bluuebunny/crossref_metadata_2025 huggingface dataset:
A numerical study of the applicability of the Boussinesq approximation for a fluid‐saturated porous medium
Authors: Gartling D. K. , Hickox C. E.
Published: August 2005

The regions of applicability of the Boussinesq approximation are investigated for natural convection in a fluid‐saturated porous medium. A perturbation method is used to assess the relative importance of individual terms in the differential equations which describe the natural convection process. Specific limits to the validity of the Boussinesq approximation are identified for water and air. For water, it is shown that the restrictions imposed by the classical Boussinesq approximation can be relaxed by allowing for the variation of thermophysical properties with temperature while still retaining the incompressible form of the continuity relation. Results of the analysis are verified through numerical calculations performed for steady natural convection in a planar, water‐saturated porous region.
A study of penalty elements for incompressible laminar flows
Authors: Dhatt Gouri , Hubert Guy
Published: August 2005

A finite element model is developed based on the penalty formulation to study incompressible laminar flows. The study includes a number of new quadrilateral and triangular elements for 2‐dimensional flows and a number of new hexahedral and tetrahedral elements for 3‐dimensional flows. All elements employ continuous velocity approximations and discontinuous pressure approximations respecting the LBB condition of numerical instability. An incremental Newton–Raphson method coupled with the Broyden method is used to solve the non‐linear equations. Several numerical examples (colliding flow, cavity flow, etc.) are presented to assess the efficiency of elements.
Improved averaging method for turbulent flow simulation. Part II: Calculations and verification
Authors: Dakhoul Youssef M. , Bedford Keith W.
Published: August 2005

This is the second of two articles intended to develop, apply and verify a new method for averaging the momentum and mass transport equations for turbulence. Part I presented the theoretical development of a new space‐time filter (STF) averaging procedure. The new method, as well as all existing averaging procedures, are applied to the one‐dimensional transient equations of momentum and scalar transport in a Burgers' flow field. Dense‐grid ‘exact’ results from the unaveraged equations are presented to depict the dynamic behaviour of the flow field and serve as a basis for verifying the coarse‐grid STF predictions. In this paper, a finite difference procedure is used to numerically solve the new STF averaged equations, as well as the other forms of the averaged equations derived in Part I. All averaged equations are solved on the same coarse grid. The velocity and scalar fields, predicted from each equation form, are intercompared according to a verification procedure based on the statistical and spectral properties of the results. It is found that the new STF procedure improves coarse‐grid dynamic predictions over the existing methods of averaging.
Transition bifurcation branches in non‐linear water waves
Authors: Toro E. F.
Published: August 2005

We are concerned with the numerical computation of progressive free surface gravity waves on a horizontal bed. They are regarded as families of bifurcation branches (λ,A)Q of constant discharge Q.

Numerically we determine two transition values Q1 and Q2 with corresponding transition bifurcation branches that classify waves into three disjoint branch sets B1, B2 and B3. Their members are families of waves (λ,A)Q satisfying the conditions 0<Q2 ⩽Q, Q <Q2 ⩽Q and Q <Q2 <B/27, respectively.

The bifurcation patterns are analysed in some detail from the computed bifurcation diagram, which shows that in B1 bifurcation is to the left and the amplitude A increases as the wavelength λ decreases; in B2 bifurcation is to the right and turning points are observed nearly at breaking point. In B3 bifurcation is to the right and A increases monotonically with λ.
Measurement of velocity and kinetic energy of turbulence in swirling flows and their numerical prediction
Authors: Sampath S. , Ganesan V.
Published: August 2005

Swirling flows are often employed in gas turbine combustion systems and high intensity industrial furnaces. A detailed analysis of the turbulence in the flow is necessary to achieve optimum combustion conditions. In this paper a method has been described to measure the turbulence levels in three directions using a hot wire anemometer. So far there is no established method available for measurement of turbulence in swirling and recirculating flows.

The present method, it is hoped, will bridge the gap. The merit of the present method is the use of a single‐wire probe rather than the X‐probe. The method has been used for the measurement of turbulence levels in swirling recirculating flows generated by vane swirlers. From the measured turbulence levels, the kinetic energy of turbulence has been calculated and the results are compared with a well‐established numerical prediction method.

Mean velocity measurements have also been made using a 3‐hole Pitot probe. The agreement between the measured and predicted values is quite satisfactory.
Modelling a recirculating density‐driven turbulent flow
Authors: Devantier Bruce A. , Larock Bruce E.
Published: August 2005

A mathematical model of turbulent density‐driven flows is presented and is solved numerically. A form of the k–ϵ turbulence model is used to characterize the turbulent transport, and both this non‐linear model and a sediment transport equation are coupled with the mean‐flow fluid motion equations. A partitioned, Newton–Raphson‐based solution scheme is used to effect a solution. The model is applied to the study of flow through a circular secondary sedimentation basin.
An algebraic grid generation technique for time‐varying two‐dimensional spatial domains
Authors: Yang S.‐L. , Shih T. I‐P.
Published: August 2005

An efficient and versatile algebraic grid generation technique is presented for generating grid points in irregularly shaped and time‐varying spatial domains. The method presented is based on the ‘two‐boundary technique’ of Smith. The usefulness and the feasibility of the grid generation technique were demonstrated by (1) generating grid points inside one of the combustion chambers of a motored two‐dimensional rotary engine and (2) obtaining numerical solutions for the flow field inside one of those combustion chambers.
On the efficient evaluation of certain integrals in the Galerkin F. E. Method
Authors: Staniforth A. , Beaudoin C.
Published: August 2005

The use of linear finite elements in fluid dynamic problems requires the evaluation of integrals of polynomial expressions, which arise from product terms in the equations of motion. An algorithm based on Simpson quadrature is presented and its efficiency compared with that of the more usual one, based on Gaussian quadrature. For both algorithms, the integrations are exact provided that the polynomial integrand is at most cubic. It is found that the Simpson algorithm is twice as efficient as the corresponding Gaussian one, for the evaluation of integrals in one, two and three space dimensions. This doubling of efficiency is a consequence of the vanishing of the basis functions at certain points, a property that can be exploited in the Simpson algorithm, but not in the Gaussian one. It is thought that the use of the Simpson algorithm will prove to be beneficial in many finite element fluid dynamic codes, because the evaluation of product terms generally represents a significant fraction of the total computational cost.
Application of A pressure gradient method to an FEM flow analysis
Authors: Mochimaru Yoshihiro
Published: August 2005

A pressure gradient method employing pressure gradients as dependent variables is applied to a finite‐element‐method flow analysis for a two‐dimensional incompressible Newtonian fluid flow. In a numerical analysis, a triangular element is adopted, a velocity vector and a pressure gradient vector being assigned as dependent variables at the nodal points. Velocity and pressure gradient are interpolated linearly in space, and a discretizing formulation can be made using a suitably selected weighting function. An example of application is shown for an unsteady‐state development of a recirculating circular cavity flow, the numerical results to which are in good agreement with those obtained analytically or by other numerical means.
Computer extended series for a thermally driven gas centrifuge
Authors: Berger M. H.
Published: August 2005

Linearized, multidimensional, thermally driven flow in a gas centrifuge can be approximately described in regions away from the ends by Onsager's homogeneous pancake equation.1 Upon reformulation of the general problem, we find a new, simple and rigorous closed form, analytical solution by assuming a special separable solution and replacing the usual Ekman end cap boundary conditions with idealized impermeable, free slip boundary conditions. Then the flow may be described by an ordinary differential equation with solutions in terms of simple, classical functions. By identifying a small parameter, say ϵ, defining the semi‐long bowl approximation, and assuming a power series expansion in ϵ, a sequence of asymptotic approximations to the master potential is obtained. Not surprisingly, the leading order term involves the well known ‘long bowl’ solution. Using the so‐called ‘solving’ property of the 1‐D pancake Green's function,2 we determine the next higher order solution. This recursive process is carried out on the computer to find all the terms up to O(ϵ4).

Consequently, the solution of some complex rotating, viscous, heat conducting flow problems that normally require large mainframe computers can be better understood.
Synthesis of thermal effects in misaligned hydrodynamic journal bearings
Authors: Medwell J. O. , Gethin D. T.
Published: August 2005

The analysis presented herein deals with the evaluation of pressure and temperature fields which are generated in thin fluid films of varying thickness. The particular problem of a misaligned journal bearing has been studied by solving simultaneously the Reynolds and energy equations, which also include the effects of viscous dissipation and the variation of fluid viscosity with temperature.

The method has been used to predict pressure and temperature fields as well as global performance parameters for a typical journal bearing operation.
Numerical predictions for unsteady viscous flow past an array of cylinders
Authors: Cerutti Edward A. , Kinney Robert B. , Paolino Michael A.
Published: August 2005

The unsteady two‐dimensional flow around an array of circular cylinders submerged in a uniform onset flow is analysed. The fluid is taken to be viscous and incompressible. The array of cylinders consists of two horizontal rows extending to infinity in the upstream and downstream directions. The centre‐to‐centre distance between adjacent cylinders is fixed at three diameters, and the rows are staggered. Advantage is taken of spatially periodic boundary conditions in the flow direction. This reduces the computational domain to a rectangular region surrounding a single circular cylinder. Two cases, for Reynolds numbers of 1000 and 10,000, are presented.
The effect of the stability of mixed finite element approximations on the accuracy and rate of convergence of solution when solving incompressible flow problems
Authors: Silvester D. J. , Thatcher R. W.
Published: August 2005

The stability of two different mixed finite element methods for incompressible flow problems are theoretically analysed. The effect of the stability of the mixed approximation on the accuracy and the rate of convergence of solution is assessed for two non‐trivial problems. The numerical results presented indicate that if the stability of the mixed approximation is not guaranteed then both pressure and velocity solutions are markedly less accurate. In one of the cases considered the ultimate convergence of both the pressure and the velocity solutions is seriously in doubt.
Finite element computation of a turbulent flow over a two‐dimensional backward‐facing step
Authors: Autret A. , Grandotto M. , Dekeyser I.
Published: August 2005

The present paper is devoted to the computation of turbulent flows by a Galerkin finite element method. Effects of turbulence on the mean field are taken into account by means of a (k‐ε) turbulence model. The wall region is treated through wall laws and, more specifically, Reichardt's law. An inlet profile for ε is proposed as a numerical treatment for physically meaningless values of k and ε. Results obtained for a recirculating flow in a two‐dimensional channel with a sudden expansion in width are presented and compared with experimental values.
Numerical simulation of the horizontal Bridgman growth. Part III: Calculation of the interface
Authors: Wouters P. , Schaftingen J. J. Van , Crochet M. J. , Geyling F. T.
Published: August 2005

We study the transient motion of the solidification front during the growth of semiconductor crystals in the horizontal Bridgman geometry. The calculation is based on a two‐dimensional flow. We use finite elements which deform with the motion of the interface. The energy equation is coupled with the isothermal constraint of the interface in an implicit transient algorithm. Several examples show the oscillatory motion of the interface caused by the periodic flow of the melt, and they reveal the importance of the growth rate on the shape of the interface.
Stream function solution of Navier‐Stokes problems with inter‐element penalties
Authors: Utku M. , Carey G. F.
Published: August 2005

In this note, we apply a finite element stream function formulation with inter‐element penalties to the Navier‐Stokes equations. The approach is an extension of a technique previously introduced for Stokes, flow. The solution is obtained by iterative linearization using successive approximation, and results for a standard numerical test case are given.
Analysis of superposed fluids by the finite element method: Linear stability and flow development
Authors: Yiantsios Stergios , Higgins Brian G.
Published: August 2005

A Galerkin finite element method is described for studying the stability of two superposed immiscible Newtonian fluids in plane Poiseuille flow. The formulation results in an algebraic eigenvalue problem of the form Aλ2 + Bλ + C = 0 which, after transforming to a standard generalized eigenvalue problem, is solved by the QR algorithm. The numerical results are in good agreement with previous asymptotic results. Additional results show that the finite element method is ideally suited for studying linear stability of superposed fluids when parameters characterizing the flow fall outside the range amenable to perturbation methods. The applicability of the finite element method to similar eigenvalue problems is demonstrated by analysing the steady‐state spatial development of two superposed fluids in a channel.
A finite element method for transient compressible flow in pipelines
Authors: Bisgaard C. , Sørensen H. H. , Spangenberg S.
Published: August 2005

A finite element method is developed to solve the partial differential equations describing the unsteady flow of gas in pipelines. Excellent agreement is obtained between simulated results and experimental data from a fullscale gas pipeline. The method is used to describe very transient flow (blowout), and to determine the performance of leak detection systems, and proves to be very stable and reliable.
Application of the VOF method to the sloshing of a fluid in a partially filled cylindrical container
Authors: Partom I. S.
Published: August 2005

In a previous work we solved numerically the steady‐state motion of an ideal fluid that fills a moving cylindrical container with partitions, and were able to compute the equivalent moments of inertia.

Here we extend this work in two steps. First we introduce time dependence and then free surfaces, and are able to compute the transient motion of the fluid not filling the container. The main body of the work has to do with the treatment of free surfaces. Our approach is an extention to three dimensions of the volume of fluid method of Hirt and Nichols. The solution algorithm is outlined, and two examples that demonstrate its capability are presented.
A self‐adaptive gridding for inviscid transonic projectile aerodynamics computation
Authors: Hsu Chen‐Chi , Tu Chyuan‐Gen
Published: August 2005

An adaptive grid generation technique based on modified variational principles coupled with an exponential clustering has been developed and tested successfully for the computation of steady inviscid transonic projectile aerodynamics. The isoperimetric problem for adaptive gridding is to extremize a grid smoothness functional subject to grid orthogonality and resolution functionals; however, the Lagrange multipliers have been assumed to be variables with zero variation and are properly chosen as functions of local grid size to enhance locally the grid resolution as well as to maintain the weight of three grid characteristics the same over the entire flow field. With computed pressure gradient as the control function for grid adaptation, the resulting Euler equations cannot provide sufficient grid resolution in the boundary layer region of the projectile geometry; hence, a clustering technique is needed to redistribute the points along the normal grid lines. A grid generation code has been developed and coupled to an axisymmetric thin‐layer Navier‐Stokes code for self‐adaptive grid generation. For the three transonic flow cases considered, M∞ = 0.91, 0.96 and 1.10, the distribution of surface pressure calculated from the inviscid option of the Navier‐Stokes code is indeed in excellent agreement with published measured data.
Augmented Lagrangian technique applied to a spatially periodic, harmonic Navier‐Stokes problem
Authors: Borne Lionel
Published: August 2005

An application and an extension (to complex variables) of the classical augmented Lagrangian method is performed. Finite element computations are realized in the two‐dimensional case of an harmonic Navier‐Stokes problem with periodic boundary conditions. A formulation (extended from the traditional Stokes problem) involving a simple Lagrangian, solved by the Uzawa algorithim, was previously used.1 This treatment proved unsatisfactory for large frequencies. The efficient and well‐known augmented Lagrangian technique solved by the Uzawa algorithm is used to overcome these shortcomings. Other, better techniques could be used. Nevertheless the simple method used here is efficient. Moreover the numerical implementation needs little memory storage, which is an important factor in this particular case. The well‐known conditioning technique employed is shown to be well‐adapted in this case, a fact which emerges from the study of the non‐symmetric problem involved. Finally, many tests, computations and experimental data are presented.
Two‐dimensional numerical calculation of the flow field about a scoop inlet by the piecewise linear method
Authors: Mikami Hisashi
Published: August 2005

The piecewise linear method (PLM) based on time operator splitting is used to solve the unsteady compressible Euler equations describing the two‐dimensional flow around and through a straight wall inlet placed stationary in a rapidly rotating supersonic flow. The PLM scheme is formulated as a Lagrangian step followed by an Eulerian remap. The inhomogeneous terms in the Euler equations written in cylindrical coordinates are first removed by Sod's method and the resulting set of equations is further reduced to two sets of one‐dimensional Lagrangian equations, using time operator splitting. The numerically generated flow fields are presented for different values of the back pressure imposed at the downstream exit of the inlet nozzle. An oblique shock wave is formed in front of the almost whole portion of the inlet entrance, the incoming streamlines being deflected towards the higher pressure side after passing through the oblique shock wave and then bending down to the lower pressure side. A reverse flow appears inside the inlet nozzle owing to the recovery pressure of the incoming streams being lower than the back pressure of the inlet nozzle.
Vectorized multigrid fluid flow calculations on a CRAY X‐MP/48
Authors: Vanka S. P. , Misegades K. P.
Published: August 2005

This paper discusses aspects of vectorizing a recently developed calculation procedure for multidimensional recirculating fluid flows. The solution algorithm uses a coupled Gauss‐Seidel relaxation operator in conjunction with the multigrid technique. The vectorization is performed on a CRAY X‐MP/48 using a single processor. In this paper, the vectorization techniques used and the observed speed‐ups are presented for a model problem of laminar flow in a two‐dimensional square cavity. Large scale calculations with up to one quarter of a million finite difference cells (512 x 512) have been made in 45s of CPU time.
Petrov‐Galerkin methods for natural convection in directional solidification of binary alloys
Authors: Adornato Peter M. , Brown Robert A.
Published: August 2005

A Petrov‐Galerkin finite element method is presented for calculation of the steady, axisymmetric thermosolutal convection and interface morphology in a model for vertical Bridgman crystal growth of nondilute binary alloys. The Petrov‐Galerkin method is based on the formulation for biquadratic elements developed by Heinrich and Zienkiewicz and is introduced into the calculation of the velocity, temperature and concentration fields. The algebraic system is solved simultaneously for the field variables and interface shape by Newton's method. The results of the Petrov‐Galerkin method are compared critically with those of Galerkin's method using the same finite element grids. Significant improvements in accuracy are found with the Petrov‐Galerkin method only when the mesh is refined and when the formulation of the residual equations is modified to account for the mixed boundary conditions that arise at the solidification interface. Calculations for alloys with stable and unstable solute gradients show the occurrence of classical flow transitions and morphological instabilities in the solidification system.
Consistency, stability and convergence of the finite‐difference equations for flow about a rotating sphere in an axial stream
Authors: El ‐Shaarawi M. A. I. , El‐Bedeawi S. A.
Published: August 2005

The finite‐difference equations which have previously been developed to solve the problem of laminar boundary layer flow about a rotating sphere in an axial stream are analysed according to the available numerical stability theories. This analysis is necessary to determine the restrictions on velocities and mesh sizes required to obtain a convergent numerical solution. Convergence can be achieved if both consistency and stability of the finite‐difference equations are fulfilled. The analysis reported in the present paper shows that the developed finite‐difference equations are consistent with their original partial differential equations. Also, the analysis proves that the developed finite‐difference procedure is numerically stable for all mesh sizes as long as the downstream meridional velocity is non‐negative, i.e.as long as no flow reversals occur within the domain of solution.
An ocean modelling system with turbulent boundary layers and topography: numerical description
Authors: Dietrich David E. , Marietta M. G. , Roache Patrick J.
Published: August 2005

The Sandia ocean modelling system (SOMS) is a system of three‐dimensional, fully conservative, partially implicit numerical models based on primitive equations and a staggered Arakawa ‘c’ grid. A thin‐shell bottom boundary layer submodel coupled to a free‐stream submodel resolves boundary layers together with realistic topography. Both submodels use stretched vertical co‐ordinates and an optional Mellor‐Yamada level‐2·5 turbulence closure. Rigid top pressures are determined by vertical integration of the conservation equations using a hydrostatic approximation. SOMS reproduces previously published results, but with notable advantages in speed and economy.
Finite element procedures for time‐dependent convection–diffusion–reaction systems
Authors: Tezduyar T. E. , Park Y. J. , Deans H. A.
Published: August 2005

New finite element procedures based on the streamline‐upwind/Petrov‐Galerkin formulations are developed for time‐dependent convection‐diffusion‐reaction equations. These procedures minimize spurious oscillations for convection‐dominated and reaction‐dominated problems. The results obtained for representative numerical examples are accurate with minimal oscillations.

As a special application problem, the single‐well chemical tracer test (a procedure for measuring oil remaining in a depleted field) is simulated numerically. The results show the importance of temperature effects on the interpreted value of residual oil saturation from such tests.
A finite element procedure for viscoelastic flows
Authors: Fortin M. , Esselaoui D.
Published: August 2005

A finite element method for the simulation of viscoelastic flows has been developed. It uses a weak formulation of the method of characteristics to treat the viscoelastic constitutive law. Numerical results in a 4:1 contraction are presented and are discussed with respect to previous computations. New phenomena are put in evidence and new questions are opened in this already controversial problem.
An experiment with arithmetic precision in linear algebra computations
Authors: Duff I. , Laminie J. , Lichnewsky A. , Thomasset F.
Published: August 2005

Several techniques for experimental determination of floating point precision in practical computations are examined, and applied to linear algebra algorithms. These techniques are simple enough to be directly applicable to existing production codes, requiring a very limited amount of software on many machines, and yet they yield interesting information on the numerical precision of a computation.

Our choice of linear algebra algorithms includes a direct solver (namely the MA32 program from the Harwell Library) and several variants of preconditioned conjugate gradients (the methods DIAG, INV, MINV and POL of Reference 1). The results may be of interest as method selection criteria, and thus complement Mflop performance data available from several sources.
Flow past symmetric convex profiles with open wakes
Authors: Dormiani M. , Bruch J. C. , Sloss J. M.
Published: August 2005

A fixed domain approach and a Baiocchi type transformation in conjunction with a modified Schwarz alternating iteration scheme are used to solve problems of flow past truncated convex shaped profiles between walls in a logarithmic hodograph plane. The flows are such that an open wake or cavity is formed behind the profile. The basic numerical scheme consists of the successive over‐relaxation finite difference approach over the whole domain of the problem with the use of a projection operation over only part of the domain. The numerical results that are obtained using this approach for the cases of a truncated circular arc profile and a wedge profile are compared with published results and are found to be in good agreement.
A new approach to the solution of the Navier‐Stokes equations
Authors: Grossman George W. , Barron Ronald M.
Published: August 2005

In the present paper a numerical algorithm is given for solving a standard problem in fluid dynamics, that of inviscid, irrotational, incompressible flow over an arbitrary symmetric profile. The purpose of the paper is to propose an alternative approach to solve certain fluid dynamic flows. This paper may be thought of as the first of a possible series of papers solving new and fundamental problems. In a sense, this new approach asks the question: what is the simplest and most efficient method of solving the problem considered by finite difference methods. It is believed that the following algorithm answers this question. Standard second‐order finite difference techniques, such as SLOR and ADI, are used to solve numerically a mixed boundary value problem comprised of a pair of elliptic partial differential equations with constant coefficients.
Prediction of incompressible flow separation with the approximate factorization technique
Authors: Michelassi V. , Benocci C.
Published: August 2005

This paper describes one application of the approximate factorization technique to the solution of incompressible steady viscous flow problems in two dimensions.

The velocity‐pressure formulation of the Navier‐Stokes equations written in curvilinear non‐orthogonal co‐ordinates is adopted. The continuity equation is replaced with one equation for the pressure by means of the artificial compressibility concept to obtain a system parabolic in time. The resulting equations are discretized in space with centred finite differences, and the steady state solution obtained by a time‐marching ADI method requiring to solve 3 x 3 block tridiagonal linear systems.

An optimized fourth‐order artificial dissipation is introduced to damp the numerical instabilities of the artificial compressibility equation and ensure convergence.

The resulting solver is applied to the prediction of a wide variety of internal flows, including both streamlined boundaries and sharp corners, and fast convergence and good results obtained for all the configurations investigated.
Improved relaxation schemes for transonic potential calculations
Authors: Hafez M. , Lovell D.
Published: August 2005

A block relaxation scheme, grouped in a red‐black ordering, is applied to transonic aerofoil calculations using body‐fitted co‐ordinates. The scheme is simple and easily vectorizable. Detailed comparisons with the approximate factorization method (AF2) are presented and it is shown that the new scheme is competitive in all cases considered. Transonic results, of engineering accuracy, on an 0‐type grid of 149 × 30 points, are usually obtained within 200 iterations (≃ 40s on a Cyber 175).
Entropy and vorticity corrections for transonic flows
Authors: Hafez M. , Lovell D.
Published: August 2005

Different models for inviscid transonic flows are examined. The common assumptions that the flow is isentropic and irrotational are critically evaluated. Entropy and vorticity correction procedures for potential and stream function formulations are presented, together with the details of the treatment of shocks and wakes, and drag and lift calculations. The non‐uniqueness problem of the potential formulation is studied using different artificial viscosity forms. Numerical results are compared with Euler solutions.
A boundary‐type finite element model for water surface wave problems
Authors: Kashiyama Kazuo , Kawahara Mutsuto
Published: August 2005

A new combinative method of boundary‐type finite elements and boundary solutions is presented to study wave diffraction‐refraction and harbour oscillation problems. The numerical model is based on the mild‐slope equation. The key feature of this method is that the discretized matrix equation can be formulated only by the calculation of a line integral, since the interpolation equation which satisfies the governing equation in each element is used. The numerical solutions are compared with existing analytical, experimental, observed and other numerical results. The present method is shown to be an effective and accurate method for water surface wave problems.
A numerical method for acoustic oscillations in tubes
Authors: Gary John M.
Published: August 2005

A numerical method to obtain the neutral curve for the onset of acoustic oscillations in a helium‐filled tube is described. Such oscillations can cause a serious heat loss in the plumbing associated with liquid helium dewars. The problem is modelled by a second‐order, ordinary differential eigenvalue problem for the pressure perturbation. The numerical method to find the eigenvalues and track the resulting points along the neutral curve is tailored to this problem. The results show that a tube with a uniform temperature gradient along it is much more stable than one where the temperature suddenly jumps from the cold to the hot value in the middle of the tube.
Flux difference splitting for the Euler equations in one spatial co‐ordinate with area variation
Authors: Glaister P.
Published: August 2005

An approximate (linearized) Riemann solver is presented for the solution of the Euler equations of gas dynamics in one spatial co‐ordinate. This includes cylindrically and spherically symmetric geometries and also applies to narrow ducts with area variation. The method is Roe's flux difference splitting with a technique for dealing with source terms. The results of two problems, a spherically divergent infinite shock and a converging cylindrical shock, are presented. The numerical results compare favourably with those of Noh's recent survey and also with those of Ben‐Artzi and Falcovitz using a more complicated Riemann solver.
A finite element convergence study for shear‐thinning flow problems
Authors: Karagiannis A. , Mavridis H. , Hrymak A. N. , Vlachopoulos J.
Published: August 2005

The solution of the non‐linear set of equations arising from the application of the finite element method to non‐Newtonian fluid flow problems often requires large amounts of computer time. Four iteration schemes (Picard, Newton‐Raphson, Broyden and Dominant Eigenvalue method) are compared in three different flow geometries using a shear‐thinning fluid model. Points of comparison involve the computer time necessary to converge the equations, ease of implementation, radius of convergence and rate of convergence.
A boundary element formulation for natural convection problems
Authors: Kitagawa Koichi , Wrobel Luiz C. , Brebbia Carlos A. , Tanaka Masataka
Published: August 2005

This paper presents a boundary element formulation employing a penalty function technique for two‐dimensional steady thermal convection problems. By regarding the convective and buoyancy force terms in Navier‐Stokes equations as body forces, the standard elastostatics analysis can be extended to solve the Navier‐Stokes equations. In a similar manner, the standard potential analysis is extended to solve the energy transport equation. Finally, some numerical results are included, for typical natural convection problems, in order to demonstrate the efficiency of the present method.
Laminar natural convection in a partially divided rectangular cavity at high Rayleigh number
Authors: Winters Keith H.
Published: August 2005

Finite element predictions of two‐dimensional laminar natural convection in a partially divided rectangular cavity at high Rayleigh number are presented. The walls are differentially heated, the horizontal surfaces are insulated and the cavity contains a partial vertical divider which is centrally located and whose height is varied. Detailed results are presented for an aluminium half‐divider in water for Rayleigh number up to 1011 and compared directly with recent experiments in a cavity of aspect ratio 1/2. The predicted flow and heat transfer are in good agreement with the measurements and confirm the existence of a high Rayleigh number regime with characteristic behaviour that differs significantly from that found at lower Rayleigh number. In addition, the effects of the divider height, the divider conductivity, the fluid Prandtl number and the cavity aspect ratio are studied. The results show that a direct simulation of the complex flow and heat transfer that occurs in partially divided cavities is possible for realistic physical conditions.
Turbulent flow in a tube containing an offset rod
Authors: Rapley C. W.
Published: August 2005

A numerical finite volume prediction method for arbitrary‐shaped passages has been applied to the case of fully developed axial turbulent flow past a rod eccentrically placed in a circular tube. The numerical method was based on an orthogonal curvilinear mesh and employed an algebraic stress transport model to calculate the full three‐dimensional velocity field directly from the governing partial differential equations. This study is one of a series of applications of this prediction method to a range of different non‐circular passages that have been made in order to establish the capabilities and usefulness of this type of procedure. The present eccentric rod case was the subject of a comprehensive experimental investigation by Kacker1 which has enabled a detailed comparison to be made between the present predictions and the measurements. This comparison included local distributions of axial velocity, wall shear stress and secondary velocities; and although found to be satisfactory overall, some differences in detail revealed possible shortcomings in the measurement of secondary flow. This, together with other previously reported cases, indicates, that, although the present method cannot be expected to replace experiment in providing turbulent passage flow data, it has an important role to play in interpreting and supplementing experiments.
The numerical solution of Stokes flow in a domain with re‐entrant boundaries by the boundary element method
Authors: Mitra A. K. , Ingber M. S.
Published: August 2005

Numerical solutions are presented for two‐dimensional low Reynolds number flow in a rotating tank with stationary barriers. The boundary element method is employed, assuming straight panels and quadratic source distribution. The feasibility of repositioning the nodes as a way to minimize the error is explored. A stretching parameter places smaller elements near the re‐entrant regions. Elementary error analysis shows uniform improvement in the solution with stretching. The changing eddy pattern for different numbers and sizes of the barriers is compared with experimental results.
Transient three‐dimensional flow in an enclosure with a hot spot on a vertical wall
Authors: Kuhn D. , Oosthuizen P. H.
Published: August 2005

A numerical method for the solution of the vector potential/vorticity vector formulation of the transient, fully three‐dimensional Navier‐Stokes energy and continuity equations has been applied to simulate the development of natural convective flow within a ‘box’ after a sudden temperature change on a vertical portion of the wall. Only one cavity size has been considered, this having a vertical height of three times its width and a horizontal length of six times its width. A single heated rectangular hot spot or ‘element’ on an otherwise adiabatic wall is centred between the vertical end walls. The opposite vertical wall is held at the intial fluid temperature, and all other walls are assumed to be adiabatic. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy force. The numerical method is an underrelaxation Gauss‐Seidel method using finite differencing at each time step. Solutions have been obtained for a Prandtl number of 0.71, for Rayleigh numbers, based on the width, of between 0 and 100000 and for a number of heated element locations and sizes.
Numerical solutions of high‐Re recirculating flows in vorticity‐velocity form
Authors: Guj G. , Stella F.
Published: August 2005

A numerical method for computing high‐Re laminar steady flows is presented. The incompressible Navier‐Stokes equations are expressed in terms of vorticity‐velocity variables, discretized in space by finite differences on a staggered grid and advanced in time by a scalar alternating direction implicit (ADI) procedure, which allows a fully vectorized computer code. The accuracy and efficiency of the present formulation are discussed in comparison with the standard ω‐ψ and u, v, P forms. Numerical results are presented for two test cases: the driven cavity at Re up to 5000 and the backward‐facing step at Re up to 800.
A Navier‐Stokes code for S‐shaped diffusers—a review
Authors: Loeffler Albert L.
Published: August 2005

Three‐dimensional, compressible, internal flow solutions obtained using a thin‐layer Navier‐Stokes code are presented. The code, formulated by P.D. Thomas, is based on the Beam‐Warming implicit factorization scheme; the boundary conditions also are formulated implicitly. Turbulent flow is treated through the use of the Baldwin‐Lomax two‐layer, algebraic eddy viscosity model. Steady‐state solutions are obtained by solving numerically the time‐dependent equations from given initial conditions until the time‐dependent terms become negligible. The configuration considered is a rectangular cross‐section, S‐shaped centreline diffuser duct with an exit/inlet area ratio of 2.25. The Mach number at the duct entrance is 0.9, with a Reynolds number of 5.82 × 105. Convergence to the final results required about 2700 time steps or 11 hours of CPU time on our CRAY‐1M computer. The averaged residuals were reduced by about two orders of magnitude during the computations. Several regions of separated flow exist within the diffuser. The separated flow region on the upper wall, downstream of the second bend, is by far the largest and extends to the exit plane.
A collocation method over staggered grids for the Stokes problem
Authors: Bernardi Christine , Maday Yvon
Published: August 2005

This paper is devoted to the description and the detailed numerical analysis of a new spectral collocation method for the Stokes problem in a square, involving three staggered grids.
Boundary‐type finite element method for wave propagation analysis
Authors: Kawahara Mutsuto , Sakurai Hideyuki , Kashiyama Kazuo
Published: August 2005

The boundary‐type finite element method has been investigated and applied to the Helmholz and mild‐slope equations. Four types of interpolation function are examined based on trigonometric function series. Three‐node triangular, four‐node quadrilateral, six‐node triangular and eight‐node quadrilateral elements are tested; these are all non‐conforming elements. Three types of numerical example show that the three‐node triangular and four‐node quadrilateral elements are useful for practical analysis.
Laminar flow and heat transfer in a periodically converging‐diverging channel
Authors: Garg Vijay K. , Maji P. K.
Published: August 2005

A finite difference solution for laminar viscous flow through a sinusoidally curved converging‐diverging channel is presented. The physical wavy domain is transformed into a rectangular computational domain in order to simplify the application of boundary conditions on the channel walls. The discretized conservation equations for mass, momentum and energy are derived on a control volume basis. The pseudo‐diffusive terms that arise from the co‐ordinate transformation are treated as source terms, and the resulting system of equations is solved by a semi‐implicit procedure based on line relaxation. Results are obtained for both the developing and the fully developed flow for a Prandtl number of 0.72, channel maximum width‐to‐pitch ratio of 1.0, Reynolds number ranging from 100 to 500 and wall amplitude‐to‐pitch ratio varying from 0.1 to 0.25. Results are presented here for constant fluid properties and for a prescribed wall enthalpy only.
Generalized potential flow theory and direct calculation of velocities applied to the numerical solution of the Navier‐Stokes and the Boussinesq equations
Authors: Zijl Wouter
Published: August 2005

A formulation based on three scalar functions or potentials is applied to analyse the Navier‐Stokes and Boussinesq equations in three dimensions. In this formulation an explicit expression for the pressure exists, the so‐called generalized Bernoulli equation. Therefore the scalar functions formulation may be considered as a generalization of the well‐known potential flow and Bernoulli theory for irrotational fluid motion. The many advantages of this formulation applied to three‐dimensional Navier‐Stokes and Boussinesq flow will be discussed, and a numerical example is given as an illustration.
Magnetohydrodynamic flow past a porous rotating disk in a circular magnetic field
Authors: Kishore Kumar S. , Thacker William I. , Watson Layne T.
Published: August 2005

This paper studies the effects of a circular magnetic field on the flow of a conducting fluid about a porous rotating disk. Using modern quasi‐Newton and globally convergent homotopy methods, numerical solutions are obtained for a wide range of magnetic field strengths, suction and injection velocities and Alfven and disk speeds. Results are presented graphically in terms of three non‐dimensional parameters. There is excellent agreement with previous work and asymptotic formulae.
Acceleration of the pressure correction method for a rotating Navier‐Stokes problem
Authors: Lonsdale G. , Walsh J. E.
Published: August 2005

The behaviour of the pressure correction method is studied for the solution of the incompressible steady‐state Navier‐Stokes and continuity equations in a rotating cylindrical‐polar co‐ordinate system, the specific problem being that of laminar source‐sink flow between two corotating discs. Modifications to improve the linearization and the handling of the rotation terms are introduced, and we compare three extended pressure correction schemes and also the use of a multigrid algorithm in part of the calculation procedure as a linear solver.
Finite element, stream function‐vorticity solution of secondary flow in the channels of a rod bundle
Authors: Slagter W.
Published: August 2005

A finite element method has been applied to predict the overall features of the fully developed turbulent flow in the non‐circular channels of a rod bundle. The finite element discretization is based on the conventional Galerkin method using an isoparametric quadrilateral element with mixed interpolation.

The primary axial flow and turbulent kinetic energy distributions have been predicted for fully developed turbulent flow conditions right up to the wall. The secondary velocity is represented by the stream function‐vorticity formulation and the no‐slip boundary conditions are explicitly introduced in the nonlinear equations by a boundary vorticity formula. The Newton‐Raphson method is applied to the stream function‐vorticity equations and solved simultaneously by the frontal solution technique.

A one‐equation eddy viscosity model of turbulence and an algebraic stress transport model have been used to predict primary axial velocity, secondary velocities and turbulent kinetic energy. The predictions obtained for a central subchannel of an equilateral‐triangular rod array with p/d= 1.3 are in reasonable agreement with experimental data.
Magnetohydrodynamic flow on a half‐plane
Authors: Sezgin Münevver
Published: August 2005

We investigate the magnetohydrodynamic flow (MHD) on the upper, half of a non‐conducting plane for the case when the flow is driven by the current produced by an electrode placed in the middle of the plane. The applied magnetic field is perpendicular to the plane, the flow is laminar, uniform, steady and incompressible. An analytical solution has been developed for the velocity field and the induced magnetic field by reducing the problem to the solution of a Fredholm's integral equation of the second kind, which has been solved numerically. Infinite integrals occurring in the kernel of the integral equation and in the velocity and magnetic field were approximated for large Hartmann numbers by using Bessel functions. As the Hartmann number M increases, boundary layers are formed near the non‐conducting boundaries and a parabolic boundary layer is developed in the interface region. Some graphs are given to show examples of this behaviour.
Non‐linear transient phenomena in a complex recirculating flow: A numerical investigation
Authors: Freitas Christopher J. , Street Robert L.
Published: August 2005

A role of numerical methods in engineering research is illustrated in the present work, namely the use of computer algorithms as experimental facilities. A complex recirculating flow in a three‐dimensional cavity was simulated and an extensive data base was generated which complements data measured in concurrent physical experiments. The objective of this numerical investigation was to improve understanding of physical phenomena in recirculating flows. The dominant physical phenomena in this shear‐driven flow simulation are Taylor‐Görtler vortices. These structures are intimately coupled with the primary recirculating flow and the effects of end‐wall viscous damping.