bluuebunny/crossref_metadata_2025 huggingface dataset:
Laminar flow in a complex geometry: A comparison
Authors: Napolitano M. , Orlandi P.
Published: August 2005

This paper reports on the outcome of a workshop of the IAHR Working Group on Refined Modelling of Flows on the subject of computing laminar flows in complex geometries. Flow inside a channel with a smooth expansion was chosen by the organizers of the workshop as a suitable test case for assessing the capabilities of current numerical methods. The results obtained by fifteen participant groups are presented and compared against a suitable benchmark solution. The most important considerations that emerged at the workshop are briefly reported and the conclusions arising from an analysis and comparison of the various solutions are finally provided.
Dynamic and convective results for a developing laminar unsteady flow
Authors: Creff R. , Andre P. , Batina J.
Published: August 2005

Dynamic and thermal results for developing laminar pulsed flows in a duct are presented. They have been investigated by means of a finite difference model. This flow is described in terms of an unsteady pulsed flow superimposed on a steady incompressible one with the following main assumptions: a sinusoidal modulation for the pulsation and a uniform wall temperature. Results emphasize the importance of this entry region, where four simultaneous developments occur: steady—dynamic and thermal—and unsteady—dynamic and thermal.
A random vortex simulation of wind‐flow over a building
Authors: Summers D. M. , Hanson T. , Wilson C. B.
Published: August 2005

The random vortex method of Chorin1 provides a numerical simulation of high‐Reynolds number flow in two dimensions. The method can be used to model the viscous interaction of wind with a surface‐mounted obstacle of arbitrary cross‐section. In this paper the method has been used to investigate the flow of wind over common building shapes; an inlet profile is chosen to represent the stationary aspects of the atmospheric boundary layer. The evolution of flow over a short time‐interval after flow initialization is depicted, and a mean value of pressure coefficient, Cp, is calculated over the building perimeter. Some comparison is made with published wind‐tunnel measurements for the case of a surface‐mounted square‐section block and for a building model with 10° roof pitch.
Experiments with several elements for viscous incompressible flows
Authors: Fortin M. , Fortin A.
Published: August 2005

We present a numerical procedure to eliminate internal nodes from elements designed to approximate incompressible flow problems. We compare six elements in academic and industrial like flow problem and we discuss their relative qualities. A surprising conclusion is that richer elements may behave less well than simple ones if a good enforcement of incompressibility is not maintained.
On the numerical computation of laminar boundary layers at a phase‐changing, gas‐liquid interface
Authors: Klotz Stephen P. , Street Robert L.
Published: August 2005

The two‐dimensional, laminar boundary‐layer equations of heat, mass and momentum at a smooth, phase‐changing, gas‐liquid interface are solved numerically by the Keller Box method. The gas and liquid regimes are embedded in a single marching scheme which computes interfacial parameters implicitly. Results of both self‐similar and non‐similar boundary‐layer computations are presented and effects of mild pressure gradient, a mean current in the liquid, and free‐stream vapour concentration on the interfacial parameters are analysed.

In order to assess the accuracy of the method, several self‐similar problems are solved by Runge‐Kutta integration and results are compared to those obtained by the finite‐difference scheme. Agreement is excellent in all cases.
Conservative calculations of non‐isentropic transonic flows
Authors: Hafez M. M. , Habashi W. G. , Kotiuga P. L.
Published: August 2005

The classical potential formulation of inviscid transonic flows is modified to account for non‐isentropic effects. The density is determined in terms of the speed as well as the pressure, which in turn is calculated from a second‐order mixed‐type equation derived via differentiating the momentum equations.

The present model differs in general from the exact inviscid Euler equations since the flow is assumed irrotational. On the other hand, since the shocks are not isentropic, they are weaker and are placed further upstream compared to the classical potential solution. Furthermore, the streamline leaving the aerofoil does not necessarily bisect the trailing edge.

Results for the present conservative calculations are presented for non‐lifting and lifting aerofoils at subsonic and transonic speeds and compared to potential and Euler solutions.
An improved Vorticity–Potential method for three‐dimensional duct flow simulations
Authors: Yang Herong , Camarero Ricardo
Published: August 2005

An improved Vorticity–Potential method is presented for the numerical solutions of three‐dimensional duct flow problems. The solution procedure requires first a potential solution. Then the viscous effects are added through the vorticity transport equation. By using body‐fitted coordinates, the method is applied to simulate the incompressible laminar flows in a square elbow and in a twisted square elbow.
On numerical modelling of embedded subsonic flow
Authors: Davis M. P. , Mace A. C. H. , Markatos N. C.
Published: August 2005

An analytical model has been developed for computing embedded subsonic flow in rocket plumes from underexpanded axisymmetric supersonic nozzles. Numerical procedures based on the analysis have been incorporated in a simplified, non‐reacting exhaust structure program and calculations for representative plume conditions performed. The technique is numerically stable and has provided satisfactory predictions of Mach–disc associated embedded subsonic flow.
An evaluation of eight discretization schemes for two‐dimensional convection‐diffusion equations
Authors: Patel M. K. , Markatos N. C.
Published: August 2005

A comparative study of eight discretization schemes for the equations describing convection‐diffusion transport phenomena is presented. The (differencing) schemes considered are the conventional central, upwind and hybrid difference schemes,1,2 together with the quadratic upstream,3,4 quadratic upstream extended4 and quadratic upstream extended revised difference4 schemes. Also tested are the so called locally exact difference scheme5 and the power difference scheme.6 In multi‐dimensional problems errors arise from ‘false diffusion’ and function approximations. It is asserted that false diffusion is essentially a multi‐dimensional source of error. Hence errors associated with false diffusion may be investigated only via two‐ and three‐dimensional problems. The above schemes have been tested for both one‐ and two‐dimensional flows with sources, to distinguish between ‘discretization’ errors and ‘false diffusion’ errors.7 The one‐dimensional study is reported in Reference 7. For 2D flows, the quadratic upstream difference schemes are shown to be superior in accuracy to the others at all Peclet numbers, for the test cases considered. The stability of the schemes and their CPU time requirements are also discussed.
Local pressure oscillation and boundary treatment for the 8‐node quadrilateral
Authors: Carey G. F. , McLay R.
Published: August 2005

The 8‐node (serendipity) velocity basis with C° bilinear pressure is a popular element but has been observed to yield poor pressures. We present some details of numerical experiments that indicate the local nature of the error and the effects of mesh refinement, increasing Reynolds number and regularity of the data. This leads to a strategy for appropriately modifying the data near the corners that is effective in improving the computed pressure approximation.
Rotating disk with uniform suction in streaming flow
Authors: Szeri A. Z. , Lai C. Y. , Kayhan A. A.
Published: August 2005

We investigate the flow as it occurs above a single rotating disk when uniform suction is applied at the disk surface. It has been demonstrated by others that at zero suction repeated branching of the solution occurs as the parameter s is varied, where s is the ratio of the angular velocity of the fluid at infinity to the angular velocity of the disk. We show multiplicity of solution also at −0·82⩽α⩽1·15, where α is the suction parameter; for large absolute values of α the solution fails to turn back on itself and we obtain only the von Karman solution.

We then generalize the von Karman solution for flow above a single rotating disk with uniform suction to include non‐axisymmetric solutions due to streaming at infinity. These solutions are continuous in an arbitrary parameter, the streaming velocity at infinity; for zero value of this parameter the asymmetric flow degenerates into the classical von Karman flow. Thus the classical solution is never isolated when considered within the framework of the Navier–Stokes equations: there are asymmetric solutions in every neighbourhood of the von Karman solution.
Simulation of forming processes by FEM with a Bingham fluid model
Authors: Bercovier M. , Engelman M. , Fortin M. , Goldberger N.
Published: August 2005

We model the forming process as a fluid flow. A finite element program, FIDAP, which analyses flow problems, was used to calculate velocity and strain rates at points throughout the material during the deformation process. This allows predictions to be made on the shape and quality of the resulting part. The stress‐strain relation we used models the plastic flow of metals (Bingham fluids). The FEM approximation of such a fluid is tested by comparing results for a simple analytical example. In forming processes provision must be made for friction between dye and workpiece, and the program was modified accordingly. Two classical ring forming simulations are compared to published results.
Numerical simulation of storm surges in Bangladesh using a multi‐level model
Authors: Sinha P. C. , Dube S. K. , Roy G. D. , Jaggi Sunil
Published: August 2005

A comparative study with a vertically integrated model and the multi‐level model has shown that the former can remain a good substitute for the latter in the prediction of sea‐surface elevation as long as the bottom friction coefficients in the vertically integrated models are properly specified.
Comparison of iterative and direct solution methods for viscous flow calculations in body‐fitted co‐ordinates
Authors: Braaten M. E. , Shyy W.
Published: August 2005

An investigation has been conducted to study the relative performance between the line iterative and direct sparse matrix solution procedures for viscous flow calculations. A key focus point is to assess the method of speeding up the computation in the context of the body‐fitted co‐ordinate system. A series of test problems has been set up to investigate the effects of mesh skewness, Reynolds number and grid size on the two methods. The fully coupled fully implicit treatment of the equations in the direct sparse matrix method leads to rates of convergence that are much more rapid than the iterative method. Whereas the convergence rate of the iterative method is found to decrease monotonically with increasing global mesh skewness and Reynolds number, the direct method is quite insensitive to these parameters. However, the increased complexity of the equations in curvilinear co‐ordinates causes the storage requirements and the cost per iteration of the direct method to be even higher than in corresponding methods using Cartesian co‐ordinates. Consequently, the total CPU time for the direct method is found to be proportional to N2 (where N is the total number of nodes), which compares unfavourably with the iterative method, where CPU time varies as N.1,5 Hence, increases in grid size penalize both the CPU time and computer storage requirements of the direct method more severely than the iterative method. These findings make the straightforward adoption of the direct sparse matrix method less attractive in the curvilinear co‐ordinate system. However, the importance of the coupling between the equations on speeding up the convergence of the solution procedure is clearly demonstrated, suggesting possible alternatives for achieving code speed‐up.
Numerical solution of the supersonic laminar flow over a two‐dimensional compression corner using an implicit approach
Authors: Madhavan N. S. , Swaminathan V.
Published: August 2005

The use of an implicit numerical scheme, analogous to MacCormack's1, for the supersonic laminar two‐dimensional compression corner flow problem using unsteady Navier–Stokes equations is demonstrated. The technique entails a reduction of about 70 per cent in the computation time for a Courant number of 5, but it is characterized by an increase of approximately 20 per cent in computer memory requirement.
A finite element approximation of the unsteady two‐dimensional Navier–Stokes equations
Authors: Van De Vosse F. N. , Śegal A. , Van Steenhoven A. A. , Janssen J. D.
Published: August 2005

In this paper a penalty finite element solution method for the unsteady Navier–Stokes equations for two‐dimensional incompressible flow is described. The performances of the Euler implicit (EI) and the Crank–Nicolson (CN) time integration methods are analysed. Special attention is payed to the undamped pressure oscillations which can occur when the Crank–Nicolson integration rule is used in combination with the penalty function method. Stability and convergence properties are illustrated by means of the computation of fully developed oscillating flow between two flat plates. Furthermore, the von Karman vortex street past a circular cylinder is computed to demonstrate the behaviour of the time integration schemes for a more complicated flow. It is concluded that the EI method has its advantages over the CN method with respect to the damping of numerical oscillations. However, for flows with an important convective contribution, where physically originated oscillations may be present, the CN method is preferable.
Mesh effects on the computation of non‐linear gravity waves of arbitrary discharge
Authors: Toro E. F.
Published: August 2005

Numerical computations of non‐linear gravity waves are presented and the effects of mesh variations on the results are discussed.

Waves are regarded as two‐parameter families (λ,A)Q of arbitrary discharge Q, and computations are carried out using a new Kantorovich algorithm.

Mesh effects are to a large extent dependent on the particular wave region under consideration. Three such regions are identified and typical examples are computed and discussed.
Orbital flow past a cylinder: A numerical approach
Authors: Borthwick A.
Published: August 2005

Orbital flow past a cylinder is relevant to offshore structures. The numerical scheme presented here is based on a finite‐difference solution of the Navier–Stokes equations. Alternating‐directional‐implicit (ADI) and successive‐over‐relaxation (SOR) techniques are used to solve the vorticity‐transport and stream‐function equations. Theoretical simulations to low Reynolds number flows (up to 1000) are discussed for cases involving uniform flow past stationary and rotating cylinders and orbital flow past a cylinder. The separation points for cylinders that are rotating or immersed in an orbital flow are deduced from velocity profiles through the boundary layer using a hybrid mesh scheme. During the initial development of orbital flow surface vorticity on the impulsively started cylinder dominates the flow. A vortex then detaches from behind the cylinder and establishes the flow pattern of the orbit. After some time a collection of vortices circles the orbit and distorts its shape a great deal. These vortices gradually spiral outward as others detach from the cylinder and join the orbital path.
A finite element approximation of steady flow through a rotating non‐aligned straight tube
Authors: Noronha W. P. , Berman J.
Published: August 2005

A finite element solution is developed for a penalty function formulation of the equations which govern the steady motion of a Newtonian fluid through a pipe that rotates about an axis not parallel to its own. The motion in this system is driven by the Coriolis acceleration, which has components in the axial direction as well as in the transverse plane of the pipe. The relative magnitudes of these components significantly affect the qualitative and quantitative nature of the primary and secondary flow field. The present results compare favourably with those of previously reported experimental and theoretical studies over a wide range of flow regimes.
Turbulent boundary‐layer analysis using finite elements
Authors: Sharma M. , Carey G. F.
Published: August 2005

The use of finite element methods for turbulent boundary‐layer flow is relatively recent and of limited extent.1 In the present study, we extend the group variable approach of Fletcher and Fleer2,3 to treat turbulent boundary layer flows with heat transfer using a two‐equation turbulence model. The main concepts in the formulations include a Dorodnitsyn‐type transformation which uses a velocity component as the transverse variable, a ‘variational’ formulation for the transformed equations using special test functions and development of a two‐equation turbulence model in terms of the turbulent kinetic energy and turbulence dissipation rate as additional field variables. Several numerical test cases have been examined comparing the results with finite difference calculations and comparing the two‐equation turbulence model with an algebraic turbulence model.
Analysis of lubricated squeezing flow
Authors: Papanastasiou A. C. , Macosko C. W. , Scriven L. E.
Published: August 2005

A thin film of low‐viscosity lubricating liquid between a solid wall and a viscous material reduces shear stress on the latter and tends to make it flow as though it were slipping along the wall. The result when the lubricated material is being squeezed out of the gap between approaching parallel plates is flow more nearly irrotational, or extensional, the more effective the lubricating film on the plates. Two Newtonian analyses of this flow situation are reported. One is an approximate, asymptotic analytical solution for Newtonian lubricating flow in the films and combined mixed flow, shear and extension, in the viscous layer. The second is a full two‐dimensional axisymmetric solution of the momentum and continuity equations along with the kinematic condition which governs the motion of the interface. Both analyses indicate that there are two limiting flow regimes, depending on the ratio of the thickness of each of the two phases to radius and on the viscosity ratio of the two liquids. In one limit the flow is parallel squeezing and the lubricant layer slowly thins and persists a long time. In the other the lubricant is expelled preferentially. Implications of the results are discussed for rheological characterization of viscoelastic liquids and for prediction of lubricated or autolubricated flows in processing situations.
Solution of three‐dimensional natural convection about a vertical square rod in a cylindrical enclosure
Authors: Glakpe E. K. , Watkins C. B. , Kurien B.
Published: August 2005

The problem of three‐dimensional laminar natural convection in a vertical enclosure with an inner square rod is treated by a numerical method in boundary‐fitted co‐ordinates. The inner and outer cylinders are heated and cooled, respectively, to maintain different constant surface temperatures. The horizontal enclosure surfaces are maintained at adiabatic conditions. The Prandtl number is that of air, 0·703, and the Rayleigh numbers span the conduction, transition and boundary layer regimes of flow. The radius ratio is 1, and the aspect ratio (cylinder length divided by maximum annular gap) is 1. The results of the study provide data useful in the design and performance assessment of nuclear reactor spent fuel shipping casks.
A spectral method with staggered grid for incompressible Navier‐Stokes equations
Authors: Montigny‐Rannou F. , Morchoisne Y.
Published: August 2005

In order to solve the Navier‐Stokes equations by spectral methods, we develop an algorithm using a staggered grid to compute the pressure. On this grid, an iterative process based on an artificial compressibility matrix associates the pressure with the continuity equation. This method is very accurate and avoids naturally most of the effects of parasite modes appearing in classical spectral methods with a velocity—pressure formulation.
Finite element analysis of flow in a gas‐filled rotating annulus
Authors: Berger M. H.
Published: August 2005

Linearized multidimensional flow in a gas centrifuge can be described away from the ends by Onsager's pancake equation. However a rotating annulus results in a slightly different set of boundary conditions from the usual symmetry at the axis of rotation. The problem on an annulus becomes ill‐posed and requires some special attention. Herein we treat axially linear inner and outer rotor temperature distributions and velocity slip. An existence condition for a class of non‐trivial, one‐dimensional solutions is given. New exact solutions in the infinite bowl approximation have been derived containing terms that are important at finite gap width and non‐vanishing velocity slip. The usual one‐dimensional, axially symmetric solution is obtained as a limit. Our previously reported finite element algorithm has been extended to treat this new class of problems. Effects of gap width, temperature and slip conditions are illustrated. Lastly, we report on the compressible, finite length, circular Couette flow for the first time.
A hydrometeorological, three‐dimensional model of thermal energy releases into environmental media
Authors: Markatos N. C. , Pericleous K. , Simitovic R.
Published: August 2005

A computer model has been developed to study thermal energy releases into the environment. A typical application of the model is the study of the behaviour of cooling‐tower effluent under different weather and operating conditions. The model employs the full three‐dimensional transport equations describing the conservation of mass, momentum and energy. The flow is treated as single‐phase and the behaviour of any droplets present is calculated indirectly. The model takes into account such hydrometeorological phenomena as the effects of humidity, wind direction and speed, density variations and the presence and precipitation of droplets. Sample results from cooling tower applications are presented and discussed.
Application of conjugate‐gradient‐like methods to a hyperbolic problem in porous‐media flow
Authors: Obeysekare Upul R. B. , Allen Myron B. , Ewing Richard E. , George John H.
Published: August 2005

This paper presents the application of a preconditioned conjugate‐gradient‐like method to a non‐self‐adjoint problem of interest in underground flow simulation. The method furnishes a reliable iterative solution scheme for the non‐symmetric matrices arising at each iteration of the non‐linear time‐stepping scheme. The method employs a generalized conjugate residual scheme with nested factorization as a preconditioner. Model runs demonstrate significant computational savings over direct sparse matrix solvers.
Application of an explicit TVD scheme for unsteady, axisymmetric, muzzle brake flow
Authors: Cooke C. H.
Published: August 2005

Operator splitting in the presence of source terms is necessary in order to apply Harten's second‐order accurate, total‐variation‐diminishing (TVD), shock‐capturing scheme to higher‐dimensional problems. By employing Godunov boundary treatment at the muzzle brake, such splitting is applied to the problem of muzzle brake flow simulation for the case of blasts which are impeded, by vertical and slanted baffles, respectively. Results from numerical studies of various types of wall boundary condition treatment which are consistent with Harten's TVD scheme are indicated.
Studies in numerical computations of recirculating flows
Authors: Castro I. P. , Jones J. M.
Published: August 2005

This paper considers the use of various finite differencing schemes for the computation of flows involving regions of recirculation. Standard first‐order hybrid schemes, vector (or skew) schemes and second‐order schemes are used to predict laminar flows in a channel containing a constriction and over a normal flat plate with a downstream splitter plate. In the former case the results are compared with those of other workers and with the implications of analytic theories for the viscous dominated flow around the sharp corner.

Attention is concentrated on the effects of errors arising from the use of non‐uniform grids and it is shown that higher‐order differencing schemes are generally much less susceptible to these than the simpler schemes. The major conclusion is that for flows containing regions where pressure gradients largely balance the convective terms in the momentum equations, in addition to other regions where convection and diffusion balance, higher order differencing schemes are likely to be essential if accurate predictions are required on grids without excessive numbers of nodes. It is argued that similar conclusions must hold for high Reynolds number turbulent flows.
Finite element analysis in combustion phenomena
Authors: Chung T. J. , Kim Y. M. , Sohn J. L.
Published: August 2005

This paper is concerned with the exposition of finite element applications to combustion problems. The subject of computational fluid dynamics, including combustion calculations, has long been dominated by finite differences. Recently, however, the finite element method has emerged as a potential candidate for computational modelling in fluid mechanics. It is well known that reactive fluids with combustion present additional complications because of disparity in reaction rates commonly referred to as ‘stiff’. The present paper reviews basic questions arising from combustion problems in applications of finite element techniques to the solution of problems associated with chemical kinetics, diffusion, waves, convection, etc. Finally, an example of a hydrogen‐oxygen reaction is presented for practical applications. Extension to the finite element modelling of turbulence, sprays, boundary layers, shock waves, etc. in combustion must await significant developments of numerical strategies associated with a more complete understanding of physical phenomena and chemical kinetics.
Arbitrary Lagrangian–Eulerianc finite element method for unsteady, convective, incompressible viscous free surface fluid flow
Authors: Ramaswamy Balasubramaniam , Kawahara Mutsuto
Published: August 2005

In this paper, free surface flow problems involving large free surface motions are analysed using finite element techniques. In solving these problems an arbitrary Lagrangian‐Eulerian (ALE) kinematical description of the fluid domain is adopted, in which the nodal points can be displaced independently of the fluid motion. This formulation leads to an easy and accurate treatment of fluid‐fluid interfaces, and greater distortions in the fluid motions can be handled than would be allowed by a purely Lagrangian method.

This paper describes the basic methodology, presents finite element approximations and discusses such matters as stability, accuracy and rezoning. The generality and the advantage of the present method are discussed, and its versatility is demonstrated through a few numerical experiments.
Finite element flux‐corrected transport (FEM–FCT) for the euler and Navier–Stokes equations
Authors: Löhner Rainald , Morgan Ken , Peraire Jaime , Vahdati Mehdi
Published: August 2005

A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux‐corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady‐state examples are solved to illustrate the performance of the algorithm.
A numerical model for non‐linear wave diffraction around large offshore structures
Authors: Li Baoyuan , Lu Yulin
Published: August 2005

The present paper describes a numerical model for predicting the non‐linear wave forces exerted on large coastal or offshore structures. The interaction is calculated from a known initial condition corresponding to still water in the immediate vicinity of the structure. A prescribed incident wave of large amplitude approaches the structure. The boundary constraints on the free surface are considered in the fully non‐linear versions. Not far away from the structure, an artificial open boundary is considered with a suitable description of the radiation boundary condition for an incident wave propagating inwards, and in addition the scattering wave being absorbed. The finite difference method and time stepping are adopted for numerical calculation in the present model. For illustration the wave forces on a surface‐piercing vertical cylinder subjected to two different incident wave trains were evaluated. Reasonably good agreement could be obtained between the numerical results and the analytical solution given by Isaacson.1.
Comments on ‘the group velocity of some numerical schemes’
Authors: Gresho Philip M. , Lee Robert L.
Published: August 2005

The proper phase and group speeds when quadratic finite elements are applied to the one‐dimensional pure advection equation are presented and the myth of a spurious computational mode is dispelled.
A design method for two‐dimensional cascades of turbomachinery blades
Authors: Hart M. , Whitehead D. S.
Published: August 2005

A design method for two‐dimensional cascades of turbomachinery blades is presented. A finite element potential flow program is extended to allow fluid to transpire through the blade surface, the displaced surface streamline defining a new blade geometry. The potential changes are related linearly to the transpired flow rates. New surface velocities may then be specified as a function of surface distance, in accordance with boundary layer considerations. Closure and smoothness of the new blade are successfully achieved, while large changes in the blade geometry are possible.
Analysis of convective diffusion problem with first‐order chemical reaction by boundary element method
Authors: Okamoto Naotaka
Published: August 2005

A boundary element method is presented for a steady state convective diffusion problem with a first‐order chemical reaction. In the chemical reaction system the usual conservation law for calculation of the diagonal components of the matrix H cannot be satisfied. Thus in the boundary element formulation the emphasis is laid on how to compute these diagonal components. The main aim of this paper is to present the method of numerical quadrature to obtain the principal values, using the splitting technique to treat the singular integration.
Identification of non‐Darcy groundwater flow parameters
Authors: Goodwill I. M. , Kalliontzis C.
Published: August 2005

Non‐Darcy groundwater flow parameters are identified for three different flow systems. In the first system, which is essentially one‐dimensional, the parameters are determined by means of an integral method. A rectangular parametric grid is used for the identification of the non‐Darcy friction coefficients in the second system, which is two‐dimensional. The parameters in the third system, which involves a hybrid simulation of three‐dimensional flow, are optimized by adopting a constrained non‐linear programming technique. This technique combines Cauchy's steepest‐descent method together with the modeller's subjective judgement of the results at the end of each iterative step. The paper is concluded with a brief description of the additional research which is thought to be necessary before the difficulties of optimizing the non‐Darcy flow parameters can be overcome.
Unsteady boundary layer and its separation over a heated circular cylinder
Authors: Kim Jae‐Soo , Chang Keun‐Shik
Published: August 2005

A numerical method is developed to solve the coupled unsteady laminar momentum and thermal boundary layers over a circular cylinder impulsively started from rest. The present non‐iterative finite difference method, which requires relatively fewer grid points in the reversed flow region than any other method, can easily handle the separating boundary layer flows. The results indicate that the present method has accuracy comparable with the earlier methods, while consuming computer time approximately one order of magnitude less.

The present numerical method allowed investigation of the effect of buoyancy parameter on the starting boundary layer. The time‐dependent behaviour of the boundary layer is studied in terms of the appearance of the singularity, the distribution of skin friction and wall heat flux, and the wall position of the inflection point of the velocity profile. The transient as well as buoyancy‐dependent patterns of the streamlines and isotherms are also studied.
The boundary integral equation method for the solution of wave‐obstacle interaction
Authors: Williams K. J.
Published: August 2005

The boundary integral equation method constitutes the basis of a number of computer programs used for the solution of wave‐obstacle interaction problems. For the case of obstacles in a constant depth fluid, the method assumes that the velocity potential at any point in the fluid may be represented by a distribution of Green's function sources over the immersed surface of the obstacle. Application of the obstacle kinematic boundary condition gives rise to an integral equation which may be solved, using numerical discretization, for the unknown source strength distribution function. Subsequent evaluation of the discretized velocity potential permits evaluation of the hydrodynamic interaction parameters.

A series of numerical solutions have been carried out for a range of substantially rectangular obstacles, in a two‐dimensional domain, using varying levels of immersed profile discretization. The results, presented in the form of fixed and floating mode wave reflection and transmission, together with the motion response of the floating obstacle, demonstrate the significant sensitivity of the evaluated parameters to variations in the level of discretization.
Preconditioned conjugate gradients for solving the transient Boussinesq equations in three‐dimensional geometries
Authors: Dupont S. , Marchal J. M.
Published: August 2005

In this paper we present a new version of the ‘modified finite element method’ (MFEM) presented by Gresho, Chan, Lee and Upson.1 The main modification of the original algorithm is the introduction of a cost‐effective and memory‐saving iterative solver for the discretized Poisson equation for the pressure. The vectorization of the preconditioner has been especially considered. For low Prandtl number problems we also split the advection‐diffusion operator of the energy equation into explicit and implicit parts. In that sense the present approach is related to the recent implicitization of the diffusive terms introduced by Gresho and Chan2 and by Gresho.3 The algorithm is applied to the study of buoyancy‐driven flow oscillations occuring in a horizontal crucible of molten metal under the action of a horizontal temperature gradient.
Two‐dimensional analysis of pressure transients in pipelines
Authors: Nathan G. K. , Tan J. K. , Ng K. C.
Published: August 2005

The paper presents a two‐dimensional model for the investigation of pressure transients in pipelines. The governing equations have been established and a method of solving the equations using the centre implicit method is presented. The theoretically predicted values are compared with the experimentally determined pressure transients for horizontal pipelines with a valve at the end. The two‐dimensional model gives results which are accurate than those of the one‐dimensional model and are in good agreement with the experimental results.
A total linearization method for solving viscous free boundary flow problems by the finite element method
Authors: Kruyt N. P. , Cuvelier C. , Segal A. , van der Zanden J.
Published: August 2005

In this paper a total linearization method is derived for solving steady viscous free boundary flow problems (including capillary effects) by the finite element method. It is shown that the influence of the geometrical unknown in the totally linearized weak formulation can be expressed in terms of boundary integrals. This means that the implementation of the method is simple. Numerical experiments show that the iterative method gives accurate results and converges very fast.
On the smoothing properties of the SIMPLE pressure‐correction algorithm
Authors: Shaw G. J. , Sivaloganathan S.
Published: August 2005

A local mode Fourier analysis is used to assess the suitability of the SIMPLE pressure‐correction algorithm to act as a smoother in a multigrid method. The necessary ellipticity of the Navier‐Stokes equations and their discrete representation are established. The theoretical analysis is compared with practical results.
A Petrov‐Galerkin method for the numerical solution of the Bradshaw‐Ferriss‐Atwell turbulence model
Authors: Stewart I. B. , Unsworth K.
Published: August 2005

The Bradshaw‐Ferriss‐Atwell model for 2D constant property turbulent boundary layers is shown to be ill‐posed with respect to numerical solution. It is shown that a simple modification to the model equations results in a well‐posed system which is hyperbolic in nature. For this modified system a numerical algorithm is constructed by discretizing in space using the Petrov‐Galerkin technique (of which the standard Galerkin method is a special case) and stepping in the timelike direction with the trapezoidal (Crank‐Nicolson) rule. The algorithm is applied to a selection of test problems. It is found that the solutions produced by the standard Galerkin method exhibit oscillations. It is further shown that these oscillations may be eliminated by employing the Petrov‐Galerkin method with the free parameters set to simple functions of the eigenvalues of the modified system.
Magnetohydrodynamic flow in electrodynamically coupled rectangular ducts
Authors: Sezgin Munevver
Published: August 2005

In Sezgin1,2 the problems considered are the magnetohydrodynamic (MHD) flows in an electrodynamically conducting infinite channel and in a rectangular duct respectively, in the presence of an applied magnetic field. In the present paper we extend the solution procedure of these papers to two rectangular channels connected by a barrier which is partially conductor and partially insulator. The problem has been reduced to the solution of a pair of dual series equations and then to the solution of a Fredholm's integral equation of the second kind. The infinite series obtained were transformed to finite integrals containing Bessel Junctions of the second kind to avoid the computations of slowly converging infinite series and infinite integrals with oscillating integrands. The results obtained compared well with those of Butsenieks and Shcherbinin3 which were obtained for the perfectly conducting barrier separating the flows.
Mixed convection about a non‐isothermal vertical surface in a porous medium
Authors: Seetharamu K. N. , Dutta Pradip
Published: August 2005

The problem of mixed convection about non‐isothermal vertical surfaces in a saturated porous medium is analysed using boundary layer approximations. The analysis is made assuming that the surface temperature varies as an arbitrary function of the distance from the origin. A perturbation technique has been applied to obtain the solutions. Using the differentials of the wall temperature, which are functions of distance along the surface, as perturbation elements, universal functions are derived for various values of the governing parameter Gr/Re. Both aiding and opposing flows are considered. The universal functions obtained can be used to estimate the heat transfer and fluid velocity inside the boundary layer for any type of wall temperature variation. As a demonstration of the method, heat transfer results have been presented for the case of the wall temperature varying as a power function of the distance from the origin. The results have been studied for various combinations of the parameters Gr/Re and the power index m, taking both aiding and opposing flows into consideration. On comparing these results with those obtained by a similarity analysis, the agreement is found to be good.
On the self‐induced motion of vortex sheets
Authors: Bera Rajendra K.
Published: August 2005

An accurate numerical scheme has been devised to study the self‐induced motion of an infinitely thin, free vortex sheet of finite span in an unbounded, inviscid, incompressible fluid. The new numerical scheme has been tested against two vortex sheet problems for which exact solutions have also been obtained. The agreement between the numerical and exact solutions is excellent. The scheme has been further tested against two more examples for which analytical solutions for small times were available. Here too the agreement is excellent.
A unified approach to direct and inverse boundary layer solutions
Authors: Kaufman K. C. , Hoffman G. H.
Published: August 2005

A unified approach is presented for solving the two‐dimensional incompressible boundary layer equations. Solutions are obtained for direct and inverse options using the same equation formulation by a simple interchange of boundary conditions. A modified form of the mechul function scheme obtains inverse solutions with specification of transformed wall shear, skin friction coefficient or displacement thickness distributions. Direct solutions may be obtained without altering the block tridiagonal structure of the system by simply requiring no corrections on the streamwise pressure gradient parameter. Fourth‐order spline discretization approximates normal derivatives with two‐ and three‐point backward differences approximating streamwise derivatives, yielding a fully implicit solution method. The resulting spline/finite difference equations are solved by Newton‐Raphson iteration together with partial pivoting. The results of the study demonstrate the importance of proper linearization of all equations. The successful use of spline discretization is also tied to the use of strong two‐point boundary conditions at the wall for cases involving reversed flow. Numerical solutions are presented for several non‐similar flows and compared with published results.
A finite element model for the dissolution of corrosion pits in the presence of fluid flow
Authors: Harb John N. , Alkire Richard C.
Published: August 2005

Simulation of the dissolution of an active corrosion pit in the presence of fluid flow was carried out with the use of finite element techniques. The model included multiple species in solution, reaction equilibria and transport by diffusion, convection and migration. The mathematical model was used to examine the effect of fluid flow on the pitting of nickel in neutral chloride solution. The pit dissolution rate was found to decrease with increasing flow owing to potential field effects. The capabilities demonstrated in this paper represent a significant advancement in the modelling of pitting corrosion phenomena.
Trefftz method for hydrodynamic pressure on rigid dams with non‐vertical upstream face
Authors: Wu Yung‐Chao , Yu Ding‐Jong
Published: August 2005

Based on a two‐dimensional potential flow theory, earthquake‐induced hydrodynamic pressures on a rigid dam with a non‐vertical upstream face are examined by the Trefftz method. The effect of surface waves on the hydrodynamic pressure distribution is discussed in detail. Numerical values are given for different wave effect parameters and different geometries of the dam–water interface.
Velocity–pressure integrated versus penalty finite element methods for high‐Reynolds‐number flows
Authors: Kim S.‐W. , Decker Rand A.
Published: August 2005

Velocity–pressure integrated and consistent penalty finite element computations of high‐Reynolds‐number laminar flows are presented. In both methods the pressure has been interpolated using linear shape functions for a triangular element which is contained inside the biquadratic flow element. It has been shown previously that the pressure interpolation method, when used in conjunction with the velocity‐pressure integrated method, yields accurate computational results for high‐Reynolds‐number flows. It is shown in this paper that use of the same pressure interpolation method in the consistent penalty finite element method yields computational results which are comparable to those of the velocity–pressure integrated method for both the velocity and the pressure fields. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine grid finite difference computational results. Advantages and disadvantages of the two finite element methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid‐driven cavity flow of Reynolds number 10 000, a laminar backward‐facing step flow and a laminar flow through a nest of cylinders.
A multigrid method for steady incompressible Navier–Stokes equations based on partial flux splitting
Authors: Dick E.
Published: August 2005

Flux splitting is applied to the convective part of the steady Navier–Stokes equations for incompressible flow. Partial upwind differences are introduced in the split first‐order part, while central differences are used in the second‐order part. The discrete set of equations obtained is positive, so that it can be solved by collective variants of relaxation methods. The partial upwinding is optimized in the same way as for a scalar convection–diffusion equation, but involving several Peclet numbers. It is shown that with the optimum partial upwinding accurate results can be obtained. A full multigrid method in W‐cycle form, using red–black successive under‐relaxation, injection and bilinear interpolation, is described. The efficiency of this method is demonstrated.
Performance of iterative methods for Newtonian and generalized Newtonian flows
Authors: Carey G. F. , Wang K. C. , Joubert W. D.
Published: August 2005

We consider the use of accelerated gradient‐type iterative methods for solution of Newtonian and certain non‐Newtonian (power‐law and Bingham models) viscous flow problems. The formulations are based on penalty and mixed finite element methods, and such factors as the effect of the penalty parameter, asymmetry, continuation and preconditioning are examined.
Process splitting of the boundary conditions for the advection–dispersion equation
Authors: Aiyesimoju Kolawole O. , Sobey Rodney J.
Published: August 2005

Rational strategies are considered for the specification of the intermediate boundary condition at an inflow boundary where process splitting (fractional steps) is adopted in solving the advection–dispersion equation. Three lowest‐order methods are initially considered and evaluation is based on comparisons with an analytical solution. For flow and dispersion parameter ranges typical of rivers and estuaries, the given boundary condition for the complete advection–dispersion equation at the end of the complete time step provides a satisfactory estimate of the intermediate boundary value. This was further confirmed by the development and evaluation of two higher‐order methods. These required non‐centred discrete approximations for spatial derivatives, which offset any special advantages from the higher truncation error order.