducing too many degrees of freedom. Finally numerical results are compared to experimental data.
Isothermal flow past a blowing sphere
Authors: Cliffe K. A. , Lever D. A.
Published: August 2005

Steady, axisymmetric, isothermal, incompressible flow past a sphere with uniform blowing out of the surface is investigated for Reynolds numbers in the range 1 to 100 and surface velocities up to 10 times the free stream value. A stream‐function‐velocity formulation of the flow equations in spherical polar co‐ordinates is used and the equations are solved by a Galerkin finite‐element method. Reductions in the drag coefficients arising from blowing are computed and the effects on the viscous and pressure contributions to the drag considered. Changes in the surface pressure, surface vorticity and flow patterns for two values of the Reynolds number (1 and 40) are examined in greater detail. Particular attention is paid to the perturbation to the flow field far from the sphere.
A transient solution method for the finite element incompressible Navier‐Stokes equations
Authors: Yoshida Yutaka , Nomura Takashi
Published: August 2005

A numerical procedure for solving the time‐dependent, incompressible Navier‐Stokes equations is presented. The present method is based on a set of finite element equations of the primitive variable formulation, and a direct time integration method which has unique features in its formulation as well as in its evaluation of the contribution of external functions. Particular processes regarding the continuity conditions and the boundary conditions lead to a set of non‐linear recurrence equations which represent evolution of the velocities and the pressures under the incompressibility constraint. An iteration process as to the non‐linear convective terms is performed until the convergence is achieved in every integration step. Excessively artificial techniques are not introduced into the present solution procedure. Numerical examples with vortex shedding behind a rectangular cylinder are presented to illustrate the features of the proposed method. The calculated results are compared with experimental data and visualized flow fields in literature.
An efficient matrix solver for finite‐element analysis of non‐Newtonian fluid flow problems
Authors: Liu Ta‐Jo
Published: August 2005

When the Galerkin finite‐element method with a nine‐node isoparametric Lagrangian element is applied to solve non‐Newtonian fluid flow problems, a considerable amount of computing time is required to solve the discretized non‐linear system of equations by Newton's method. A method proposed by Broyden has been modified to compute the Jacobian matrix associated with Newton's method. This modified Broyden's method can be combined with the frontal method to efficiently solve the linearized finite‐element equations during the iteration. Numerical results of a sample problem concerning the determination of the pressure‐drop/flow‐rate relationship for power‐law fluids in rectangular ducts show that the application of this new method can reduce computing time substantially.