bluuebunny/crossref_metadata_2025 huggingface dataset:
Statistical analysis for static responses of structures with stochastic shape
Authors: Liu Hanbing , Chen Su‐Huan
Published: August 2005

The paper presents a probabilistic boundary element method for analysis of structural responses to static loading, when the shape parameters of structures are considered as random variables. We can use this method to evaluate the mean values and standard deviations of the responses, and estimate the stochastic errors of structural character resulting from manufacturing errors.
Finite element solution of steady natural convection equations by a false diffusion method
Authors: Sen Swarnendu , Sarkar A.
Published: August 2005

Use of upwind finite element methods was so far confined to forced convection problems. The present work is devoted to the application of false diffusion techniques to phenomena involving natural convection. A range of Rayleigh numbers in which the discretization by the conventional Galerkin scheme fails is considered. A false diffusion method similar to the Streamline upwind technique has been employed to avoid cross‐wind diffusion. The upwind parameter is changed continually until a true solution is obtained. The present scheme provides convenient means for obtaining gradually improved guesses from which a more accurate solution can be obtained using the conventional Galerkin method. The criterion for the determination of a true solution is established, and hot‐wall Nusselt number values are documented in tabular form.
Incompressibility and axisymmetry: A modified B method
Authors: Jinka Ashoka G. K. , Lewis Roland W.
Published: August 2005

The paper deals with a B‐type strain projection method with specific reference to axisymmetric incompressible solids. Essentially the \documentclass{article}\pagestyle{empty}\begin{document}$ \overline{\overline {\rm{B}}} $\end{document} (B double bar) method, which is reported in the present study, is based on Hughes' B‐bar approach utilizing modified shape functions to represent the radial displacement and geometry. As a consequence of adopting these procedures the \documentclass{article}\pagestyle{empty}\begin{document}$ \overline{\overline {\rm{B}}} $\end{document} method results in an exact satisfaction of incompressibility constraints. The rationale of the \documentclass{article}\pagestyle{empty}\begin{document}$ \overline{\overline {\rm{B}}} $\end{document} method leads to the modified mean‐dilatation approach for the case of an axisymmetric incompressible problem. It is interesting to note in the present work that the explicit influence of enhanced hoop strain is eliminated from the discrete divergence condition.
Finite‐deformation interface formulation for frictionless contact problems
Authors: Kowalczyk Piotr
Published: August 2005

An interface finite element for non‐linear analysis of frictionless contact problems is presented. A constitutive equation relates stresses in the interface layer to the deformation gradient with respect to an imaginary reference configuration where the layer thickness is constant and finite. The equation of equilibrium is written in the same configuration, while the boundary conditions involve stresses related to an actual reference configuration used in the formulation for the contacting bodies. Finite element discretization is introduced for the layer in order to calculate the unknown field of displacements. Computational examples demonstrate properties of the contact element and its range of applicability in the analysis of large deformation contact problems including relative sliding of curved surfaces.
A BEM formulation of new boundary stress components
Authors: Xiao‐Yan Lei
Published: August 2005

The paper presents boundary integral equation to two‐dimensional elasticity with the stress component σijtitj as one of the boundary values, where ti are direction cosines of the tangent on the boundary. This form of BEM has an advantage in that the stress component σijtitj on the boundary can be calculated directly from the numerical solution. The present formulation for planar problems uses two kernels, one of which is logarithmic singular and the other is 1/r singular. The effectiveness of the approach is also discussed through some test examples.
Numerical viscosities of difference schemes
Authors: Ramshaw John D.
Published: August 2005

Numerical viscosities of finite‐difference schemes are usually obtained from truncation‐error analyses based on Taylor series expansions. Here we observe that numerical viscosities can also be obtained very simply and directly from the growth factor ξ in a conventional Fourier stability analysis. A general formula is derived for the numerical viscosity in terms of the first and second derivatives of ξ with respect to the wavenumber k, evaluated at k = 0. A single Fourier analysis therefore suffices to determine both stability limits and numerical viscosities.
Higher‐order numerical methods for third‐order non‐linear boundary value problems
Authors: Tirmizi Ikram A.
Published: August 2005

A sixth‐order and a ninth‐order method are developed for the numerical solution of special non‐linear third‐order boundary value problems y‴ = ø(x,y), a< x < b, y(a) = A1, y″(a) = B2 and y(b) = A2. The method arise from a four‐point recurrence relation. Convergence analysis of the sixth‐order method is discussed. The methods are tested on a problem. Modification to these methods are obtained for problems with boundary conditions of the form y(a) = A1, y'(a) = B1 and y(b) = A2.
Further developments towards a new virtual‐pulse time integral methodology for general non‐linear transient thermal analysis
Authors: Tamma K. K. , Chen X. , Sha D.
Published: August 2005

New developments of describing the theoretical basis towards an effective virtual‐pulse (VIP) time integral methodology are proposed for general non‐linear transient heat transfer problems. Primarily to validate the proposed methodology of computation, simple numerical test cases are provided and comparisons are also drawn with the implicit second‐order‐accurate Crank‐Nicolson method. For the models tested, the proposed method has comparable or improved accuracy and stability characteristics. The VIP methodology introduced here for tackling non‐linear thermal problems offers attractive features and is a viable alternative to traditional time‐stepping practices. Efforts are underway to demonstrate the practical applicability to multi‐dimensional thermal analysis.
A new type of B3‐spline interpolation
Authors: van Erp G. M. , Yuen S. W. , Swannell P.
Published: August 2005

A new type of B3‐spline interpolation is presented. This new formulation allows the user to introduce interior point and line supports in much the same way as in a conventional finite element formulation. The bandedness and efficiency of the standard B3‐spline interpolation are retained. The new formulation can be incorporated into existing B3‐spline formulations with very little effort. Several examples are presented to demonstrate the versatility of the new approach.
A note on the calculation of consistent tangent operators for Von Mises and Drucker‐Prager plasticity
Authors: De Borst René , Groen Arend E.
Published: August 2005

A comparison is made of implementations of consistent tangent operators that arise in implicit integration of Von Mises and Drucker‐Prager yield criteria. When computing the consistent tangent operator a matrix inversion has to be performed at integration point level. The consequences of different formulations of the consistent tangent operator on the numerical accuracy are assessed.
Application of the spline prism method to analyse vibration of thick rectangular plates with two opposite edges simply supported
Authors: Mizusawa T. , Takagi S.
Published: August 2005

The paper presents an application of the spline prism method to analyse vibration of isotropic, thick rectangular plates with two opposite edges simply supported. Three‐dimensional spline prism models are formulated by combining B‐spline functions with beam eigenfunctions. Because of the orthogonality of the beam functions, three‐dimensional problems are reduced to a series of two‐dimensional ones. To demonstrate the accuracy and convergence of the semi‐numerical method, the results are compared with those obtained by other numerical methods. Good convergence and accuracy are obtained. The effects of the ratio of thickness to width and the aspect ratio on the frequencies of thick rectangular plates with several boundary conditions are analysed, and the results are compared with those calculated by the Mindlin plate theory.
Analytical solutions of mass transport problems for error estimation of finite/infinite element methods
Authors: Zhao Chongbin , Steven G. P.
Published: August 2005

In order to make an exact estimation of discretization error for finite/infinite element methods, it is necessary to develop analytical solutions for some transient mass transport problems in infinite media. These transient mass transport problems may be viewed as the benchmark problems for the discretization error estimation of a new numerical method so that they generally have the following characteristics: (1) their initial and boundary conditions can be exactly modelled by the finite/infinite element method; (2) their solutions can be rigorously expressed in a closed form. In this paper, several of the aforementioned problems have been constructed and solved mathematically for transient mass transport problems in both 1D and 2D infinite media.
Inflow and outflow boundary conditions in the finite element solution of the streamfunction–vorticity equations
Authors: Manzan M. , Comini G.
Published: August 2005

The appropriate specification of boundary conditions is the main difficulty in the finite element solution of the streamfunction–vorticity equations for two‐dimensional incompressible laminar flows. In this context, we show that the appropriate specification of both the outflow and the inflow boundary conditions is required for the successful modelling of two well known test problems.
A B‐spline finite element method for the regularized long wave equation
Authors: Gardner L. R. T. , Gardner G. A. , Dag I.
Published: August 2005

A B‐spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method with quadratic B‐spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution range. Time integration of the resulting system of ordinary differential equations is effected using a Crank‐Nicolson approximation. Standard problems are used to validate the algorithm, which is then used to model the smooth development of an undular bore.
Modified calculation of the dissipation term in thermoplastic finite element equations
Authors: Szabó László , Varga Imre
Published: August 2005

In the paper, a simple modification of the internal dissipation term in coupled thermoplastic finite element equations is presented. A modified form of the heat capacity and the thermomechanical coupling matrices are derived. These modifications are based on a decomposition of the internal dissipation term into two parts, which depend on the total strain rate and the rate of temperature change, respectively.
A quadratic boundary element for potential problems in 2D with no numerical integration
Authors: Verhoeven N. A. , Morgan K.
Published: August 2005

Both the logarithmic and derivative kernel integrations for potential problems, solved with quadratic isoparametric boundary elements, contain quartic functions of the integration parameter. It is shown that such functions can be written as the product of two quadratic functions with real coefficients. The derivative kernel integration is then represented as the sum of two integrals, which can be evaluated analytically. The logarithmic kernel integration can be similarly split but needs a Taylor series expansion of the Jacobian of the integration to enable analytical integration. The use of this Taylor series expansion means that the method presented is limited to problems involving weakly curved elements.
Discrete element dynamic response of elastoplastic shells subjected to impulsive loading
Authors: Riera Jorge D. , Iturrioz Ignacio
Published: August 2005

The determination of the dynamic response of plate and shell structures is carried out employing a discrete representation of the continuum, associated with an explicit integration scheme in the time domain. Comparisons with experimental results certify the accuracy and reliability of the proposed method.
A Fourier boundary integral method for solving Laplace's equation in two dimensions
Authors: Huestis Stephen P.
Published: August 2005

Laplace's equation in two dimensions can be solved by a boundary integral method which imposes the required consistency relation between the boundary function and its outward normal gradient. Rather than incorporating this into a standard boundary element approach for the Dirichlet problem, the known boundary function and the unknown boundary gradient are here expressed as truncated Fourier series expansions. The consistency relation then becomes an algebraic relation between expansion coefficients, whose matrix entries can be found by appropriate applications of the fast Fourier transform. This is solved for the boundary gradient coefficients; the solution can then be evaluated at any interior point. Numerical experiments explore the effect of the truncation level, and indicate that reasonable accuracy can be attained without needing a prohibitively large number of Fourier coefficients.
Solution of multiple‐edge crack problem of elastic half‐plane by using singular integral equation approach
Authors: Chen Y. Z. , Hasebe Norio
Published: August 2005

The complex potential for a single‐edge crack problem of an elastic half‐plane is proposed. The complex potential is obtained by distributing the dislocation density along the crack configuration, and satisfies the traction‐free condition along the boundary of the half‐plane. The multiple‐edge crack problem of an elastic half‐plane can be considered as a superposition of many single‐edge crack problems. Bearing this in mind, a singular integral equation for the multiple‐edge crack problem is formulated, where the distributing dislocation density serves as the unknown function and the traction applied on the crack faces serves as the right‐hand side in the resulting integral equation. A semi‐open quadrature rule is used to solve the singular integral equation. Several numerical examples are given. The ‘shadow effect’ is observed, which means the stress intensity factor at a crack tip is negligible if the crack is placed in some particular ‘shadow area’.
Improved element stresses for node and element patches using superconvergent patch recovery
Authors: Wiberg N.‐E. , Abdulwahab F. , Ziukas S.
Published: August 2005

Methods to calculate improved postprocessed stresses in elements for the superconvergent patch recovery technique are developed. Based on improved stresses on node patches, the improved element stresses are obtained by using weighting of patch solutions from different patch assembly points. An alternative method is to directly calculate the element stresses for an element patch based on weighted information. Numerical examples show that the performances of the two procedures are of about the same quality.
A new boundary element/mathematical programming method for contact problems with friction
Authors: Zhu Changming
Published: August 2005

The contact condition is described as a linear complementarity form with penalty parameters. Based on the boundary element discretization, a mathematical programming method for elastic contact problems with friction is presented. This method avoids the tiresome iterative procedures used in previous work and, if there is no unloading, only one incremental step is necessary for a solution. Two examples are given to demonstrate the correctness and effectiveness of the method.
A special incremental–iterative solution technique for non‐linear structural analysis including snap‐through
Authors: Ravichandran R. V. , Sridharan S.
Published: August 2005

A special incremental‐iterative solution method for non‐linear finite element structural analysis including snap‐through is presented. As an alternative to the direct solution methods, a special iterative strategy along with the pseudoload method is employed within each Newton‐Raphson iteration step. Two new developments concerning the pseudoload method and the special iterative strategy, which were originally conceived and applied for the non‐linear analysis of shells of revolution using a semi‐analytical method, are presented. Firstly, the underlying principles of the method are utilized in solving general non‐linear structural mechanics problems. Secondly, the capability of the method is enhanced for tracing the load‐displacement curve beyond the critical load by integrating the arc length method. Special modifications are proposed to handle situations with a non‐positive‐definite tangential stiffness matrix. Numerical examples with snap‐through and snap‐back phases in the load‐deflection path are presented to demonstrate the applicability and accuracy of this approach. Results obtained from this numerical study verify the usefulness of this method as an alternative to the conventional direct methods or iterative methods of solving linearized equations in an incremental non‐linear analysis.
Free and forced vibrations of a Timoshenko beam with any number of translational and rotational springs and lumped masses
Authors: Wu Jong‐Shyong , Huang Chang‐Guey
Published: August 2005

The free vibration and the forced dynamic responses of a uniform cantilever Timoshenko beam carrying any number of concentrated masses, translational and rotational springs and subjected to various external loadings are studied by means of the analytical‐and‐numerical‐combined method (ANCM), where the locations and the magnitudes of the masses, springs and loadings are arbitrary. First of all, the (exact) closed‐form solutions for the natural frequencies and the normal mode shapes of the ‘unconstrained’ Timoshenko beam (without carrying any concentrated elements) are determined; then the eigenvalue equation for free vibration analysis and the equation of motion for forced vibration analysis of the ‘constrained’ Timoshenko beam (carrying the prescribed concentrated elements) are derived analytically by applying the expansion theorem and the mode superposition methodology; finally the approximate natural frequencies and mode shapes of the ‘constrained’ Timoshenko beam and its dynamic responses due to external excitations are calculated numerically. It is found that the ANCM presented in the paper has the advantages of both the pure analytical method (to be able to save computing time) and the pure numerical method (to be able to solve various practical problems).
A generalized Newton–Raphson method using curvature
Authors: Lee In‐Won , Jung Gil‐Ho
Published: August 2005

A numerical method for finding the roots of any function is developed. This method considers a circle using the concept of curvature instead of the tangential line in the Newton‐Raphson method. The compared results between the proposed method and the Newton‐Raphson method are listed. The proposed method has a wider convergent region of initial points and finds more proper solutions than the Newton‐Raphson method. In particular, the paper proposes that the curvature method is replaced by the modified Newton method discussed by Ralston in dealing with multiple roots.
Comparison of three commercially available antibodies for flow cytometric monitoring of P‐glycoprotein expression in tumor cells
Authors: Krishan Awtar , Sauerteig Antonieta , Stein Jeanne H.
Published: August 2005

Cellular drug resistance to natural products is often due to the presence of an efflux pump which reduces intracellular drug content and chemosensitivity. A 170 kD cell surface resident P‐glycoprotein is believed to act as the efflux pump. In the present report, we have compared three commercially available antibodies C‐219, JSB‐1, and mdr(Ab‐1) for use in flow cytometric detection of P‐glycoprotein positive cells. Our data show that C219 gives uniformly good results in a variety of murine and human tumor cell lines for detection of P‐glycoprotein positive cells. We have also compared data of C219 stained cells analyzed in parallel on a flow cytometer equipped with a small laser (15 mW) and a large laser (5 watt) cell sorter. Data obtained on these two instruments are comparable. A staining protocol and data on dual staining of cells for DNA content by propidium iodide and P‐glycoprotein expression after FITC labeling are also presented.
Flow cytometric and biochemical analysis of dose‐dependent effects of sodium butyrate on human endometrial adenocarcinoma cells
Authors: Saito Satoshi , Crissman Harry A. , Nishijima Mitsushige , Kagabu Teruo , Nishiya Iwao , Cram L. Scott
Published: August 2005

Sodium butyrate (SB) treatment was previously shown to produce seven‐fold increases in estrogen hormone receptor binding sites of human endometrial adenocarcinoma (IK) cells. Flow cytometric analysis and histone gel electrophoresis were used to examine cell cycle, cell metabolism, and nuclear histone fractions in IK cells treated with different concentrations of SB. SB‐treated cells stained with fluorochromes specific for DNA, RNA, or general protein were analyzed by flow cytometry (FCM).

Changes in accessibility to three DNA stains and gel electrophoresis were used to analyze rearrangements in chromatin structure. SB caused an accumulation of cells in the G1 phase and inhibited DNA synthesis, but not cellular levels of RNA and protein. Hoechst accessibility to A‐T rich regions on DNA was dramatically increased after removal of SB. H1 histones were dephosphorylated and core histones were acetylated during SB‐treatment.

Information obtained in these studies may be useful for correlating cellular and biochemical events with SB‐induced increases in nuclear steroid hormone binding sites.
Mono and Bridged Azolium Picrates as Energetic Salts
Authors: Jin Chuan‐Ming , Ye Chengfeng , Piekarski Crystal , Twamley Brendan , Shreeve Jean’ne M.
Published: August 2005

The energetic mono and bridged imidazolium, triazolium and tetrazolium picrates 7–10, 14, and 16, the dipicrates 23, 25, and 26 and the dinitrates 24, and 27 were synthesized by the quaternization of azolium derivatives (1, 2, 13, 15, 19 and 20) with picric acid and nitric acid or by metathesis of the corresponding quaternary salts (3, 6, 21 and 22) with silver picrate or silver nitrate. The structures of 14 and 16 were determined by single‐crystal X‐ray diffraction analysis confirming quaterization on the triazolium and tetrazolium rings. Their physical and thermodynamic properties were determined. In some cases, the salts are thermally stable to ca. 300 °C and they exhibit densities averaging ca. 1.6 g/cm3. Nearly all have positive heats of formation with the highest calculated value, ΔfHom = 611.6 kJ/mol, found for 3‐azido‐1,4‐dimethyl‐1,2,4‐triazolium picrate (10). (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005)
The cause and cure (!) of the spurious pressures generated by certain fem solutions of the incompressible Navier‐Stokes equations: Part 2
Authors: Sani R. L. , Gresho P. M. , Lee R. L. , Grifftths D. F. , Engelman M.
Published: August 2005

The spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier‐Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two‐dimensions and one element in three‐dimensions. The automatic pressure filter associated with the penalty method is also explained. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.
Hermitian space‐time finite elements for estuarine mass transport
Authors: Sobey R. J.
Published: August 2005

Space‐time finite element solutions of the convection–dispersion equation using higher‐order nodal continuity and Hermitian polynomial shape functions are described. Five separate elements ranging from a complete linear element with C0,0 nodal continuity to a complete first‐order Hermitian element with C1,1 nodal continuity are subjected to detailed analysis. Wave deformation analyses identify the source of leading or trailing edge oscillations, trailing edge oscillations being the major source of difficulty. These observations are confirmed by numerical experiments which further demonstrate the potential of higher‐order nodal continuity. The performance of the complete first‐order Hermitian element is quite satisfactory and measurably superior to the linear element.
Finite element, stream function–vorticity solution of steady laminar natural convection
Authors: Stevens W. N. R.
Published: August 2005

Stream function–vorticity finite element solution of two‐dimensional incompressible viscous flow and natural convection is considered. Steady state solutions of the natural convection problem have been obtained for a wide range of the two independent parameters. Use of boundary vorticity formulae or iterative satisfaction of the no‐slip boundary condition is avoided by application of the finite element discretization and a displacement of the appropriate discrete equations. Solution is obtained by Newton–Raphson iteration of all equations simultaneously. The method then appears to give a steady solution whenever the flow is physically steady, but it does not give a steady solution when the flow is physically unsteady. In particular, no form of asymmetric differencing is required. The method offers a degree of economy over primitive variable formulations. Physical results are given for the square cavity convection problem. The paper also reports on earlier work in which the most commonly used boundary vorticity formula was found not to satisfy the no‐slip condition, and in which segregated solution procedures were attempted with very minimal success.
Turbulent heat transfer via the F.E.M.: Heat transfer in rod bundles
Authors: Taylor C. , Thomas C. E. , Morgan K.
Published: August 2005

Heat transfer associated with forced convection between bundles of cylindrical fuel rods is analysed using the finite element method. A subchannel technique is employed and the numerical results are compared with previous experimental and numerical values. The solid and fluid zones are analysed, for temperature distribution, as a single domain.
An ‘assumed deviatoric stress–pressure–velocity’ mixed finite element method for unsteady, convective, incompressible viscous flow: Part I: Theoretical development
Authors: Yang Chien‐Tung , Atluri Satya N.
Published: August 2005

A formulation of a mixed finite element method for the analysis of unsteady, convective, incompressible viscous flow is presented in which: (i) the deviatoric‐stress, pressure, and velocity are discretized in each element, (ii) the deviatoric stress and pressure are subject to the constraint of the homogeneous momentum balance condition in each element, a priori, (iii) the convective acceleration is treated by the conventional Galerkin approach, (iv) the finite element system of equations involves only the constant term of the pressure field (which can otherwise be an arbitrary polynomial) in each element, in addition to the nodal velocities, and (v) all integrations are performed by the necessary order quadrature rules. A fundamental analysis of the stability of the numerical scheme is presented. The method is easily applicable to 3‐dimensional problems. However, solutions to several problems of 2‐dimensional Navier‐Stokes' flow, and their comparisons with available solutions in terms of accuracy and efficiency, are discussed in detail in Part II of this paper.
Free surface wave motions and interactions
Authors: Miner E. W. , Fritts M. J. , Griffin O. M. , Ramberg S. E.
Published: August 2005

This paper investigates the problems involved in the numerical simulation of free surface wave motions and surface wave effects on marine structures. Various approaches that might be taken in meeting these problems are discussed, and their relative advantages and disadvantages are considered. One particular approach combines a Lagrangian formulation of the governing equations, a triangular grid and a finite‐difference solution procedure. Since this approach has some distinct advantages in the numerical calculation of fluid flows which include a free surface, it formed the basis for the development of one particular computer code, SPLISH. Sufficient progress has been made with the SPLISH code to demonstrate the attractiveness of numerical calculations for wave flow problems. Recent computational results demonstrate that realistic time‐varying local flow fields, pressures and forces on and near structures such as a half‐cyclinder on the ocean floor can be determined from numerical calculations for certain conditions. Good agreement is found in comparison of the numerical results from SPLISH, recent linear wave Green's function and fifth‐order asymptotic solutions for wave motion over a bottom seated half‐cylinder, and an experimental simulation in a wave channel.
A transient finite element analysis of natural convection around a horizontal hot cylinder
Authors: Miyauchi Yasuyuki , Masuda Michio , Shimizu Masatsugu
Published: August 2005

This paper presents an advanced method for a 2‐dimensional analysis of transient natural convection by finite element method. The present method, based on stream function—vorticity formulation, could get rid of numerical errors and constraint of perpendicular mesh subdivision, since we excluded a finite difference approximation of vorticity on no‐slip boundaries. A considerable effect of upwind weighting function was examined. The method was successfully applied to a problem of natural convection around a horizontal hot cylinder.
A modified dodge algorithm for the parabolized Navier–Stokes equations and compressible duct flows
Authors: Cooke C. H. , Dwoyer Douglas M.
Published: August 2005

A revised version of Dodge's split‐velocity method for numerical calculation of compressible duct flow has been developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front‐to‐back continuity during the calculation. The (chequerboard) zebra algorithm is applied to solution of the three‐dimensional continuity equation in conservative form. A second‐order A‐stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A chequerboard iteration is ued to solve the resulting implicit non‐linear systems of finite‐difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results has been obtained for some flows with well‐known solutions.
A multi‐vortex model of leading‐edge vortex flows
Authors: Peace A. J.
Published: August 2005

A multi‐vortex model of the vortex sheets shed from the sharp leading edges of slender wings is considered. The method, which is developed within the framework of slender‐body theory, is designed to deal with those situations in which more than one centre of rotation is formed on the wing, for example on a slender wing with lengthwise camber or with a strake. Numerical results are presented, firstly for situations where comparison can be made with a vortex sheet model and secondly for cases, such as those described above, where a vortex sheet model is unable to describe the flow. Where comparison is available, agreement is good and in the cases where more than one vortex system is present interesting interactions are obtained.
Fractional step algorithm for estuarine mass transport
Authors: Sobey R. J.
Published: August 2005

A successful and economical fractional step algorithm for the convection‐dispersion‐reaction equation is described. Exact solutions are adopted for the reaction and convection steps, the latter by the introduction of a moving co‐ordinate system. The dispersion step uses an optimized finite difference algorithm which specifically accommodates the grid non‐uniformity. The excellent performance of the algorithm is confirmed by numerical experiments together with computations of the Fourier response and integrated square error characteristics.
Application of a high accuracy finite difference technique to steady, free surface flow problems
Authors: Chapman Raymond S. , Kuo Chin Y.
Published: August 2005

The spatially third‐order accurate QUICK finite difference technique is applied to the solution of the depth‐integrated equations of motion for steady, subcritical, free surface flow in a wide, shallow, rectangular channel with and without an abrupt expansion. The conservative, control‐volume discretization of the equations of motion and the use of QUICK in approximating required cell and cell face average quantities is discussed. Results presented show that it is possible to obtain stable solutions for advective free surface flows without resorting to implicit numerical smoothing.
Numerical modelling of wind flow over buildings in two dimensions
Authors: Hanson T. , Summers D. M. , Wilson C. B.
Published: August 2005

Numerical solutions to the Navier–Stokes equation may provide designers with predictions of the wind environment of buildings under design. To investigate this possibility, two complementary solution procedures are implemented for two‐dimensional geometry: a random vortex method to depict the flow evolution, and a control volume method to depict the steady flow field. These are both illustrated by specific application to the case of a building form with a roof of arbitrary pitch.
Selective lumping finite element method for nearshore current
Authors: Kawahara Mutsuto , Kashiyama Kazuo
Published: August 2005

A finite element method for the analysis of nearshore current, which is one of the principal currents in coastal seas, is presented in this paper. Because the nearshore current is induced by the variable distribution of the surface waves, it is necessary to analyse two main characteristics of the wave, i.e. direction and height. The current can be computed using the resulting wave characteristics. The present method makes it possible to employ procedures for which the same methods of solution are applicable for all basic equations of wave direction, height and current flow. The linear interpolation function is used for the discretization of spatial variables and a selective lumping two step explicit scheme is employed for the numerical integration in time. The numerical solutions obtained are compared with analytical, experimental and observed ones. From these comparative studies, it is concluded that the present finite element method provide a useful tool for the analysis of nearshore current.
Simulations of flows and water depth in a dendritic river system
Authors: Yeh G. T.
Published: August 2005

This paper presents the development of a channel hydrodynamic model for simulating the behaviour of flows and water depths in a river network that may consist of any number of joined and branched rivers/streams, including both tidal and non‐tidal rivers. The model employs a numerical method—an integrated compartment method (ICM). The method greatly facilitates the set‐up of algebraic equations for the discrete field approximating the corresponding continuous field.

Most of the possible boundary conditions that may be anticipated in real‐world problems are considered. These include junctions, prescribed flow, prescribed water depth (or cross‐sectional area), and rating curve boundaries. The use of ICM makes the implementation of these four types of boundary conditions relatively easy.

The model is applied to two case studies: first to a single river and then to a network of five river branches in a watershed. Results indicate that the model can simulate the behaviour of the hydrodynamic variables that are required to compute chemical transport in a river‐stream network.
A finite element method to solve the Navier‐Stokes equations using the method of characteristics
Authors: Huffenus J. P. , Khaletzky D.
Published: August 2005

We present a simple and efficient finite element method to solve the Navier‐Stokes equations in primitive variables V, p. It uses (a) an explicit advection step, by upwind differencing. Improvement with regard to the classical upwind differencing scheme of the first order is realized by accurate calculation of the characteristic curve across several elements, and higher order interpolation; (b) an implicit diffusion step, avoiding any theoretical limitation on the time increment, and (c) determination of the pressure field by solving the Poisson equation. Two laminar flow calculations are presented and compared to available numerical and experimental results.
A collocation method for convection dominated flows
Authors: Chawla T. C. , Leaf G. , Minkowycz W. J.
Published: August 2005

A collocation method based on multiple regions with moving boundaries placed in a flow field in which convection effects dominate, is proposed. By making the moving boundaries of the regions coincide with moving sharp fronts present in the solution of convection dominated problems, and thereby allowing higher concentration of meshes to be placed about the fronts, the proposed method is able to achieve very high accuracy. By having a moving mesh, the Peclet number characterizing the flow field depends upon velocity relative to a moving mesh in a region. Consequently by choosing proper velocities of the moving boundaries, the value of this Peclet number can be made as small as desired. The traditional collocation method based on centred discretization, when applied to each region in the field, produces oscillation free solutions even when the values of Peclet number based on absolute velocity are extremely large. In view of these characteristics the method appears to be an excellent candidate for the solution of any two‐phase flow problem containing sharp fronts.
On the accuracy of boundary fitted finite‐difference calculations
Authors: Ferreri J. C. , Ventura M. A.
Published: August 2005

A description is given of the effects of the discretization of the domain of integration on the accuracy of the results obtained with boundary‐fitted finite differences. Three‐dimensional unsteady heat conduction problems and two dimensional Navier‐Stokes equations are considered. Comparisons with analytic solutions are given for all cases. It is shown that grid shapes influence the accuracy of the results and quantitative error evaluations are provided for some interesting cases.
Elasto‐hydrodynamic lubrication: A non‐linear complementarity problem
Authors: Kostreva Michael M.
Published: August 2005

The classical problem of elasto‐hydrodynamic lubrication of cylinders in line contact is formulated as a non‐linear complementarity problem. A direct algorithm is applied to the approximation obtained by finite differences. Implementation considerations are emphasized. The new method provides reliable and automatic location of the previously troublesome lubricant free boundary. Numerical results reveal the qualitative behaviour of the pressure distribution and the lubricant film thickness under variation of key physical parameters.
A modified finite element method for solving the time‐dependent, incompressible Navier‐Stokes equations. Part 1: Theory
Authors: Gresho Philip M. , Chan Stevens T. , Lee Robert L. , Upson Craig D.
Published: August 2005

Beginning with the Galerkin finite element method and the simplest appropriate isoparametric element for modelling the Navier‐Stokes equations, the spatial approximation is modified in two ways in the interest of cost‐effectiveness: the mass matrix is ‘lumped’ and all coefficient matrices are generated via 1‐point quadrature. After appending an hour‐glass correction term to the diffusion matrices, the modified semi‐discretized equations are integrated in time using the forward (explicit) Euler method in a special way to compensate for that portion of the time truncation error which is intolerable for advection‐dominated flows. The scheme is completed by the introduction of a subcycling strategy that permits less frequent updates of the pressure field with little loss of accuracy. These techniques are described and analysed in some detail, and in Part 2 (Applications), the resulting code is demonstrated on three sample problems: steady flow in a lid‐driven cavity at Re ≤ 10,000, flow past a circular cylinder at Re ≤ 400, and the simulation of a heavy gas release over complex topography.
Two‐step explicit finite element method for two‐layer flow analysis
Authors: Kasahara Koichi , Hara Heihachiro , Kawahara Mutsuto
Published: August 2005

A finite element method for the analysis of two‐layer density flows is presented in this paper. The standard Galerkin method based on linear interpolation functions is used to yield discrete spatial variables. For numerical integration in time, an explicit two‐step selective lumping method is used. Here it is applied to a flow analysis of Ishikari Bay, at the mouth of Ishikari River. This case demonstrates a procedure that yields a numerically stable solution.
Numerical computation of transient shocked chemically reactive flows
Authors: Rajan S.
Published: August 2005

Using the ability of the method of characteristics to evaluate shock fronts in an accurate manner, a formulation is presented which incorporates the effect of rapid exothermic chemical reactions in the flow. The formulation is applied to the computation of the unsteady reactive flow field behind a cylindrial expanding blast wave propagating in a mixture of hydrogen and oxygen. Details of the computational procedure are described. Results are presented for a sample problem and compared with those for the non‐reactive case to illustrate the influence of chemical reactions.
Stability of flow over a rotating disk
Authors: Szeri A. Z. , Giron A.
Published: August 2005

The perturbation equations which characterize the stability of flow over a rotating infinite disk are derived via strict order of magnitude analysis. These equations contain viscous terms not considered by Stuart,1 curvature and Coriolis terms not considered by Brown,2 and axial velocity terms not considered by Kobayashi et al.3 The strategy for reducing the problem to an algebraic system is Galerkin's method with B‐spline discretization. In comparison with the Poiseuille flow solutions of Orszag,4 the method is shown to perform well without placing undue demands on computing capability. Critical values of Reynolds number, wave length, vortex orientation and number of spiral vortices calculated by the present method compare favourably with experimental data of Kobayashi et al.
A finite element for incompressible plane flows of fluids with memory
Authors: Bernstein Barry , Malkus David S. , Olsen Elwood T.
Published: August 2005

Flows of fluids with single‐integral memory functionals are considered. Evaluation of the stress at a material point involves the deformation history of that point, and a dominant computational cost in finite element approximation is the construction of streamlines. It is shown that the simple crossed‐triangle macro‐element is in many ways an ideal finite element for the difficult non‐linear, non‐self‐adjoint problem. The question as to whether this element produces convergent velocity and pressure solutions is addressed in the light of its failure to satisfy the discrete LBB condition. The effect of the element's ill‐disposed (‘spurious’) pressure modes is discussed, and a pressure smoothing scheme is given which gives good results in Newtonian and non‐Newtonian flows at various Reynolds and Deborah numbers. As an example of the element's success in modelling such flows, the problem of pressure differences in flows over transverse slots is studied numerically. The results are compared with experimental observations of such flows. The effect of fluid memory on the relation between first normal‐stress differences and pressure differences is investigated.
A residual method of finite differencing for the elliptic transport problem and its application to cavity flow
Authors: Bhattacharyya T. K. , Datta A. B.
Published: August 2005

A residual method of finite differencing the governing differential equation for the elliptic transport problem is presented. The new finite differencing technique is applied to (1) the one‐dimensional transport problem and (2) the cavity flow problem for numerical illustrations. The results indicate the validity of the residual method of finite differencing. The usual method of term‐by‐term finite differencing, and considerations such as central differencing, hybrid differencing and upwind differencing are not needed in the present residual method.
Turbulent flow in a duct with cusped corners
Authors: Rapley C. W.
Published: August 2005

An orthogonal‐cuvilinear‐mesh‐based finite volume calculation method has been applied to the problem of fully developed turbulent flow in the tri‐cusped cornered duct formed when parallel circular rods touch in triangular array. Algebraic stress relations combined with the k‐ϵ turbulence model are used for calculation of the required stresses. A single circulation of turbulence‐driven cross‐plane secondary flow from the core into the duct corner has been predicted in a one‐sixth symmetry region of the duct and the convective transport effects of this flow are seen to have much influence on local mean flow distributions. The turbulence field predicted by the k‐ϵ model showed significant damping in the cusped corner region where turbulent viscosities approached the laminar value. Satisfactory agreement was obtained with the limited local and overall mean flow measurements available.
A critical evaluation of seven discretization schemes for convection–diffusion equations
Authors: Patel M. K. , Markatos N. C. , Cross M.
Published: August 2005

A comparative study of seven discretization schemes for the equations describing convection‐diffusion transport phenomena is presented. The (differencing) schemes considered are the conventional central‐ and upwind‐difference schemes, together with the Leonard,1 Leonard upwind1 and Leonard super upwind difference1 schemes. Also tested are the so called locally exact difference scheme2 and the quadratic‐upstream difference scheme.3,4 In multidimensional problems errors arise from ‘false‐diffusion’ and function approximations. It is asserted that false diffusion is essentially a multidimensional source of error. No mesh constraints are associated with errors in function approximation and discretization. Hence errors associated with discretization only may be investigated via one‐dimensional problems. Thus, although the above schemes have been tested for one‐ and two‐dimensional flows with sources, only the former are presented here. For 1D flows, the Leonard super upwind difference scheme and the locally exact scheme are shown to be far superior in accuracy to the others at all Peclet numbers and for most source distributions, for the test cases considered. Furthermore, the latter is shown to be considerably cheaper in computational terms than the former. The stability of the schemes and their CPU time requirements are also discussed.
Some results concerning approximation of regularized compressible flow
Authors: Dinh Hung , Carey Graham F.
Published: August 2005

We summarize here some theoretical results for fictitious gas regularization of compressible flow and give error estimates for the finite element approximation to the regularized problem.