bluuebunny/crossref_metadata_2025_split huggingface dataset:
Modelling a recirculating density‐driven turbulent flow
Authors: Devantier Bruce A. , Larock Bruce E. 
Published: August 2005

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

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

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

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

AbstractLinearized, multidimensional, thermally driven flow in a gas centrifuge can be approximately described in regions away from the ends by Onsager's homogeneous pancake equation.1 Upon reformulation of the general problem, we find a new, simple and rigorous closed form, analytical solution by assuming a special separable solution and replacing the usual Ekman end cap boundary conditions with idealized impermeable, free slip boundary conditions. Then the flow may be described by an ordinary differential equation with solutions in terms of simple, classical functions. By identifying a small parameter, say ϵ, defining the semi‐long bowl approximation, and assuming a power series expansion in ϵ, a sequence of asymptotic approximations to the master potential is obtained. Not surprisingly, the leading order term involves the well known ‘long bowl’ solution. Using the so‐called ‘solving’ property of the 1‐D pancake Green's function,2 we determine the next higher order solution. This recursive process is carried out on the computer to find all the terms up to O(ϵ4).Consequently, the solution of some complex rotating, viscous, heat conducting flow problems that normally require large mainframe computers can be better understood.
Synthesis of thermal effects in misaligned hydrodynamic journal bearings
Authors: Medwell J. O. , Gethin D. T. 
Published: August 2005

AbstractThe analysis presented herein deals with the evaluation of pressure and temperature fields which are generated in thin fluid films of varying thickness. The particular problem of a misaligned journal bearing has been studied by solving simultaneously the Reynolds and energy equations, which also include the effects of viscous dissipation and the variation of fluid viscosity with temperature.The method has been used to predict pressure and temperature fields as well as global performance parameters for a typical journal bearing operation.
Numerical predictions for unsteady viscous flow past an array of cylinders
Authors: Cerutti Edward A. , Kinney Robert B. , Paolino Michael A. 
Published: August 2005

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

AbstractNew finite element procedures based on the streamline‐upwind/Petrov‐Galerkin formulations are developed for time‐dependent convection‐diffusion‐reaction equations. These procedures minimize spurious oscillations for convection‐dominated and reaction‐dominated problems. The results obtained for representative numerical examples are accurate with minimal oscillations.As a special application problem, the single‐well chemical tracer test (a procedure for measuring oil remaining in a depleted field) is simulated numerically. The results show the importance of temperature effects on the interpreted value of residual oil saturation from such tests.
A finite element procedure for viscoelastic flows
Authors: Fortin M. , Esselaoui D. 
Published: August 2005

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

AbstractSeveral techniques for experimental determination of floating point precision in practical computations are examined, and applied to linear algebra algorithms. These techniques are simple enough to be directly applicable to existing production codes, requiring a very limited amount of software on many machines, and yet they yield interesting information on the numerical precision of a computation.Our choice of linear algebra algorithms includes a direct solver (namely the MA32 program from the Harwell Library) and several variants of preconditioned conjugate gradients (the methods DIAG, INV, MINV and POL of Reference 1). The results may be of interest as method selection criteria, and thus complement Mflop performance data available from several sources.
Flow past symmetric convex profiles with open wakes
Authors: Dormiani M. , Bruch J. C. , Sloss J. M. 
Published: August 2005

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

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