bluuebunny/crossref_metadata_2025_split huggingface dataset:
Accuracy of a deterministic particle method for Navier‐Stokes equations
Authors: Choquin J. P. , Lucquin‐Desreux B. 
Published: August 2005

AbstractThe accuracy of a deterministic particle method in approximating the solution of the Navier‐Stokes equations is investigated. The convective part is solved using a classical vortex method for inviscid fluids, and an iterative procedure is added to improve the interpolation of the vorticity function. In our examples the vorticity is radially symmetric. For a regular initial data, a discrete quadratic error on the velocity and the vorticity is considered. Otherwise, for a singular initial data, the exact and computed angular moments of the vorticity are compared.
The analysis of glass melting processes using three‐dimensional finite elements
Authors: Murnane R. A. , Johnson W. W. , Moreland N. J. 
Published: August 2005

AbstractTraditionally glass process problems have been studied using laboratory and two‐dimensional computer simulation techniques to quantify the melting, cooling and distribution of the molten glass and its quality. Although these approaches are adequate for a large number of simple glass systems, there are processes with asymmetric geometries and operating conditions which cannot neglect the effect of the third dimension. During the past few years, with the advent of commercial parallel processors and corresponding software, extensive progress has been made with the implementation of full three‐dimensional glass flow simulations. Several development applications using FIDAP will be illustrated for electric melters, circular refiners and contoured forehearths. The discussion will cover the problem set‐ups, mesh generation, solution strategy, post‐processing and results. The advantages and developmental needs of FIDAP will be highlighted from the point of view of applied glass process engineering.
Finite element simulation of 3D turbulent free shear flows
Authors: Pelletier Dominique , Camareo Ricardo 
Published: August 2005

AbstractThis paper reviews past and current efforts in developing a simple but robust turbulence model for free shear flows. Much of this work has been published previously and this paper is a rearrangement aimed at the conference. The model is presented and is interfaced with FIDAP to solve three‐dimensional flows and a pusher—prop configuration. The eight‐node brick, the penalty formulation and the Broyden method are used to solve the Navier‐Stokes equations. The propeller is modelled as an actuator disc and the direct simulation of a given propeller is considered in detail. Good results are obtained for the square jet. For propeller cases detailed comparison with wind tunnel measurements shows excellent prediction of the velocity and pressure for flows of this complexity.
Comparison with experiment for TVD calculations of blast waves from a shock tube
Authors: Cooke Charlie H. , Fansler Kevin S. 
Published: August 2005

AbstractHarten's second‐order‐accurate total‐variation‐diminishing (TVD) scheme is applied to calculation of flow from the open end of a shock tube. Comparison of numerical results with available experimental data for overpressure at selected points around the shock tube exit shows good agreement. Numerically indicated positions of the moving shock front and Mach stem also compare well with flow shadowgraph data. Where the problem geometry is sufficiently simple and rectangular gridding can be used, Harten's method affords a good choice for blast wave calculations.
Momentum transport in a turbulent mixing layer
Authors: Chein Reiyu , Chung J. N. , Troutt T. R. 
Published: August 2005

AbstractThe turbulent momentum transport phenomena in a two‐dimensional mixing layer are investigated numerically by a discrete vortex method. The numerical model and calculations are verified through a comparison with existing numerical simulations and experimental measurements. The main emphasis is placed on the exploration of the detailed time‐dependent instantaneous local momentum fluctuations and on the comparison of numerical results with available experimental measurements. The current simulations confirm qualitatively the various trends in the turbulent momentum flux and fluctuating components of the velocity in the mixing layer found with several experimental results. The study shows that similarity exists in turbulent momentum quantities along the axial direction of the mixing layer. The calculations also show a definite correlation between the passage of a large‐scale structure and a burst in the turbulent momentum flux. The probability density functions of the fluctuating quantities are shown to be mostly Gaussian‐like, with only a few exceptions.
Finite difference methods for solving the two‐dimensional advection–diffusion equation
Authors: Noye B. J. , Tan H. H. 
Published: August 2005

AbstractUsing weighted discretization with the modified equivalent partial differential equation approach, several accurate finite difference methods are developed to solve the two‐dimensional advection–diffusion equation following the success of its application to the one‐dimensional case. These new methods are compared with the conventional finite difference methods in terms of stability and accuracy. The new methods are more accurate and often more stable than the conventional schemes.
Numerical analysis of the developing fluid flow in a circular duct rotating steadily about a parallel axis
Authors: Gethin D. T. , Johnson A. R. 
Published: August 2005

AbstractA numerical analysis of the flow pattern in the inlet region of a circular pipe rotating steadily about an axis parallel to its own is presented. Both finite cell and finite element methods are used to analyse the problem and they give qualitatively similar results which show that a swirling fluid motion is induced in the pipe inlet region. The analyses show that the direction of swirl is opposite to that of the pipe rotation when viewed along the flow axis and that its magnitude depends on the speed of pipe rotation and throughflow Reynolds number. Neither numerical analysis predicts the marked upturn in friction factor (or pressure drop) which has been observed experimentally. However, a dependence on the pipe inlet boundary conditions is demonstrated.
Effects of grid staggering on numerical schemes
Authors: Shih T. M. , Tan C. H. , Hwang B. C. 
Published: August 2005

AbstractNine finite difference schemes using primitive variables on various grid arrangements were systematically tested on a benchmark problem of two‐dimensional incompressible Navier–Stokes flows. The chosen problem is similar to the classical lid‐driven cavity flow, but has a known exact solution. Also, it offers the reader an opportunity to thoroughly evaluate accuracies of various conceptual grid arrangements.Compared to the exact solution, the non‐staggered grid scheme with higher‐order accuracy was found to yield an accuracy significantly better than others. In terms of ‘overall performance’, the so‐called 4/1 staggered grid scheme proved to be the best. The simplicity of this scheme is the primary benefit. Furthermore, the scheme can be changed into a non‐staggered grid if the pressure is replaced by the pressure gradient as a field variable.Finally, the conventional staggered grid scheme developed by Harlow and Welch also yields relatively high accuracy and demonstrates satisfactory overall performance.
Conjugate gradient methods and ILU preconditioning of non‐symmetric matrix systems with arbitrary sparsity patterns
Authors: Langtangen Hans Petter 
Published: August 2005

AbstractPreconditioning techniques based on incomplete Gaussian elimination for large, sparse, non‐symmetric matrix systems are described. A certain level of fill‐in may be specified in the incomplete factorizations. All methods considered may be applied to matrices with arbitrary sparsity patterns, for instance those associated with the general preprocessor algorithms or adaptive mesh techniques. The preconditioners have been combined with five conjugate gradient‐like methods and tested on finite element discretized scalar convection‐diffusion equations in 2D and 3D. It is found from numerical experiments that an amount of fill‐in corresponding to about 50% of the number of original non‐zero matrix entries is the optimal choice for this class of preconditioners. The preconditioners show almost no sensitivity to grid distortion. In problems with significantly variable coefficients or anisotropy the preconditioners stabilize the basic iterative schemes in addition to reducing the computational work substantially, mostly by more than 90%. The modified preconditioning technique, where fill‐in is added on the main diagonal, performs in general better than the standard incomplete LU factorization, but is inferior to the latter in 3D problems and for matrix systems with complicated sparsity patterns.
A finite element analysis of the steady laminar entrance flow in a 90° curved tube
Authors: Van De Vosse F. N. , Van Steenhoven A. A. , Segal A. , Janssen J. D. 
Published: August 2005

AbstractA standard Galerkin finite element penalty function method is used to approximate the solution of the three‐dimensional Navier–Stokes equations for steady incompressible Newtonian entrance flow in a 90° curved tube (curvature ratio δ = 1/6) for a triple of Dean numbers (κ = 41, 122 and 204). The computational results for the intermediate Dean number (κ = 122) are compared with the results of laser–Doppler velocity measurements in an equivalent experimental model. For both the axial and secondary velocity components, fair agreement between the computational and experimental results is found.
Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady euler equations
Authors: Bruneau Charles‐Henri , Laminie Jacques , Chattot Jean‐Jacques 
Published: August 2005

AbstractA variational method for solving directly the full steady Euler equations is presented. This method is based on both Newton's linearization and a least squares formulation. The validity of the Euler model and boundary conditions to capture the vortex sheet is discussed. A finite element approximation of the groups of conservative variables is described and results are given for 3D subsonic flows as well as supersonic flows past a flat plate at high angle of attack.
Robust semidirect finite difference methods for solving the Navier–Stokes and energy equations
Authors: Macarthur J. Ward , Patankar Suhas V. 
Published: August 2005

AbstractSemidirect solution techniques can be an effective alternative to the more conventional iterative approaches used in many finite difference methods. This paper summarizes several semidirect techniques which generally have not been applied to the Navier–Stokes and energy equations in finite difference form. The methods presented use both successive substitution and Jacobian‐based updates as well as two variations of Broyden's full matrix update. A hybrid method is also presented, as is a norm‐reducing search technique that can be used to enhance the convergence characteristics of any semidirect approach. These methods have been compared with the well known iterative methods SIMPLE and SIMPLER. The comparison was performed on the natural convection and driven cavity problems. The semidirect methods proved to be reliably convergent without the need for a priori specification of variable under‐relaxation factors, which was necessary with the iterative methods. Natural convection and driven cavity solutions have been readily obtained with the proposed methods for Rayleigh and Reynolds numbers up to 109 and 106 respectively. Of the semidirect techniques, the hybrid approach was the most robust. From an arbitrary zero initial guess this method was able to obtain a solution to the natural convection problem for Rayleigh numbers three orders of magnitude larger than was possible with the Newton‐Raphson update. The computational effort required by the semidirect methods is comparable to that required by the iterative methods; however, the memory requirements can be significantly greater.
Numerical study of the axially symmetric motion of an incompressible viscous fluid in an annulus between two concentric rotating spheres
Authors: Yang Jen‐Kang , Nigro Nicholas J. , Elkouh Abdel F. , Gagliardi John C. 
Published: August 2005

AbstractThe research reported herein involved the study of the transient motion of a system consisting of an incompressible Newtonian fluid in an annulus between two concentric, rotating, rigid spheres. The primary purpose of the research was to study the use of a numerical method for analysing the transient motion that results from the interaction between the fluid in the annulus and the spheres which are started suddenly by the action of prescribed torques. The problems considered in this research included cases where: (a) one or both spheres rotate with prescribed constant angular velocities and (b) one sphere rotates due to the action of an applied constant or impulsive t̀orque.In this research the coupled solid and fluid equations were solved numerically by employing the finite difference technique. With the approach adopted in this research, only the derivatives with respect to spatial variables were approximated with the use of the finite difference formulae. The steady state problem was also solved as a separate problem (for verification purposes), and the results were compared with those obtained from the solution of the transient problem. Newton's algorithm was employed to solve the algebraic equations which resulted from the steady state problem, and the Adams fourth‐order predictor–corrector method was employed to solve the ordinary differential equations for the transient problem. Results were obtained for the streamfunction, circumferential function, angular velocity of the spheres and viscous torques acting on the spheres as a function of time for various values of the system dimensionless parameters.
Comparison of k–ϵ and algebraic Reynolds stress models for swirling diffuser flow
Authors: Armfield S. W. , Fletcher C. A. J. 
Published: August 2005

AbstractA brief overview of classes of turbulent swirling flow in conical diffusers is given, together with a description of appropriate numerical schemes for each class. Numerical results obtained for the class of moderate swirl in a 20° diffuser and for the class of no swirl in an 8° diffuser are compared with experimental results. The results are obtained using a multi‐sweep scheme solving the full steady state time‐averaged Navier–Stokes equations. Turbulence quantities are approximated using two types of algebraic Reynolds stress model and two types of k–ϵ model. One of the algebraic Reynolds stress models includes extra production terms associated with the Christoffel symbols in cylindrical co‐ordinates, and one of the k–ϵ models includes a swirl‐related modification to the ϵ equation. It is demonstrated that the standard k–ϵmodel gives poor prediction of the mean flow, and it is necessary to at least use the modified form or one of the two algebraic Reynolds stress models.
On TVD difference schemes for the three‐dimensional Euler equations in general co‐ordinates
Authors: Takakura Yoko , Ishiguro Tomiko , Ogawa Satoru 
Published: August 2005

AbstractAn improved treatment for the Harten–Yee and Chakravarthy–Osher TVD numerical flux functions in general co‐ordinates is presented. The proposed formulation is demonstrated by a series of numerical experiments for three‐dimensional flows around the ONERA‐M6 wing. The numerical results indicate that it is important to use a suitable artificial compression parameter in order to obtain more accurate solutions around the leading edge of the wing. The two TVD numerical fluxes give excellent results: they capture the shock wave without numerical oscillations, they capture the rapid expansion around the leading edge sharply, they have self‐adjusting mechanisms regarding numerical viscosity and they also have robustness.
An investigation of pressure transients in pipelines with two‐phase bubbly flow
Authors: Ng K. C. , Yap C. 
Published: August 2005

AbstractThis paper presents a two‐dimensional model for the analysis of the pressure transient of a two‐phase homogeneous bubbly mixture flowing in a pipeline and the numerical integration using the centre implicit method (CIM). Experiments were conducted to confirm the proposed sonic speed equation of an air–water mixture for an air concentration of less than 1%. The 2D CIM model is compared with the method of characteristics (MoC) for a two‐phase bubbly flow in a pipeline. The comparisons show that the proposed 2D CIM model generally gives good agreement with the method of characteristics.
The simple layer potential method of fundamental solutions for certain biharmonic problems
Authors: Karageorghis Andreas , Fairweather Graeme 
Published: August 2005

AbstractA novel formulation of the method of fundamental solutions for the numerical solution of plane biharmonic problems, based on the simple layer potential representation of Fichera, is presented. The applicability and accuracy of the method are demonstrated by examining its performance on a set of practical problems arising in Stokes fluid flow.
Vorticity—velocity formulation in the computation of flows in multiconnected domains
Authors: Stella F. , Guj G. 
Published: August 2005

AbstractThe thermofluid dynamic fields in two‐dimensional multiconnected domains are analysed by solving the Navier–Stokes equations with the Boussinesq approximation in the vorticity–velocity formulation. The need of an integral condition for the pressure to be single‐valued on each independent irreducible loop, in analogy with the ω–Ψ formulation, is demonstrated. The field equations are discretized by a finite difference technique and solved at the steady state via an alternating direction implicit method of a scalar type. Two test cases at low Reynolds and Rayleigh numbers are considered: the multiconnected driven cavity and an annulus with isothermal walls and stationary or rotating inner cylinder.
Numerical studies of slow viscous rotating flow past a sphere. III
Authors: Raghavarao C. V. , Pramadavalli K. 
Published: August 2005

AbstractThe flow of steady incompressible viscous fluid rotating about the z‐axis with angular velocity ω and moving with velocity u past a sphere of radius a which is kept fixed at the origin is investigated by means of a numerical method for small values of the Reynolds number Reω. The Navier–Stokes equations governing the axisymmetric flow can be written as three coupled non‐linear partial differential equations for the streamfunction, vorticity and rotational velocity component. Central differences are applied to the partial differential equations for solution by the Peaceman–Rachford ADI method, and the resulting algebraic equations are solved by the ‘method of sweeps’.The results obtained by solving the non‐linear partial differential equations are compared with the results obtained by linearizing the equations for very small values of Reω. Streamlines are plotted for Ψ = 0·05, 0·2, 0·5 for both linear and non‐linear cases. The magnitude of the vorticity vector near the body, i.e. at z = 0·2, is plotted for Reω = 0·05, 0·24, 0·5. The correction to the Stokes drag as a result of rotation of the fluid is calculated.
A singular finite element for Stokes flow: The stick–slip problem
Authors: Georgiou Georgios C. , Olson Lorraine G. , Schultz William W. , Sagan Susan 
Published: August 2005

AbstractAbrupt changes in boundary conditions in viscous flow problems give rise to stress singularities. Ordinary finite element methods account effectively for the global solution but perform poorly near the singularity. In this paper we develop singular finite elements, similar in principle to the crack tip elements used in fracture mechanics, to improve the solution accuracy in the vicinity of the singular point and to speed up the rate of convergence. These special elements surround the singular point, and the corresponding field shape functions embody the form of the singularity. Because the pressure is singular, there is no pressure node at the singular point. The method performs well when applied to the stick–slip problem and gives more accurate results than those from refined ordinary finite element meshes.
Convergence properties of high‐Reynolds‐number separated flow calculations
Authors: Rubin S. G. , Himansu A. 
Published: August 2005

AbstractThe convergence properties of an iterative solution technique for the Reduced Navier–Stokes equations are examined for two‐dimensional steady subsonic flow over bump and trough geometries. Techniques for decreasing the sensitivity to the initial pressure approximation, for fine meshes in particular, are investigated. They are shown to improve the robustness of the relaxation process and to decrease the computational work required to obtain a converged solution. A semi‐coarsening multigrid technique that has previously been found to be particularly advantageous for high‐Reynolds‐number (Re) flows with flow separation and with highly stretched surface‐normal grids is applied herein to further accelerate convergence. Solutions are obtained for the laminar flow over a trough that is more severe than has been considered to date. Sufficient axial grid refinement in this case leads to a shock‐like reattachment and, for sufficiently large Re, to a local ‘divergence’ of the numerical computations. This ‘laminar flow breakdown’ appears to be related to an instability associated with high‐frequency fine‐grid modes that are not resolvable with the present modelling. This behaviour may be indicative of dynamic stall or of incipient transition. The breakdown or instability is shown to be controllable by suitable introduction of transition turbulence models or by laminar flow control, i.e. small amounts of wall suction. This lends further support to the hypothesis that the instability is of a physical rather than numerical character and suggests that full three‐dimensional analysis is required to properly capture the flow behaviour. Another inference drawn from this investigation is that there is a need for careful grid refinement studies in high‐Re flow computations, since coarser grids may yield oscillation‐free solutions that cannot be obtained on finer grids.
Variations on Fourier wave theory
Authors: Sobey Rodney J. 
Published: August 2005

AbstractA review of the analytical and numerical background of Fourier wave theory establishes the commonality of existing formulations and identifies a number of analytical and numerical assumptions that are unnecessary. Some formulations in particular lack flexibility in excluding the possibility of Stokes' second definition of phase speed. A generalized formulation is introduced for comparative purposes and it is shown that published solutions differ only in the approach to the limit wave. Detailed consideration of truncation order confirms that it is the crucial parameter, especially at extreme wave heights. All formulations considered are shown to provide acceptable solutions for small to moderately extreme waves.
A Newton's method scheme for solving free‐surface flow problems
Authors: Dandy David S. , Leal L. Gary 
Published: August 2005

AbstractA Newton's method scheme is described for solving the system of non‐linear algebraic equations arising when finite difference approximations are applied to the Navier–Stokes equations and their associated boundary conditions. The problem studied here is the steady, buoyancy‐driven motion of a deformable bubble, assumed to consist of an inviscid, incompressible gas. The linear Newton system is solved using both direct and iterative equation solvers. The numerical results are in excellent agreement with previous work, and the method achieves quadratic convergence.