bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical prediction of turbulent flow over a two‐dimensional ridge
Authors: Mouzakis F. N. , Bergels G. C. 
Published: August 2005

AbstractPredictions are presented of the two‐dimensional turbulent flow over a triangular ridge. The time‐averaged Reynolds equations are written in an orthogonal curvilinear co‐ordinate system and transformed to finite difference form after discretization in physical space. Turbulence is simulated by the two‐equation κ‐ε model of turbulence. In the first part of the paper the basics of the numerical method are presented and in the second part comparisons are made between predictions and available laboratory data. Therefore the validity and reliability of the method as well as its flexibility in treating complex recirculating flows are assessed. Results of engineering significance are presented of the effect of the ridge slope on the length of the recirculation region and on the overspeed factor on top of the ridge.
The application of finite element analysis to the solution of Stokes wave diffraction problems
Authors: Clark P. J. , Bettess P. , Hearn G. E. , Downie M. J. 
Published: August 2005

AbstractA new finite‐element based method of calculating non‐linear wave loads on offshore structures in extreme seas is presented in this paper. The diffraction wave field is modelled using Stokes wave theory developed to second order. Wave loads and free surface elevations are obtained for fixed surface‐piercing structures by solving a boundary value problem for the second‐order velocity potential. Special attention has been given to the radiation condition for the second‐order diffraction field. Results are presented for three test examples, the vertical cylinders of Kim and Yue and of Chakrabarti, and an elliptic cylinder. These results demonstrate that early problems with the application of second‐order theory arising from inadequate radiation conditions have been overcome.
An axisymmetric model of separated flow about a sphere using discrete vortices
Authors: Lee D. K. , Downie M. J. , Bettess P. 
Published: August 2005

AbstractA procedure for the calculation of the starting flow around a sphere in a uniform stream is presented. The flow field is simulated by a flow of ideal fluid with embedded vorticity. With the assumption that the flow remains symmetric, the vorticity field is approximated by a number of discrete circular line vortices. The image vortices to satisfy the boundary condition for the normal component of velocity on the surface of the sphere are determined by Butler's sphere theorem. The Stokes streamfunction is used for the field description. The motion of vortices is tracked by the vortex‐in‐cell method, the cells being formed by square grids.
A consistent boundary element method for free surface hydrodynamic calculations
Authors: Medina Daniel E. , Liggett James A. , Birchwood Richard A. , Torrance Kenneth E. 
Published: August 2005

AbstractFree surface phenomena are described by equations that exhibit two types of non‐linearities. The first is inherent to the equations themselves and the second is caused by the application of boundary conditions at a free surface at an unknown location. Numerical calculations usually do not specifically recognize the second non‐linearity, nor treat it in a fashion consistent with the more obvious non‐linearities in the boundary conditions. A consistent formulation is introduced in the present paper. The field equation is integrated and the free surface boundary conditions are applied on the unknown geometry by means of appropriate series expansions. The consistent formulation introduces improvements in accuracy and computing speed. The method is demonstrated on several hydrodynamic free surface problems and an error analysis is included.
A 3D finite element method for the simulation of thermoconvective flows and its performances on a vector‐parallel computer
Authors: Carriere Philippe , Jeandel Denis 
Published: August 2005

AbstractA three‐dimensional finite element method for the simulation of thermoconvective flows is presented. Vector‐parallel performances of some preconditioned conjugate gradient methods are compared for solving both large linear systems and the Stokes problem. As significant examples, numerical experiments on the steady two‐ and three‐dimensional Rayleigh‐Bénard convection at high Prandtl number are reported.
A preconditioned conjugate gradient Uzawa‐type method for the solution of the stokes problem by mixed Q1–P0 stabilized finite elements
Authors: Vincent C. , Boyer R. 
Published: August 2005

AbstractWe study the behaviour of a conjugate gradient Uzawa‐type method for a stabilized finite element approximation of the Stokes problem. Many variants of the Uzawa algorithm have been described for different finite elements satisfying the well‐known Inf‐Sup condition of Babuška and Brezzi, but it is surprising that developments for unstable ‘low‐order’ discretizations with stabilization procedures are still missing. Our paper is presented in this context for the popular (so‐called) Q1–P0 element.First we show that a simple stabilization technique for this element permits us to retain the property of a convergence factor bounded independently of the discretization mesh size. The second contribution of this work deals with the construction of a less costly preconditioner taking full advantages of the block diagonal structure of the stabilization matrix. Its efficiency is supported by 2D and. 3D numerical results.
Laminar fluid convection between concentric and eccentric heated horizontal rotating cylinders for low‐Prandtl‐number fluids
Authors: Lee T. S. 
Published: August 2005

AbstractNumerical experiments are performed to study rotational effects on the mixed convection of low‐Prandtlnumber fluids enclosed between the annuli of concentric and eccentric horizontal cylinders. The inner cylinder is assumed to be heated and rotating. The rotational Reynolds number considered is in the range where the effect of Taylor vortices is negligible. The Prandtl number of the fluid considered is in the range 0·01–1·0. The Rayleigh number considered is up to 106. A non‐uniform mesh transformation technique coupled with the introduction of ‘false transient’ parameters to the vorticity and streamfunction‐vorticity expressions was used to solve the governing set of equations. Results show that when the inner cylinder is made to rotate, the multicellular flow patterns observed in stationary cylindrical annuli subside in a manner depending on the Prandtl number of the fluids. Eventually the flow tends toward a uniform flow similar to that of a solid body rotation. For a fixed Rayleigh number and with a Prandtl number of the order of 1·0, when the inner cylinder is made to rotate, the mean Nusselt number is observed to decrease throughout the flow. For lower Prandtl number of the order 0·1–0·01 the mean Nusselt number remained fairly constant when the inner cylinder was made to rotate. The mean Nusselt numbers obtained were also compared with available data from other investigators.
Non‐linear interaction of water waves with submerged obstacles
Authors: Yeung Ronald W. , Vaidhyanathan M. 
Published: August 2005

AbstractThe interaction of two‐dimensional water waves with a fixed submerged cylinder is studied using a finite difference scheme with boundary‐fitted co‐ordinates. A mixed Eulerian–Lagrangian (MEL) formulation is used to satisfy the fully non‐linear free surface conditions. The diffraction of small‐amplitude water waves by a cylinder is examined for various wavelengths and amplitudes of the incident wave. Fourier analyses of the incident and diffracted waves are performed to determine their spectra. An example of a large‐amplitude wave breaking over a cylinder is also studied. The non‐linear numerical solutions are compared with those of experiments and linear theory where appropriate.
A multigrid method for steady incompressible navier‐stokes equations based on flux difference splitting
Authors: Dick E. , Linden J. 
Published: August 2005

AbstractThe steady Navier–Stokes equations in primitive variables are discretized in conservative form by a vertex‐centred finite volume method Flux difference splitting is applied to the convective part to obtain an upwind discretization. The diffusive part is discretized in the central way.In its first‐order formulation, flux difference splitting leads to a discretization of so‐called vector positive type. This allows the use of classical relaxation methods in collective form. An alternating line Gauss–Seidel relaxation method is chosen here. This relaxation method is used as a smoother in a multigrid method. The components of this multigrid method are: full approximation scheme with F‐cycles, bilinear prolongation, full weighting for residual restriction and injection of grid functions.Higher‐order accuracy is achieved by the flux extrapolation method. In this approach the first‐order convective fluxes are modified by adding second‐order corrections involving flux limiting. Here the simple MinMod limiter is chosen. In the multigrid formulation the second‐order discrete system is solved by defect correction.Computational results are shown for the well known GAMM backward‐facing step problem and for a channel with a half‐circular obstruction.
An extended κ–ϵ finite element model
Authors: Jaeger Marc , Dhatt Gouri 
Published: August 2005

AbstractAn extended κ–ϵ model (to include low‐Reynolds‐number regions) employing weighting functions is presented. Wall functions for the near‐wall zones are developed giving correct boundary values for the Shear stress and κ–ϵ. A finite element model using a penalty formulation for incompressible turbulent flow is applied to Solve a flow between two plates. Results with mesh boundaries situated in the near‐wall region and a: the wall are compared with measured values.
A new decoupled finite element algorithm for viscoelastic flow. Part 1: Numerical algorithm and sample results
Authors: Swarbrick S. J. , Nassehi V. 
Published: August 2005

AbstractThis paper presents an algorithm for two‐dimensional Steady viscoelastic flow Simulation in which the Solution of the momentum and continuity equations is decoupled from that of the constitutive equations. The governing equations are discretized by the finite element method, with 3 × 3 element subdivision for the stress field approximation. Non‐consistent Streamline upwinding is also used. Results are given for flow through a converging channel and through an abrupt planar 4:1 contraction.
On the accurate prediction of the wall‐normal velocity in compressible boundary‐layer flow
Authors: Pruett C. David 
Published: August 2005

AbstractWe consider a problem which arises in the numerical solution of the compressible two‐dimensional or axisymmetric boundary‐layer equations. Numerical methods for the compressible boundary‐layer equations are facilitated by transformation from the physical (x, y) plane to a computational (ξ, η) plane in which the evolution of the flow is ‘slow’ in the time‐like ξ direction. The commonly used Levy‐Lees transformation results in a computationally well‐behaved problem, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently non‐linear, and the physical wall‐normal velocity is transformed out of the problem and is not readily recovered. Conventional methods extract the wall‐normal velocity in physical space from the continuity equation, using finite‐difference techniques and interpolation procedures. The present spectrally accurate method extracts the wall‐normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall‐normal velocity, when used in conjunction with a highly accurate spectral collocation method for solving the compressible boundary‐layer equations, results in a discrete solution which satisfies the continuity equation nearly to machine precision. As demonstration of the utility of the method, the boundary layers of three prototypical high‐speed flows are investigated and compared: the flat plate, the hollow cylinder, and the cone. An important implication for classical linear stability theory is also briefly discussed.
Numerical experiments on the stability of leading edge boundary layer flow: A two‐dimensional linear study
Authors: Theofilis Vassilios 
Published: August 2005

AbstractA numerical study is performed in order to gain insight to the stability of the infinite swept attachment line boundary layer. The basic flow is taken to be of the Hiemenz class with an added cross‐flow giving rise to a constant thickness boundary layer along the attachment line. The full Navier‐Stokes equations are solved using an initial value problem approach after two‐dimensional perturbations of varying amplitude are introduced into the basic flow.A second‐order‐accurate finite difference scheme is used in the normal‐to‐the‐wall direction, while a pseudospectral approach is employed in the other directions; temporally, an implicit Crank‐Nicolson scheme is used. Extensive use of the efficient fast Fourier transform (FFT) algorithm has been made, resulting in substantial savings in computing cost.Results for the two‐dimensional linear regime of perturbations are in very good agreement with past numerical and theoretical investigations, without the need for specific assumptions used by the latter, thus establishing the generality of our method.
Computation of fluid flow with a parallel multigrid solver
Authors: Schreck E. , Perić M. 
Published: August 2005

AbstractA finite volume numerical method for the prediction of fluid flow and heat transfer in simple geometries was parallelized using a domain decomposition approach. The method is implicit, uses a colocated arrangement of variables and is based on the SIMPLE algorithm for pressure‐velocity coupling. Discretization is based on second‐order central difference approximations. The algebraic equation systems are solved by the ILU method of Stone.1 To accelerate the convergence, a multigrid technique was used. The efficiency was examined on three different parallel computers for laminar flow in a pipe with an orifice and natural convection in a closed cavity. It is shown that the total efficiency is made up of three major factors: numerical efficiency, parallel efficiency and load‐balancing efficiency. The first two factors were thoroughly investigated, and a model for predicting the parallel efficiency on various computers is presented. Test calculations indicate reasonable total efficiency and favourable dependence on grid size and the number of processors.
Development of a hybrid k‐ε turbulence model for swirling recirculating flows under moderate to strong swirl intensities
Authors: Chang Keh‐Chin , Chen Ching‐Shun 
Published: August 2005

AbstractA hybrid k‐ε turbulence model, based on the concept that the modification of anisotropic effects should not be made in the flow regions inherent to small streamline curvatures, has been developed and examined with the swirling recirculating flows, with the swirl levels ranging from 0·6 to 1·23 in abrupt pipe expansion. A fairly satisfactory agreement of model predictions with the experimental data shows that this hybrid k‐ε model can perform better simulation of swirling recirculating flows as compared to the standard k‐ε model and the modified k‐ε model proposed by Abujelala and Lilley.
Surface waves propagation in shallow water: A finite element model
Authors: Do Carmo J. S. Antunes , Santos F. J. Seabra , Barthélemy E. 
Published: August 2005

AbstractA two‐dimensional (in‐plane) numerical model for surface waves propagation based on the non‐linear dispersive wave approach described by Boussinesq‐type equations, which provide an attractive theory for predicting the depth‐averaged velocity field resulting from that wave‐type propagation in shallow water, is presented. The numerical solution of the corresponding partial differential equations by finite‐difference methods has been the subject of several scientific works. In the present work we propose a new approach to the problem: the spatial discretization of the system composed by the Boussinesq equations is made by a finite element method, making use of the weighted residual technique for the solution approach within each element. The model is validated by comparing numerical results with theoretical solutions and with results obtained experimentally.
Incompressible low‐speed‐ratio flow in non‐uniform distensible tubes
Authors: Reuderink P. J. , van de Vosse F. N. , van Steenhoven A. A. , van Dongen M. E. H. , Janssen J. D. 
Published: August 2005

AbstractThe fluid flow in distensible tubes is analysed by a finite element method based on an uncoupled solution of the equations of wall motion and fluid flow. Special attention is paid to the choice of proper boundary conditions. Computations were made for sinusoidal flow in a distensible uniform tube with the Womersley parameter α = 5, and a ratio between tube radius and wavelenth from 0·0001 to 0·5. The agreement between the numerical results and Womersley's analytic solution depends on the speed ratio between fluid and wave velocity, and is fair for speed ratios up to 0·05. The analysis of the flow field in a distensible tube with a local inhomogeneity revealed a marked influence of wave phenomena and wall motion on the velocity profiles.
Numerical solution of the generalized Serre equations with the MacCormack finite‐difference scheme
Authors: Do Carmo J. S. Antunes , Santos F. J. Seabra , Almeida A. B. 
Published: August 2005

AbstractThis paper describes a two‐dimensional numerical model to solve the generalized Serre equations. In order to solve the system equations, written in the conservative form, we use an explicit finite‐difference method based on the MacCormack time‐splitting scheme. The numerical method and the computational model are validated by comparing one‐ and two‐dimensional numerical solutions with theoretical and experimental results. Finally, the two‐dimensional model (in a horizontal plane) is tested in a domain with complicated boundary conditions.
Modelling large‐bubble formation at submerged orifices
Authors: Bugg J. D. , Rowe R. D. 
Published: August 2005

AbstractThe formation of large gas bubbles at submerged orifices is investigated numerically with a two‐dimensional, transient, finite difference model using a volume fraction specification to track the movement of the gas‐liquid interface. Experimentally observed features of large‐bubble formation such as the initial toroidal shape of the bubbles and the penetration of liquid down the pipe centreline are well predicted by the model. The expected oscillatory nature of growth is also observed. The bubble departure volume corresponds to experiments and to the model of Davidson and Schuler. At present the simulations do not extend far enough to investigate multiple‐bubble ejection and important bubble‐to‐bubble interactions during growth and after departure.
A comparison of coarse and fine grain parallelization strategies for the simple pressure correction algorithm
Authors: Lewis A. J. , Brent A. D. 
Published: August 2005

AbstractThe primary aim of this work was to determine the simplest and most effective parallelization strategy for control‐volume‐based codes solving industrial problems. It has been found that for certain classes of problems, the coarse‐grain functional decomposition strategy, largely ignored due to its limited scaling capability, offers the potential for significant execution speed‐ups while maintaining the inherent structure of traditional serial algorithms. Functional decomposition requires only minor modification of the existing serial code to implement and, hence, code portability across both concurrent and serial computers is maintained. Fine‐grain parallelization strategies at the ‘DO loop’ level are also easy to implement and largely preserve code portability. Both coarse‐grain functional decomposition and fine‐grain loop‐level parallelization strategies for the SIMPLE pressure correction algorithm are demonstrated on a Silicon Graphics 4D280S eight CPU shared memory computer system for a highly coupled, transient two‐dimensional simulation involving melting of a metal in the presence of thermal‐buoyancy‐driven laminar convection. Problems requiring the solution of a larger number of transport equations were simulated by including further scalar variables in the calculation. While resulting in slight degradation of the convergence rate, the functional decomposition strategy exhibited higher parallel efficiencies and yielded greater speed‐ups relative to the original serial code. Initially, this strategy showed a significant degradation in convergence rate due to an inconsistency in the parallel solution of the pressure correction equation. After correcting for this inconsistency, the maximum speed‐up for 16 dependent variables was a factor of 5·28 with eight processors, representing a parallel efficiency of 67%. Peak efficiency of 76% was achieved using five processors to solve for 10 dependent variables.
A collocated finite volume method for predicting flows at all speeds
Authors: Demirdžić I. , Lilek Ž. , Perić M. 
Published: August 2005

AbstractAn existing two‐dimensional method for the prediction of steady‐state incompressible flows in complex geometry is extended to treat also compressible flows at all speeds. The primary variables are the Cartesian velocity components, pressure and temperature. Density is linked to pressure via an equation of state. The influence of pressure on density in the case of compressible flows is implicitly incorporated into the extended SIMPLE algorithm, which in the limit of incompressible flow reduces to its well‐known form. Special attention is paid to the numerical treatment of boundary conditions. The method is verified on a number of test cases (inviscid and viscous flows), and both the results and convergence properties compare favourably with other numerical results available in the literature.
Direct simulation of turbulent flow and heat transfer in a channel. Part I: Smooth walls
Authors: Rutledge Jeffrey , Sleicher Charles A. 
Published: August 2005

AbstractInterest in the use of supercomputers for the direct numerical calculation of turbulence prompts the development of efficient numerical techniques so that calculation at higher Reynolds numbers might be made. This paper presents an efficient pseudo‐spectral technique, similar to but different from others that have recently appeared, for the calculation of momentum and heat transfer to a constant‐property, turbulent fluid in a two‐dimensional channel with walls at different, uniform temperature. The code uses no empiricism, although periodic boundary conditions are used for fluctuating quantities in the streamwise and spanwise directions.Calculations were made for a Prandtl number of 0·72 and Reynolds number based on friction velocity and channel half‐height of 180 or 2800 based on channel half‐height and average velocity. Calculations of mean velocity profile, turbulence intensities, skewness, flatness, Reynolds stress and eddy diffusivity of heat near a wall compare favourably with experimental results. Representative contour plots of the temperature field near the wall and of the spanwise and streamwise two‐point velocity correlations are given.Deficiencies are that the calculation requires many hours on a fast computer with a large high‐speed memory and that the grid size in each direction for appropriate resolution is approximately proportional to the square of the Reynolds number and to the Prandtl number raised to some power greater than one.