bluuebunny/crossref_metadata_2025_split huggingface dataset:
The cell Reynolds number myth
Authors: Thompson H. Doyle , Webb Brent W. , Hoffman Joe D. 
Published: August 2005

AbstractThe commonly accepted linear stability analysis for the forward‐time centred‐space (FTCS) algorithm applied to the transport equation has led to the concept of a cell Reynolds number restriction on the spatial grid size. This paper shows where the commonly accepted original analysis is in error and presents the correct stability restrictions, which are restrictions on the time step, not the spatial grid size. There is no cell Reynolds number restriction. The results are confirmed by numerical computations for the two‐dimensional driven cavity problem.
A compatible mixed design and analysis finite element method for the design of turbomachinery blades
Authors: Cedar R. D. , Stow P. 
Published: August 2005

AbstractIn this paper the development of a compatible mixed design and analysis method is presented for the quasi‐three‐dimensional finite element blade‐to‐blade program FINSUP. The method consists of two parts. The first is concerned with a method of modelling changes to a blade shape using a surface transpiration model. The second is concerned with determining the relationship between the displaced blade surface and the surface velocity distribution. It is shown that with the Newton‐Raphson procedure adopted in the method a very efficient manner of introducing the design option is possible. As a consequence the resulting program is fast and completely interactive. A number of examples are given to illustrate how the mixed design and analysis mode can be used in practical blade design.
Numerical outflow boundary conditions for the shallow‐water equations
Authors: Vreugdenhil C. B. , Booij N. 
Published: August 2005

AbstractA simple explanation is given of the occurrence of wiggles in the flow field near outflow boundaries. If the shallow‐water equations are solved numerically spurious solutions with an oscillatory character turn out to exist, which can be generated by certain additional numerical boundary conditions on the downstream side. The wiggles usually damp quickly with the distance from the boundary. Some ways of handling the downstream boundary are given which largely avoid the occurrence of wiggles.
Mesh effects on the computation of small amplitude water waves
Authors: Toro E. F. , O'Carroll M. J. 
Published: August 2005

AbstractComputational difficulties arise in the non‐linear free‐surface problem for water waves both at large amplitudes when the crest becomes nearly singular and at small amplitudes when the wave is very close to the alternative uniform flow solution. Since the limiting wavelengths for small amplitude waves are known from the Stokes linearized theory, these are used in checking results for finite‐amplitude programs. When Southwell and Vaisey1 first tried this, their methods gave an unexplained overestimate, by 6 per cent, of the limiting wavelength. This paper shows how coarse mesh effects can create such an overestimate, gives very accurate solutions at small amplitudes and considers accuracy in relation to the mesh for short and long waves.
Analytic test cases for three‐dimensional hydrodynamic models
Authors: Lynch Daniel R. , Officer Charles B. 
Published: August 2005

AbstractExact periodic solutions are generated for the 3‐D hydrodynamic equations in linearized form. A linear slip condition is enforced at the bottom, based on the velocity at the bottom. It is shown that the bottom stress can be equivalently expressed in terms of the vertically averaged velocity, and expressions for this bottom stress coefficient are derived in terms of the primary parameters of the problem. As a result, the three‐dimensional structure may be assembled from conventional solutions to (a) the 1‐D vertical diffusion equation; and (b) the 2‐D vertically averaged shallow water equations. In the latter, the bottom stress effects are shown to be complex and frequency‐dependent, and an additional rotational term is required for their representation.
On the performance of quadrilateral finite elements in the solution to the Stokes equations in periodic structures
Authors: Sáez A. E. , Carbonell R. G. 
Published: August 2005

AbstractThe use of the finite element method in solving the problem of flow of a Newtonian fluid in periodically constricted tubes is explored. The performance of eight node serendipity and nine node Lagrangian elements is compared. It was found that the Lagrangian element results in unstable velocity fields when stagnant or recirculation regions are present. This is characteristic of tubes with large expansion zones. The eight node element does not exhibit instabilities. Both elements give accurate pressure fields. This behaviour is contrary to traditional results obtained for flow problems with similar geometrical characteristics. This suggests that the periodicity of the boundary conditions might be the cause of the instabilities in the numerical solution.The use of the continuity equation to simplify the viscous terms in the Stokes equations resulted, in this particular case, in a deterioration of the rate of convergence of the algorithm.
Solution of the incompressible mass and momentum equations by application of a coupled equation line solver
Authors: Galpin P. F. , Van Doormaal J. P. , Raithby G. D. 
Published: August 2005

AbstractThis paper describes an iterative technique for solving the coupled algebraic equations for mass and momentum conservation for an incompressible fluid flow. The technique is based on the simultaneous solution for pressure and velocity along lines. In a manner similar to ADI methods for a single variable, the solution domain is entirely swept line‐by‐line in each co‐ordinate direction successively until a converged solution is obtained. The tight coupling between the equations that is guaranteed by the method results in an economical solution of the equation set.
Improvement of a pressure gradient method and its application to an unsteady flow problem
Authors: Mochimaru Yoshihiro 
Published: August 2005

AbstractThe 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

AbstractA 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

AbstractThe 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

AbstractModern 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

AbstractPropagation 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

AbstractAn 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

AbstractIt 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

AbstractThe 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

AbstractNew 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

AbstractAn 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

AbstractThe 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

AbstractWe 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

AbstractIn 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

AbstractNumerical 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

AbstractA 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

AbstractThe 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

AbstractIn 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

AbstractThis 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.