bluuebunny/crossref_metadata_2025 huggingface dataset:
Improvement of a pressure gradient method and its application to an unsteady flow problem
Authors: Mochimaru Yoshihiro
Published: August 2005

The pressure gradient method using velocity components and components of a pressure gradient as dependent variables has been modified to solve incompressible Newtonian fluid flow problems numerically. Applying this modified method to unsteady‐state development of flow in a circular cavity shows that, at least for the case of a low Reynolds number flow, relative errors produced by the proposed method are smaller for most time intervals than those produced by the primitive velocity‐pressure variable method and by the standard pressure gradient method. Also it is found that the modified and standard pressure gradient methods can be applied to the unsteady circular cavity flow at a moderate Reynolds number of at least up to 200.
Variable penalty method for finite element analysis of incompressible flow
Authors: Kheshgi Haroon S. , Scriven L. E.
Published: August 2005

A new scheme is applied for increasing the accuracy of the penalty finite element method for incompressible flow by systematically varying from element to element the sign and magnitude of the penalty parameter λ, which enters through ∇.v + p/λ = 0, an approximation to the incompressibility constraint. Not only is the error in this approximation reduced beyond that achievable with a constant λ, but also digital truncation error is lowered when it is aggravated by large variations in element size, a critical problem when the discretization must resolve thin boundary layers. The magnitude of the penalty parameter can be chosen smaller than when λ is constant, which also reduces digital truncation error; hence a shorter word‐length computer is more likely to succeed. Error estimates of the method are reviewed. Boundary conditions which circumvent the hazards of aphysical pressure modes are catalogued for the finite element basis set chosen here. In order to compare performance, the variable penalty method is pitted against the conventional penalty method with constant λ in several Stokes flow case studies.
A note on the stability and accuracy of Cn finite elements in steady diffusion‐convection problems
Authors: Okamoto Naotaka , Niki Hiroshi
Published: August 2005

The paper is concerned with stability and accuracy of an nth order Lagrangian family of finite element steady‐state solutions of the diffusion‐convection equation, and furthermore is concerned with the stability and the accuracy of on mth kind Hermitian family of finite element solutions. We discuss the stability of the numerical solution based on the fact that the characteristic finite element solution can be expressed approximately as a rational function of cell Peclet number Pec ( = uh/k). Moreover, it is shown that by eliminating derivatives and by using the interpolation method over elements a stable solution is obtained over the domain independent of Pec for P1,3, and for P2,5 the stable solution is obtained for Pec less than 44.4.
Numerical modelling of viscous non‐Newtonian effects in lubricating systems
Authors: Bourgin P. , Francois J. M. , Gay B.
Published: August 2005

Modern lubricants often exhibit shear‐thinning due to the presence of high molecular weight polymers as additives. Therefore the influence of such non‐Newtonian effects on the performances of lubricating systems must be predicted. The corresponding fluid film flow is governed by a non‐linear partial differential equation, which generalizes the classical Reynolds equation. Having prescribed adequate boundary conditions, this equation is solved by a finite element method with optimal control. The problem of the square slider bearing lubricated by the Rabinowitsch fluid is solved in order to test the accuracy of the numerical scheme. The pressure and velocity fields are given and compared with the corresponding ones obtained for the Newtonian fluid.
On the effects of irregular boundaries in finite difference models
Authors: Pedersen Geir
Published: August 2005

Propagation of periodic waves in the vicinity of irregular saw‐tooth shaped boundary in finite difference models is investigated. The reflection of an incoming wave from a single saw‐tooth boundary is found to be accompanied by a phase shift. It is shown that any wave mode propagating along such a boundary is trapped and decays in the direction normal to the boundary. A wave propagating along a channel with saw‐tooth shaped lateral boundaries is influenced by the trapped waves, which leads to a reduction of the phase velocity. Phase velocities obtained from the present normal mode analysis are compared to velocities in numerical experiments. The agreement is excellent.
Performance evaluation of an inverse integral equation method applied to turbomachine cascades
Authors: Martin D. , Ribaut M.
Published: August 2005

An improved formulation of the inverse integral equation method proposed in Reference 1 is presented which allows, in particular, a well‐posed problem to be ensured. The corresponding computation code is tested in an exhaustive manner for axial and radial compressor and turbine cascades. The agreement between the velocity field obtained with the inverse method and that resulting from a direct calculation is examined for subsonic, transonic and supersonic flows. Accuracy and reliability of the solution to the boundary condition problem are excellent for the subsonic and transonic flows. However, for the supersonic flow, the application of the method seems to be limited by the use of elementary solutions of the Laplace operator.
Stabilization of explicit methods for hyperbolic partial differential equations
Authors: Wubs F. W.
Published: August 2005

It is well known that explicit methods are subject to a restriction on the time step. This restriction is a drawback if the variation of the solution in time is so small that accuracy considerations would allow a larger time step. In this case, implicit methods are more appropriate because they do allow large time steps. However, in general, they require more storage and are more difficult to implement than explicit methods. In this paper we propose a technique by which it is possible to stabilize explicit methods for quasi‐linear hyperbolic equations. The stabilization turns out to be so effective that explicit methods become a good alternative to unconditionally stable implicit methods.
Three‐dimensional analysis of the flow in a curved hydraulic turbine draft tube
Authors: Shyy Wei , Braaten Mark E.
Published: August 2005

The three‐dimensional turbulent flow in a curved hydraulic turbine draft tube is studied numerically. The analysis is based on the steady Reynolds‐averaged Navier–Stokes equations closed with the κ‐ε model. The governing equations are discretized by a conservative finite volume formulation on a non‐orthogonal body‐fitted co‐ordinate system. Two grid systems, one with 34 × 16 × 12 nodes and another with 50 × 30 × 22 nodes, have been used and the results from them are compared. In terms of computing effort, the number of iterations needed to yield the same degree of convergence is found to be proportional to the square root of the total number of nodes employed, which is consistent with an earlier study made for two‐dimensional flows using the same algorithm. Calculations have been performed over a wide range of inlet swirl, using both the hybrid and second‐order upwind schemes on coarse and fine grids. The addition of inlet swirl is found to eliminate the stalling characteristics in the downstream region and modify the behaviour of the flow markedly in the elbow region, thereby affecting the overall pressure recovery noticeably. The recovery factor increases up to a swirl ratio of about 0˙75, and then drops off. Although the general trends obtained with both finite difference operators are in agreement, the quantitative values as well as some of the fine flow structures can differ. Many of the detailed features observed on the fine grid system are smeared out on the coarse grid system, pointing out the necessity of both a good finite difference operator and a good grid distribution for an accurate result.
Development of new triangular elements for free surface flows
Authors: Dhatt Gouri , Soulaimani Azzeddine , Ouellet Yvon , Fortin Michel
Published: August 2005

New finite elements have been developed to simulate steady and unsteady two‐dimensional free surface flows. The depth‐averaged velocity components with the free surface elevation have been used as independent variables in the model. The differences between the various elements presented lie in the choice of velocity approximation. The Newton–Raphson method has been used to solve the non‐linear system of equations. Emphasis is put on bench‐mark examples to assess the accuracy and efficiency of the elements. A simple stable new element tested herein shows promising advantages for industrial finite element codes.
Computation of internal turbulent flow with a large separated flow region
Authors: Kaul Upender K. , Kwak Dochan
Published: August 2005

An implicit two‐equation turbulence solver, KEM. in generalized co‐ordinates, is used in conjunction with the three‐dimensional incompressible Navier–Stokes solver, INS3D, to calculate the internal flow in a channel and a channel with a sudden 2:3 expansion. A new and consistent boundary procedure for a low Reynolds number form of the κ‐ε turbulence model is chosen to integrate the equations up to the wall. The high Reynolds number form of the equations is integrated using wall functions. The latter approach yields a faster convergence to the steady‐state solution than the former. For the case of channel flow, both the wall‐function and wall‐boundary‐condition approaches yield results in good agreement with the experimental data. The back‐step (sudden expansion) flow is calculated using the wall‐function approach. The predictions are in reasonable agreement with the experimental data.
Finite element stream function‐vorticity solutions of the incompressible Navier‐Stokes equations
Authors: Peeters M. F. , Habashi W. G. , Dueck E. G.
Published: August 2005

The incompressible, two‐dimensional Navier‐Stokes equations are solved by the finite element method (FEM) using a novel stream function/vorticity formulation. The no‐slip solid walls boundary condition is applied by taking advantage of the simple implementation of natural boundary conditions in the FEM, eliminating the need for an iterative evaluation of wall vorticity formulae. In addition, with the proper choice of elements, a stable scheme is constructed allowing convergence to be achieved for all Reynolds numbers, from creeping to inviscid flow, without the traditional need for upwinding and its associated false diffusion. Solutions are presented for a variety of geometries.
Numerical simulation of the horizontal Bridgman growth. Part I: Two‐dimensional flow
Authors: Crochet M. J. , Geyling F. T. , Van Schaftingen J. J.
Published: August 2005

We study the generation of periodic velocity and temperature fields in a plane horizontal crucible of molten metal under the action of a horizontal temperature gradient. The geometry and the boundary conditions are similar to those encountered in the Bridgman growth process of semiconductor crystals, although the present paper is limited to two‐dimensional flows. We use transient finite difference and finite element algorithms which lead to identical results. We demonstrate the oscillatory mechanism in two different geometries.
Pressure potential formulation of 2‐D stokes problems in multiply‐connected domains
Authors: Dierieck C.
Published: August 2005

In general Stokes problems, no boundary conditions exist for the pressure. But pressure is an L2(Ω) function and can uniquely be represented as the divergence of a precisely defined vector field. In the 2‐D case, this vector field can in turn be represented as the sum of a gradient (of a pressure‐potential) and the curl of a second scalar potential. The latter potential is entirely determined by the first one. A variational equation is obtained for such pressure potential class, which exists and is uniquely characterized. This variational problem is well‐posed. Finite element approximations can easily be realized and ensure high convergence rates for the L2(Ω) norm of the pressure.
Three‐dimensional surface water modelling using a mesh adaptive technique
Authors: Sarraf S. , Kahawita R. , Camarero R.
Published: August 2005

Numerical simulation of open water flow in natural courses seems to be doomed to one‐ or two‐dimensional numerical simulations. Investigations of flow hydrodynamics through the application of three‐dimensional models actually have very few appearances in the literature. This paper discusses the development and the initial implementation of a general three‐dimensional and time‐dependent finite volume approach to simulate the hydrodynamics of surface water flow in rivers and lakes. The slightly modified Navier‐Stokes equations, together with the continuity and the water depth equations, form the theoretical basis of the model. A body‐fitted time‐dependent co‐ordinate system has been used in the solution process, in order to accommodate the commonly complex and irregular boundary and bathymetry of natural water courses. The proposed adaptive technique allows the mesh to follow the movement of the water boundaries, including the unsteady free‐water surface.

The primitive variable equations are written in conservative form in the Cartesian co‐ordinate system, and the computational procedure is executed in the moveable curvilinear co‐ordinate system. Special stabilizing techniques are introduced in order to eliminate the oscillating behaviour associated with the finite volume formulation. Also, a new and comprehensive approximation for the pressure forces at the faces of a control volume is presented. Finally, results of several tests demonstrate the performance of the finite volume approach coupled with the adaptive technique employed in the three‐dimensional time‐dependent mesh system.
Lagrangian finite element analysis applied to viscous free surface fluid flow
Authors: Ramaswamy Balasubramaniam , Kawahara Mutsuto
Published: August 2005

A new Lagrangian finite element formulation is presented for time‐dependent incompressible free surface fluid flow problems described by the Navier‐Stokes equations. The partial differential equations describing the continuum motion of the fluid are discretized using a Galerkin procedure in conjunction with the finite element approximation. Triangular finite elements are used to represent the dependent variables of the problem. An effective time integration procedure is introduced and provides a viable computational method for solving problems with equality of representation of the pressure and velocity fields. Its success has been attributed to the strict enforcement of the continuity constraint at every stage of the iterative process. The capabilities of the analysis procedure and the computer programs are demonstrated through the solution of several problems in viscous free surface fluid flow. Comparisons of results are presented with previous theoretical, numerical and experimental results.
Explicit adaptive calculations of wrinkled flame propagation
Authors: Benkhaldoun F. , Larrouturou B.
Published: August 2005

The aim of this work is to study the propagation of a curved premixed flame in an infinite two‐dimensional tube. The numerical method combines some features of the finite‐element and of the finite‐difference methods, and uses a moving adaptive grid procedure in order to reduce the computational costs.
2‐D/3‐D finite‐element solution of the steady Euler equations for transonic lifting flow by stream vector correction
Authors: Dabaghi Fadi El , Pironneau Olivier , Periaux Jacques , Poirier GÉRard
Published: August 2005

In this paper we study the validation of the new formulation (potential‐stream vector) of the steady Euler equations in 2‐D/3‐D transonic lifting regime flow. This approach, which is based on the Helmholtz decomposition of a velocity vector field, is designed to extend the potential approximation of Euler equations for severe situations such as high transonic or rotational subsonic flows. Different results computed by a fixed point algorithm on the stream vector correction are shown and discussed by comparing them with those obtained by the full potential approach.
The computation of turbulent flows of industrial complexity by the finite element method—progress and prospects
Authors: Hutton A. G. , Smith R. M. , Hickmott S.
Published: August 2005

This paper is an expanded version of that delivered at the recent Sixth International Symposium on Finite Element Methods in Flow Problems, Antibes, France. It begins by reviewing the role of the finite element method (FEM) in turbulent flow simulation during recent years. The difficulties in incorporating sufficiently general descriptions of turbulence (i.e. two‐equation models) into successful finite‐element‐based Navier‐Stokes codes are examined and analysed in some depth. Current progress by various workers in overcoming these difficulties is reviewed and, by concentrating on one particular approach, it is demonstrated that the FEM has now matured into a powerful and flexible tool for solving two‐dimensional turbulent flows of industrial complexity. The applications presented highlight those features which render the FEM attractive in this field (viz., minimal false diffusion, arbitrary local refinement, boundary fitting capabilities and non‐structured grids). Finally, the prospects and challenges for the future are briefly discussed. In particular, the urgency and difficulty of constructing a competitive three‐dimensional capability which preserves these features is examined.
Non‐linear free surface flows and an application of the Orlanski boundary condition
Authors: Jagannathan Sridhar
Published: August 2005

The focus of this paper is the analysis of spatially two‐dimensional non‐linear free surface problems. The critical aspects of the problem concern the treatment of the non‐linear free surface, the body boundary condition for large motions and the imposition of suitable radiation conditions. To address such complexities, time domain simulation was chosen as the method of analysis. With the use of a finite domain for simulation, a major concern is with the radiation condition to be applied at the open or truncation boundary. For the two‐dimensional problem at hand, no theoretical radiation conditions are known to exist. An extension of the Orlanski open boundary condition, based on phase velocity determination at the free surface, is proposed. Three categories of problems were analysed using numerical simulation‐namely, freely moving steep waves, waves over a submerged body and forced body motion. Simulation results have been compared with linear theory and experiments.
A shock‐capturing scheme for body‐fitted meshes
Authors: Glaister P.
Published: August 2005

A finite difference scheme based on flux difference splitting is presented for the solution of the two‐dimensional Euler equations of gas dynamics in a generalized co‐ordinate system. The scheme is based on numerical characteristic decomposition and solves locally linearized Riemann problems using upwind differencing. The decomposition is for a generalized co‐ordinate system and a convex equation of state. This ensures good shock‐capturing properties when incorporated with operator splitting and the advantage of using body‐fitted co‐ordinates. The resulting scheme is applied to supersonic flow of real air' past a circular cylinder.
A spectral multi‐domain technique for viscous compressible reacting flows
Authors: Macaraeg M. G. , Streett C. L.
Published: August 2005

The first application of a spectral multi‐domain method for viscous compressible flow is presented. The method imposes a global flux balance condition at the interface so that high‐order continuity of the solution is preserved. The global flux balance is imposed in terms of a spectral integral of the discrete equations across adjoining domains. Since the discretized equations interior to each domain are solved uncoupled from each other and since the interface relation has a block structure, the solution scheme can be adapted to the particular requirement in each subdomain. To illustrate these advantages a Mach 11 shock calculation is presented to study the chemical kinetics initiated as air passes through a fully resolved shock wave.
A control point form of algebraic grid generation
Authors: Eiseman Peter R.
Published: August 2005

Local control points are established within the context of algebraic grid generation. The method of generation is based upon a multidirectional assembly of multisurface transformations that incorporates the best features of tensor product and Boolean sum constructions. Upon assembly, the resultant capability is the capacity to conform precisely to prescribed boundaries while being able to manipulate the grid through a sparse net of control points.
Linear and non‐linear mechanisms in boundary layer turbulence
Authors: Landahl Marten T.
Published: August 2005

The different stages of bursting and evolution of the fluctuation field in a turbulent boundary layer are governed by mechanisms that may be identified as either predominantly linear, i.e. governed by linear interaction with the mean shear flow, or non‐linear, i.e. with interaction between the fluctuation components also being important. Wave number‐frequency spectra reveal the presence of damped wave modes that may be modelled from the Orr‐Sommerfeld equation. Conditional sampled experimental data for streamwise velocity fluctuations in the wall layer obtained using the variable interval time averaging (VITA) method scale with the threshold level in a manner consistent with linearity. High‐amplitude wall pressure peaks show an approximately linear relationship with the associated vertical velocity fluctuations. Non‐linearity acts primarily in the near‐wall region where the fluctuation velocity is relatively the highest.
Numerical simulation methods of incompressible flows and an application to the Space Shuttle main engine
Authors: Chang J. L. C. , Kwak D. , Rogers S. E. , Yang R.‐J.
Published: August 2005

This paper discusses incompressible Navier‐Stokes solution methods with an emphasis on the pseudocompressibility method. A steady‐state flow solver based on the pseudocompressibility approach is then described. This flow solver code has been used to analyse the internal flow in the Space Shuttle main engine hot‐gas manifold. Salient features associated with this three‐dimensional realistic flow simulation are discussed. Numerical solutions relevant to the current engine analysis and the redesign effort are discussed along with experimental results. This example demonstrates the potential of computational fluid dynamics as a design tool for aerospace applications.
Flame computations by a Chebyshev multidomain method
Authors: Ehrenstein U. , Guillard H. , Peyret R.
Published: August 2005

A Chebyshev collocation method is proposed for the computation of laminar flame propagation in a two‐dimensional gaseous medium. The method is based on a domain decomposition technique associated with co‐ordinate transforms to map the infinite physical subdomains into finite computational ones. The influence matrix method is used to handle the patching conditions at the interfaces. This technique is particularly efficient since at each time step only matrix products have to be performed. The method is tested first on an elliptic model problem; it is then applied to laminar flame computations, including calculations of cellular instabilities of flame fronts.
An inverse finite element method with an application to extrusion with solidification
Authors: Alexandrou A. N. , Anturkar N. R. , Papanastasiou T. C.
Published: August 2005

The flow and solidification of planar jets are analysed by means of an efficient inverse isotherm finite element method. The method is based on a tessellation that is constructed by isotherms as characteristic co‐ordinate lines transverse to the flow direction. Thus opposite sides of finite elements lie on isotherms. The method allows the simultaneous determination of the location of the isotherms with the primary unknowns, namely, the velocity, the pressure, the temperature and the location of the free surface. Thus the determination of the location of the solidification front (which is known to pose significant computational difficulties) is automatic. This facilitates the control of the location of the solidification front by controlling macroscopic variables such as the flow rate, the cooling rate and the capillary design. The location of the solidification may then be suitably chosen to influence the frozen‐in orientation and structure in extrusion of high‐performance materials such as composites and polymers, in continuous casting of metals and in growth of crystals.
A finite element analysis of a free surface drainage problem of two immiscible fluids
Authors: Mori Masatake , Natori Makoto , Guo‐Feng Zhang
Published: August 2005

A sharp interface problem arising in the flow of two immiscible fluids, slag and molten metal in a blast furnace, is formulated using a two‐dimensional model and solved numerically. This problem is a transient two‐phase free or moving boundary problem, the slag surface and the slag–metal interface being the free boundaries. At each time step the hydraulic potential of each fluid satisfies the Laplace equation which is solved by the finite element method. The ordinary differential equations determining the motion of the free boundaries are treated using an implicit time‐stepping scheme. The systems of linear equations obtained by discretization of the Laplace equations and the equations of motion of the free boundaries are incorporated into a large system of linear equations. At each time step the hydraulic potential in the interior domain and its derivatives on the free boundaries are obtained simultaneously by solving this linear system of equations. In addition, this solution directly gives the shape of the free boundaries at the next time step. The implicit scheme mentioned above enables us to get the solution without handling normal derivatives, which results in a good numerical solution of the present problem. A numerical example that simulates the flow in a blast furnace is given.
Stable second‐order accurate iterative solutions for second‐order elliptic problems
Authors: Lin Avi
Published: August 2005

The paper describes a numerical scheme for solving a convection–diffusion elliptic system with very small diffusion coefficients. This iterative numerical procedure is unconditionally stable and converges very rapidly. Although only linear equations are considered here, this technique can be easily extended to non‐linear equations, while keeping its main features as for the linear case. The numerical experiments presented are quite general and confirm most of these features. These examples also show a good way of implementing this scheme.
Numerical perturbation method for approximate solution of poisson's equation on a moderately deforming grid
Authors: Strigberger Jack
Published: August 2005

In problems such as the computation of incompressible flows with moving boundaries, it may be necessary to solve Poisson's equation on a large sequence of related grids. In this paper the LU decomposition of the matrix A0 representing Poisson's equation discretized on one grid is used to efficiently obtain an approximate solution on a perturbation of that grid. Instead of doing an LU decomposition of the new matrix A, the RHS is perturbed by a Taylor expansion of A−1 about A0. Each term in the resulting series requires one ‘backsolve’ using the original LU.

Tests using Laplace's equation on a square/rectangle deformation look promising; three and seven correction terms for deformations of 20% and 40% respectively yielded better than 1% accuracy.

As another test, Poisson's equation was solved in an ellipse (fully developed flow in a duct) of aspect ratio 2/3 by perturbing about a circle; one correction term yielded better than 1% accuracy.

Envisioned applications other than the computation of unsteady incompressible flow include: three‐dimensional parabolic problems in tubes of varying cross‐section, use of ‘elimination’ techniques other than LU decomposition, and the solution of PDEs other than Poisson's equation.
A Newton/upwind method and numerical study of shock wave/boundary layer interactions
Authors: Liou Meng‐Sing
Published: August 2005

The objective of the paper is twofold. First we describe an upwind/central differencing method for solving the steady Navier–Stokes equations. The symmetric line relaxation method is used to solve the resulting algebraic system to achieve high computational efficiency. The grid spacings used in the calculations are determined from the triple‐deck theory, in terms of Mach and Reynolds numbers and other flow parameters. Thus the accuracy of the numerical solutions is improved by comparing them with experimental, analytical and other computational results. Secondly we proceed to study numerically the shock wave/boundary layer interactions in detail, with special attention given to the flow separation. The concept of free interaction is confirmed. Although the separated region varies with Mach and Reynolds numbers, we find that the transverse velocity component behind the incident shock, which has not been identified heretofore, is also an important parameter. A small change of this quantity is sufficient to eliminate the flow separation entirely.
Internal wave reflections and transmissions arising from a non‐uniform mesh. Part I: An analysis for the Crank–Nicolson linear finite element scheme
Authors: Cathers B. , Bates S. , O'Connor B. A.
Published: August 2005

This is the first of a series of three related papers dealing with some of the consequences of non‐uniform meshes in a numerical model. In this paper the accuracy of the Crank–Nicolson linear finite element scheme, which is applied to the linear shallow water equations, is examined in the context of a single abrupt change in nodal spacing. The (in)accuracy is quantified in terms of reflection and transmission coefficients. An incident wave impinging on the interface between two regions with different nodal spacings is shown to give rise to no reflected waves and two transmitted waves. The analysis is verified using three different wavelengths (2Δx, 4Δx 8Δx) in three ‘hot‐start’ numerical experiments with a mesh expansion factor of 2 and three experiments with a mesh contraction factor of 1/2. An energy flux analysis based on the concept of group velocity shows that energy is conserved across the interface.
Internal wave reflections and transmissions arising from a non‐uniform mesh. Part III: The occurrence of evanescent waves in the Crank‐Nicolson linear finite element scheme
Authors: Cathers B. , Bates S. , O'Connor B. A.
Published: August 2005

The numerical scheme upon which this paper is based is the 1D Crank–Nicolson linear finite element scheme. In Part I of this series it was shown that for a certain range of incident wavelengths impinging on the interface of an expansion in nodal spacing, an evanescent (or spatially damped) wave results in the downstream region. Here in Part III an analysis is carried out to predict the wavelength and the spatial rate of damping for this wave. The results of the analysis are verified quantitatively with seven ‘hot‐start’ numerical experiments and qualitatively with seven ‘cold‐start’ experiments. Weare has shown that evanescent waves occur whenever the frequency of a disturbance at a boundary exceeds the maximum frequency given by the dispersion relation. In these circumstances the ‘extended dispersion’ relation can be used to determine the rate of spatial decay.

In the context of a domain consisting of two regions with different nodal spacings, the use of the group velocity concept shows that evanescent waves have no energy flux associated with them when energy is conserved.
A total pressure correction for upstream weighted schemes
Authors: De Henau V. , Raithby G. D. , Thompson B. E.
Published: August 2005

Upwind differencing is known to lead to a substantial loss in total pressure. The present paper illustrates the importance of this error on two problems: flow in a converging–diverging duct and flow around a cylinder. A correction is proposed that reduces the total pressure error and yields dramatically improved results for the test problems.
Three‐dimensional reduced Navier–Stokes solutions for subsonic separated and non‐separated flows, using a global pressure relaxation procedure
Authors: Cohen R. , Khosla P. K.
Published: August 2005

The reduced Navier–Stokes and thin layer approximations to the Navier–Stokes equations are used to obtain solutions for viscous subsonic three‐dimensional flows. A spatial marching method is combined with a direct sparse matrix solver to obtain successive solutions in a global relaxation process. Results have been obtained for flow fields with and without regions of flow reversal.
Second‐order finite difference solutions for the flow between rotating concentric spheres
Authors: Schwengels Steve , Schultz David , Shay William
Published: August 2005

This paper describes a second‐order method to calculate approximate solutions to flow of viscous incompressible fluid between rotating concentric spheres. The governing partial differential equations are presented in the stream–vorticity formulation and are written as a series of second‐order equations. The technique employed makes use of second‐order approximations for all terms in the governing equations and is dependent upon the direction of flow at a given point. This upwind technique has allowed us to generate approximate solutions with larger Reynolds numbers than has generally been possible for second and higher‐order techniques. Solutions have been obtained with Reynolds numbers as large as 3000 and with grids as fine as a 40 × 40 mesh. Results are displayed in the form of level curves for both the stream and vorticity functions. A dimensionless quantity related to the torque acting on both spheres has been calculated from the approximate solution and compared with other results. Results with smaller Reynolds numbers such as 100 and 1000 are in excellent agreement with other published results.
Algebraic turbulence models for the computation of two‐dimensional high‐speed flows using unstructured grids
Authors: Rostand Philippe
Published: August 2005

The incorporation of algebraic turbulence models in a solver for the 2D compressible Navier–Stokes equations using triangular grids is described. A practical way to use the Cebeci–Smith model and to modify it in separated regions is proposed. The ability of the model to predict high‐speed perfect‐gas boundary layers is investigated from a numerical point of view.
Laminar flow and heat transfer over a two‐dimensional triangular step
Authors: Kumar S. G. Ravi , Narayana P. A. Aswatha , Seetharamu K. N. , Ramaswamy B.
Published: August 2005

The velocity correction algorithm is used in the finite element method to solve forced convection problems between parallel plates with a triangular step, for Reynolds numbers up to 1000. Equal‐order interpolation functions for velocity, pressure and temperature are used. The solutions show a smooth variation of pressure. The streamfunction, isotherms, isobars and velocity profiles are presented for a typical Reynolds number of 500. The skin friction and heat transfer results are presented for Reynolds numbers up to 1000.
Fundamental solutions of the streamfunction–vorticity formulation of the Navier–Stokes equations
Authors: Rodriguez‐Prada H. A. , Pironti F. F. , Sáez A. E.
Published: August 2005

A new boundary element procedure is developed for the solution of the streamfunction–vorticity formulation of the Navier–Stokes equations in two dimensions. The differential equations are stated in their transient version and then discretized via finite differences with respect to time. In this discretization, the non‐linear inertial terms are evaluated in a previous time step, thus making the scheme explicit with respect to them. In the resulting discretized equations, fundamental solutions that take into account the coupling between the equations are developed by treating the non‐linear terms as in homogeneities. The resulting boundary integral equations are solved by the regular boundary element method, in which the singular points are placed outside the solution domain.
A finite element solution of unsteady two‐dimensional flow in cascades
Authors: Whitehead D. S.
Published: August 2005

A theory is presented for unsteady two‐dimensional potential transonic flow in cascades of compressor and turbine blades using a mesh of triangular finite elements. The theory leads to a computer program, FINSUP, which is fast and has moderate storage requirements, so that it can be run on a personal computer. Comparisons with other theories in special cases show that the program is accurate in subsonic flow, and that in supersonic flow, although the wave effects are smeared by the numerical process, the results for overall blade force and moment have acceptable accuracy. The program is useful for engineering assessment of unstalled flutter of actual compressor and turbine blades.
Quasimolecular simulation of large liquid drops
Authors: Greenspan Donald
Published: August 2005

Large liquid drops are simulated by molecular aggregates called quasimolecules. The quasimolecules interact in accordance with classical molecular‐type formulae. Supercomputer examples are described and discussed for both stationary and falling water drops.
A Taylor–Galerkin‐based algorithm for viscous incompressible flow
Authors: Hawken D. M. , Tamaddon‐Jahromi H. R. , Townsend P. , Webster M. F.
Published: August 2005

In this paper the development and behaviour of a new finite element algorithm for viscous incompressible flow is presented. The stability and background theory are discussed and the numerical performance is considered for some benchmark problems. The Taylor–Galerkin approach naturally leads to a time‐stepping algorithm which is shown to perform well for a wide range of Reynolds numbers (1 ⩽Re⩽ 400).

A conventional definition forReis assumed.

Various modifications to the algorithm are investigated, particularly with respect to their effects on stability and accuracy.
Singular finite elements for the sudden‐expansion and the die‐swell problems
Authors: Georgiou Georgios C. , Schultz William W. , Olson Lorraine G.
Published: August 2005

The singular finite element method is used to solve the sudden‐expansion and the die‐swell problems in order to improve the accuracy of the solution in the vicinity of the singularity and to speed up the convergence. The method requires minor modifications to standard finite element schemes, and even coarse meshes give more accurate results than refined ordinary finite element meshes. Improved normal stress results for the sudden‐expansion problem have been obtained for various Reynolds numbers up to 100 using the singular elements constructed for the creeping flow problem. In addition, the normal stresses at the walls appear to be insensitive to the singularity powers used in the construction of the singular basis functions. The die‐swell problem is solved using the singular elements constructed for the stick–slip problem. The singular elements accelerate the convergence of the free surface dramatically.
Comparison of experimental data with the numerical simulation of planar entry flow: Role of the constitutive equation
Authors: Gotsis A. D. , Baird D. G. , Reddy J. N.
Published: August 2005

The goal of this research was to determine whether there is any interaction between the type of constitutive equation used and the degree of mesh refinement, as well as how the type of constitutive equation might affect the convergence and quality of the solution, for a planar 4:1 contraction in the finite eiement method. Five constitutive equations were used in this work: the Phan‐Thien–Tanner (PTT), Johnson–Segalman (JS), White–Metzner (WM), Leonov‐like and upper convected Maxwell (UCM) models. A penalty Galerkin finite element technique was used to solve the system of non‐linear differential equations. The constitutive equations were fitted to the steady shear viscosity and normal stress data for a polystyrene melt. In general it was found that the convergence limit based on the Deborah number De and the Weissenberg number We varied from model to model and from mesh to mesh. From a practical point of view it was observed that the wall shear stress in the downstream region should also be indicated at the point where convergence is lost, since this parameter reflects the throughput conditions. Because of the dependence of convergence on the combination of mesh size and constitutive equation, predictions of the computations were compared with birefringence data obtained for the same polystyrene melt flowing through a 4:1 planar contraction. Refinement in the mesh led to better agreement between the predictions using the PTT model and flow birefringence, but the oscillations became worse in the corner region as the mesh was further refined, eventually leading to the loss of convergence of the numerical algorithm. In comparing results using different models at the same wall shear stress conditions and on the same mesh, it was found that the PTT model gave less overshoot of the stresses at the re‐entrant corner. Away from the corner there were very small differences between the quality of the solutions obtained using different models. All the models predicted solutions with oscillations. However, the values of the solutions oscillated around the experimental birefringence data, even when the numerical algorithm would not converge. Whereas the stresses are predicted to oscillate, the streamlines and velocity field remained smooth. Predictions for the existence of vortices as well as for the entrance pressure loss (ΔPent) varied from model to model. The UCM and WM models predicted negative values for ΔPent.
A simple physical approach for deriving the characteristic equations of fluid dynamics
Authors: Wang B. N. , Hoffman J. D.
Published: August 2005

A simple physical approach for deriving the characteristic equations of fluid dynamics is presented. The approach is based on the physical concept that information propagates through a flowfield along pathlines due to particle motion and along wavelines due to acoustic wave motion. The characteristic equations and compatibility equations are derived in vector forms which are valid in any co‐ordinate system.
A finite element solution to turbulent diffusion in a convective boundary layer
Authors: Pai Prasad , Tsang T. H.
Published: August 2005

A second‐order closure turbulence model is used to simulate the plume behaviour of a passive contaminant dispersed in a convective boundary layer. A time‐splitting finite element scheme is used to solve the set of partial differential equations. It is shown that the second‐order closure model compares favourably with recent findings from laboratories, wind‐tunnel experiments and large‐eddy simulations. We also compare the second‐order closure model with the commonly used K‐diffusion model for the same meteorological conditions. Case studies also show the effects of model parameters and turbulence variables on the plume behaviour.
Radiation boundary conditions for finite element solutions of generalized wave equations
Authors: Johnsen Matthias , Paulsen Keith D. , Werner Francisco E.
Published: August 2005

On the basis of the dispersion relation of the generalized linear wave equation we derive a radiation boundary condition (RBC) that explicitly incorporates the physical parameters of the governing equation into the form of the boundary condition. Using finite element techniques we investigate the properties of the generalized RBC by examining forced and unforced solutions to the telegraph and Klein‐Gordon equations in one dimension. The results show that within the limits of the physical parameters of the problem the generalized RBC is an improvement over the Sommerfeld RBC when the governing equation contains additional terms that influence the propagation. These gains are achieved without introducing any computational overhead. A two‐dimensional example suggests that the 1D findings can generalize to higher dimensions.
A Chebyshev spectral collocation method using a staggered grid for the stability of cylindrical flows
Authors: Khorrami Mehdi R.
Published: August 2005

A staggered spectral collocation method for the stability of cylindrical flows is developed. In this method the pressure is evaluated at different nodal points than the three velocity components. These modified nodal points do not include the two boundary nodes; therefore the need for the two artificial pressure boundary conditions employed by Khorrami et al. is eliminated. It is shown that the method produces very accurate results and has a better convergence rate than the spectral tau formulation. However, through extensive convergence tests it was found that elimination of the artificial pressure boundary conditions does not result in any significant change in the convergence behaviour of spectral collocation methods.
Unsteady flow calculation in a radial flow centrifugal pump with spiral casing
Authors: Morfiadakis Evangelos E. , Voutsinas Spyros G. , Papantonis Dimitris E.
Published: August 2005

The prediction of the two‐dimensional unsteady flow established in a radial flow centrifugal pump is considered. Assuming the fluid incompressible and inviscid, the velocity field is represented by means of source and vorticity surface distributions as well as a set of point vortices. Using this representation, a grid‐free (Lagrangian) numerical method is derived based on the coupling of the boundary element and vortex particle methods. In this context the source and vorticity surface distributions are determined through the non‐entry boundary condition together with the unsteady Kutta condition. In order to satisfy Kelvin's theorem, vorticity is shed at the trailing edges of the impeller blades. Then the vortex particle method is used to approximate the convection of the free vorticity distribution. Results are given for a pump configuration experimentally tested by Centre Technique des Industries Mécaniques (CETIM). Comparisons between predictions and experimental data show the capability of the proposed method to reproduce the main features of the flow considered.
Development of a parallel computational fluid dynamics algorithm on a hypercube computer
Authors: Braaten Mark E.
Published: August 2005

One of the main factors limiting the widespread use of computational fluid dynamics codes for engineering design is their very large requirements both in terms of computer memory and CPU time. Distributed memory parallel computers offer both the potential for a dramatic improvement in cost/performance over conventional supercomputers and the scalability to large numbers of processors that is required if performance beyond that of current supercomputers is to be achieved. As part of an evaluation to explore the potential of such machines for computational fluid mechanics applications, a concurrent algorithm for the solution of the Navier‐Stokes equations has been developed and demonstrated on a hypercube parallel computer. The algorithm is based on a domain decomposition of a well‐established serial pressure correction algorithm.

The algorithm is demonstrated on both a 32‐node scalar and eight‐node vector Intel iPSC/2 for complicated two‐dimensional laminar and turbulent flow problems with different grid sizes and numbers of processors. Speed‐ups relative to a single processor of 12.9 with 16 processors and 20.2 with 32 processors are achieved on a scalar iPSC/2, demonstrating the parallel efficiency of the algorithm. Measured performance on a 32‐node scalar iPSC/2 exceeds one‐sixth that of a Cray X‐MP running the original serial algorithm. The performance of the algorithm on an eight‐node vector iPSC/2 exceeds that of the larger scalar hypercube and is about one‐fifth that of the Cray X‐MP. With cost/performance more than 10 times better than the Cray, these results dramatically show the cost effectiveness of vector hypercubes for this class of fluid mechanics algorithm.