bluuebunny/crossref_metadata_2025_split huggingface dataset:
The parametrized strongly implicit method for solving elliptic difference equations
Authors: Lin Avi 
Published: August 2005

AbstractA new method for solving elliptic difference equations is derived based on the strongly implicit method. This parametrized strongly implicit method has three free parameters which may be functions of the field's nodal point. The method has some resemblance to the SOR techniques, but in the present method the off‐diagonal entries are also over‐relaxed. The main application of this method is for transport equations such as those governing the fluid flow and heat transfer fields.
Adaptive grids in numerical fluid dynamics
Authors: Haase Werner , Misegades Kent , Naar Mathias 
Published: August 2005

AbstractA solution adaptive grid (SAG) method which redistributes the nodal points of a function according to its curvature is presented. A single, user‐selected step parameter, P, is available for controlling the maximum step size, allowing the application of the technique to a wide variety of problems. Three test cases are cited: (1) the 1‐dimensional inviscid Burgers equation, (2) the Falkner‐Skan equation and (3) the finite‐volume form of the Navier‐Stokes equations for transonic aerofoil flows. In all three cases, significant solution improvement in terms of accuracy and convergence acceleration were achieved.
Numerical simulation of three‐dimensional flow in a cavity
Authors: Freitas Christopher J. , Street Robert L. , Findikakis Angelos N. , Koseff Jeffrey R. 
Published: August 2005

AbstractPrevious three‐dimensional simulations of the lid‐driven cavity flow have reproduced only the most general features of the flow. Improvements to a finite difference code, REBUFFS, have made possible the first completely successful simulation of the three‐dimensional lid‐driven cavity flow. The principal improvement to the code was the incorporation of a modified QUICK scheme, a higher‐order upwind finite difference formulation. Results for a cavity flow at a Reynolds number of 3200 have reproduced experimentally observed Taylor‐Görtler‐like vortices and other three‐dimensional effects heretofore not simulated. Experimental results obtained from a unique experimental cavity facility validate the calculated results.
An inviscid model of unsteady aerofoil flow with fixed upper surface separation
Authors: Vezza M. , Galbraith R. A. McD. 
Published: August 2005

AbstractPresented in this paper is a new method for the prediction of unsteady, incompressible separated flow over a two‐dimensional aerofoil. The algorithm was developed from an existing unsteady potential flow model1 and makes use of an inviscid formulation for the flow field. The aerofoil is represented by vortex panels of linearly varying strength which are piecewise continuous at the corners. Discrete vortices with finite cores are used to model the separating shear layers.Following a brief summary of unsteady separation modelling, the theoretical framework is presented and the subsequent numerical implementation is discussed in detail.Results are given for flows which tend asymptotically to the steady state and conclusions are drawn regarding the usefulness of the method.
A note on the steady‐state advection‐diffusion equation
Authors: Ferreri J. C. 
Published: August 2005

AbstractIn this note we show that the numerical solution of the advection‐diffusion equation can be improved by considering the asymptotic behaviour of its analytical solution. This is accomplished by including a correction term based on the numerical differentiation of the asymptotic (Pe » 1, Pe being the Peclet number) solution. This correction forces the usual oscillations associated with centred schemes to disappear.
On numerical solutions of the time‐dependent Euler equations for incompressible flow
Authors: Saiac J.‐H. 
Published: August 2005

AbstractThis paper presents finite element methods for the non‐stationary Euler equations of a two dimensional inviscid and incompressible flow. For the time discretization, we compare numerical results obtained by the use of a leap‐frog scheme and a semi‐implicit scheme of order two.
A new method for computing solenoidal vector fields on arbitrary regions
Authors: Gustafson K. , Halasi K. , Young D. P. 
Published: August 2005

AbstractWe develop a new method for the efficient calculation of solenoidal vector fields on general regions. The method takes advantage of fast direct methods and uses boundary integral equations to satisfy boundary conditions. For the latter we give an effective scheme for computing far‐field boundary influences (based on discrete charges). Examples and numerical results are given. The method is applicable to incompressible Navier‐Stokes calculations.
Boundary conformed co‐ordinate systems for selected two‐dimensional fluid flow problems. Part I: Generation of BFGs
Authors: Häuser J. , Paap H. G. , Eppel D. , Sengupta S. 
Published: August 2005

AbstractIn this paper the generation of general curvilinear co‐ordinate systems for use in selected two‐dimensional fluid flow problems is presented. The curvilinear co‐ordinate systems are obtained from the numerical solution of a system of Poisson equations. The computational grids obtained by this technique allow for curved grid lines such that the boundary of the solution domain coincides with a grid line. Hence, these meshes are called boundary fitted grids (BFG). The physical solution area is mapped onto a set of connected rectangles in the transformed (computational) plane which form a composite mesh. All numerical calculations are performed in the transformed plane. Since the computational domain is a rectangle and a uniform grid with mesh spacings Δξ = Δη = 1 (in two‐dimensions) is used, the computer programming is substantially facilitated. By means of control functions, which form the r.h.s. of the Poisson equations, the clustering of grid lines or grid points is governed. This allows a very fine resolution at certain specified locations and includes adaptive grid generation. The first two sections outline the general features of BFGs, and in section 3 the general transformation rules along with the necessary concepts of differential geometry are given. In section 4 the transformed grid generation equations are derived and control functions are specified. Expressions for grid adaptation arc also presented. Section 5 briefly discusses the numerical solution of the transformed grid generation equations using sucessive overrelaxation and shows a sample calculation where the FAS (full approximation scheme) multigrid technique was employed. In the companion paper (Part II), the application of the BFG method to selected fluid flow problems is addressed.
Boundary conformed co‐ordinate systems for selected two‐dimensional fluid flow problems. Part II: Application of the BFG method
Authors: Häuser J. , Paap H. G. , Eppel D. , Sengupta S. 
Published: August 2005

AbstractThis paper gives the results of an application of the SWEs (shallow water equations) to a part of the Hamburg harbour area, which is a complex flow domain, using the BFG approach, outlined in Part I. The results of a grid doubling procedure generating the desired computational grid from a coarse initial mesh are also presented. A second class of problems which is addressed, demands time‐dependent co‐ordinate systems. The problems which are solved are the free surface problem for a moving wave which eventually breaks and for a wave which is reflected by the solid walls of a rectangular basin.
Numerical simulation of swirling flow in diffusers
Authors: Armfield S. W. , Fletcher C. A. J. 
Published: August 2005

AbstractA reduced form of Navier–Stokes equations is developed which does not have the usual minimum axial step size restriction. The equations are able to predict accurately turbulent swirling flow in diffusers. An efficient single sweep implicit scheme is developed in conjunction with a variable grid size domain‐conforming co‐ordinate system. The present scheme indicates good agreement with experimental results for (1) turbulent pipe flow, (2) turbulent diffuser flow, (3) turbulent swirling diffuser flow. The strong coupling between the swirl and the axial velocity profiles outside of the boundary layer region is demonstrated.
Some new methods for numerically solving the compressible laminar boundary layer equations
Authors: Friel R. G. 
Published: August 2005

AbstractFour new methods are presented: a method of accelerating the truncation error convergence, a fourth and fifth order difference scheme for discretizing the normal partial derivatives, high order quadrature formulae for integrating a stream function and a third order implicit scheme for treating the streamwise partial derivatives. These are seen to be effective in finding solutions to the boundary layer equations in which the step sizes are adaptively altered to meet an error bound.
Lagrangian finite element method for the analysis of two‐dimensional sloshing problems
Authors: Ramaswamy Balasubramaniam , Kawahara Mutsuto , Nakayama Tsukasa 
Published: August 2005

AbstractA new version of a numerical algorithm for the Lagrangian treatment of incompressible fluid flows with free surfaces is developed. The novel features of the present method are the adoptions of the Lagrangian finite element method and the velocity correction technique. The use of the velocity correction approach makes the computational scheme extremely simple in algorithmic structure. Hence, the present method is particularly attractive for large‐scale problems. The techniques discussed here are applied to some two‐dimensional sloshing problems, which may indicate the versatility and effectiveness of the present method.
Solution to the orr–sommerfeld equation for liquid film flowing down an inclined plane: An optimal approach
Authors: Lam T. T. , Bayazitoglu Y. 
Published: August 2005

AbstractThe Orr–Sommerfeld equation is solved numerically for a layer of liquid film flowing down an inclined plane under the action of gravity using the sequential gradient‐restoration algorithm (SGRA) The method consists of solving the governing equation as it is a Bolza problem in the calculus of variations. The neutral stability curves, eigenvalues and eigenfunctions to the stability problem can be determined simultaneously during the process.
Finite element ground‐water models implemented on vector computers
Authors: Pelka W. , Peters A. 
Published: August 2005

AbstractFinite element models, optimized for running on conventional serial computers, are not suitable to make use of the potentional high performance of today's vector or parallel computers. Also, automatic vectorization by the compiler or manual vectorization at the local level do not by far lead to the required and expected computational speed.A global change of the overall program logic or a complete redesign becomes necessary, i.e. a completely new generation of program systems has to be created, considering the new hardware characteristics and abilities.A new computer‐independent programming technique for finite element problems to be implemented on vector computers is proposed and the test results of scalar and vectorized program structures on a conventional serial and on a non‐conventional pipeline computer are discussed.
Review: Formulating efficient finite‐element codes for flows in regular domains
Authors: Staniforth A. 
Published: August 2005

AbstractMany fluid flow problems of current interest occur in domains that are mappable to a rectangle or a box; conformal mappings are particularly useful in this regard. We are concerned here with the efficient solution of such problems using finite elements. The central issue is the element choice, and this issue is addressed in terms of operation counts, computer memory and I/0 requirements, and the extent to which code vectorization is possible. It is concluded that rectangular (box) elements generally lead to more efficient algorithms that triangular (tetrahedral) elements. A synthesis of algorithms, based on bilinear (trilinear) elements, is presented. The algorithms have the attributes of simplicity, accuracy, stability and straightforward incorporation of boundary conditions. For bilinear and trilinear elements, it is found that product and first‐derivative terms are well‐handled by the Galerkin FE method, but that it is advantageous to go outside of the Galerkin framework when treating second‐derivative terms. It is particularly important to consider the form of the governing equations, vis‐à‐vis the choice of staggered, non‐staggered and/or mixed‐order elements, and to choose an appropriate time scheme. The described techniques have been successfully applied to a variety of problems in regular domains, including the solution of the three‐dimensional time‐dependent hydrostatic primitive equations; these are stiff and include first and second derivative terms, non‐linearities and variable coefficients due to a conformal mapping.
Numerical simulation of the horizontal Bridgman growth. Part II: Three‐dimensional flow
Authors: Dupont S. , Marchal J. M. , Crochet M. J. , Geyling F. T. 
Published: August 2005

AbstractWe study the steady‐state three‐dimensional flow which occurs in a 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. We find that three‐dimensional effects can have a dramatic influence upon the flow, which, before the onset of periodic disturbances, differs appreciably from its two‐dimensional counterpart. We also investigate the sensitivity of the flow to non‐symmetric disturbances.
Numerical studies of slow viscous rotating flow past a sphere—1
Authors: Raghavarao C. V. , Valli K. Pramada 
Published: August 2005

AbstractThe Navier‐Stokes equations for a steady, viscous rotating fluid, rotating about the z‐axis with angular velocity ω are linearized using the Stokes approximation. The linearized Navier‐Stokes equations governing the axisymmetric flow can be written as three coupled partial differential equations for the stream function, vorticity and rotational velocity components. One parameter, Reω = 2ωa2/v, enters the resulting equations. For Reω « 1, the coupled equations are solved by the Peaceman‐Rachford A.D.I. (Alternating Direction Implicit) method and the resulting algebraic equations are solved by the ‘method of sweeps’. Stream lines for ψ = 0·05, 0·2, 0·5 and magnitude of the vorticity vector z = 0·2 are plotted for Reω = 0·1, 0·3, 0·5. Correction to the Stokes drag due to the rotation of fluid is calculated.
Numerical solution of reaction–diffusion equations by compact operators and modified equation methods
Authors: Ramos J. I. , Shih T. I‐P. 
Published: August 2005

AbstractA system of reaction–diffusion equations which governs the propagation of an ozone decomposition laminar flame in Lagrangian co‐ordinates is analysed by means of compact operators and modified equation methods. It is shown that the use of fourth‐order accurate compact operators yields very accurate solutions if sufficient numbers of grid points are located at the flame front, where very steep gradients of temperature and species concentrations exist. Modified equation methods are shown to impose a restriction on the time step under certain conditions. The solutions obtained by means of compact operators and modified equation methods are compared with solutions obtained by other methods; good agreement is obtained.
Application of local co‐ordinate systems to the solution of integral equations referred to plane fluid flow problems
Authors: Sulisz Wojciech 
Published: August 2005

AbstractTwo‐dimensional fluid flow problems expressed in terms of velocity potentials or stream functions are often summarized as boundary‐value problems for the Laplace or Poisson equations, or the homogeneous or non‐homogeneous biharmonic equations. Simple local co‐ordinate systems have been applied to the solution of integral equations associated with these boundary‐value problems. This procedure has been shown to be an efficient technique in the numerical solution of fluid flow problems.
Wave propagation analysis of difference schemes for hyperbolic equations: A review
Authors: Vichnevetsky Robert 
Published: August 2005

AbstractThere are spurious phenomena in the numerical approximation of the hyperbolic equations of fluid dynamics that may be investigated by invoking concepts which originate from wave propagation theory. Many of the significant results which have been obtained by pursuing this kind of analysis are reviewed in this paper by using as an illustration a family of implicit approximations of the simple linear advection equation. Included in this family of algorithms are the common six‐point implicit finite difference scheme, the linear finite element/Galerkin scheme and the ‘box’ method.The phase and group velocities of sinusoidal solutions are brought into the analysis of the accuracy and of the spurious reflection or scattering phenomena which are created at computational boundaries and in non‐uniform grids. General properties become apparent in this Fourier/wave propagation approach to the analysis. One of these is in the form of an analogy with quantum mechanics. Another shows that certain energy norms of the errors are independent of time discretization, i.e. depend on space discretization alone.
A study of the motion in rotating containers using a boundary fitted co‐ordinate system
Authors: Raghunath R. , Sengupta S. , Haeuser J. 
Published: August 2005

AbstractNumerical solutions are often inaccurate because conventional co‐ordinate systems do not represent the complex physical boundaries accurately. In the present work, the numerical solution of linear shallow water wave equations has been obtained by transforming the physical domain into a rectangular computational domain using elliptic differential operators. This work is part of a programme to develop three‐dimensional body‐fit grid systems for environmental flows. Solutions have been obtained for a cylindrical container and also a parabolic container. The initial conditions chosen are the ones for which analytical solutions exist. The numerical solutions compare well with analytical solutions.
A taylor weak‐statement algorithm for hyperbolic conservation laws
Authors: Baker A. J. , Kim J. W. 
Published: August 2005

AbstractFinite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak‐statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and non‐linear test problems permit direct quantitative performance comparisons.
Comparison between the traction and pressure‐imposed boundary conditions in finite element flow analysis
Authors: Yagawa Genki , Eguchi Yuzuru 
Published: August 2005

AbstractA formulation is developed to impose pressure‐prescribed boundary conditions in the penalty finite element method. Some numerical experiments for the Poiseuille flow problem are performed to compare it with the conventional traction‐prescribed boundary condition. Also the incorrectness of the traction‐free outlet boundary condition for contained‐flows is studied with explanatory numerical examples. Discussion is focused on the inlet and outlet boundary conditions to simulate fully developed flows. Finally, the three‐dimensional flow in a bifurcated pipe is analysed with the proposed formulation.
Magnetohydrodynamic flow in a rectangular duct
Authors: Sezgin Münevver 
Published: August 2005

AbstractThe magnetohydrodynamic flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct, with an external magnetic field applied transverse to the flow, has been investigated. One of the duct's boundaries which is perpendicular to the magnetic field is taken partly insulated, partly conducting. An analytical solution has been developed for the velocity field and magnetic field by reducing the problem to the solution of a Fredholm integral equation of the second kind, which has been solved numerically. Solutions have been obtained for Hartmann numbers M up to 100. All the infinite series obtained are transformed to infinite integrals first and then to finite integrals which contain modified Bessel functions of the second kind. In this way, the difficulties associated with the computation of infinite integrals with oscillating integrands and slowly converging infinite series, the convergence of which is further affected for large values of M, have been avoided. It is found that, as M increases, boundary layers are formed near the non‐conducting boundaries and in the interface region, and a stagnant region is developed in front of the conducting boundary for velocity field. The maximm value of magnetic field takes place on the conducting part. These behaviours are shown on some graphs.
Use of the splitting scheme and multigrid method to compute flow separation
Authors: Qianshun Chang 
Published: August 2005

AbstractThe splitting difference scheme is used to study flow separation. Flows behind a circular cylinder are computed as a model problem. In view of the nature of the flow, the variables are transformed. The boundary condition for the pressure is given from an intermediate velocity. The free‐slip velocity boundary conditions on the rigid wall are given by interpolation. The multigrid algorithm is applied to the pressure iteration. We also choose better initial values for the model problem by means of the multigrid algorithm idea.
Fully developed flow in a curved pipe of arbitrary curvature ratio
Authors: Soh W. Y. , Berger S. A. 
Published: August 2005

AbstractIt is generally assumed in curved pipe flow analyses that the curvature ratio, δ, of the pipe is very small, in which case the flow depends on a single parameter, the Dean number. This is not the case if δ is not very small. To determine the importance of this effect we have numerically solved the full Navier‐Stokes equations, in primitive variable form, for arbitrary values of δ. A factored ADI finite‐difference scheme has been used, employing Chorin's artificial compressibility technique. The results show that the central‐difference calculation on a staggered grid is stable, without adding artificial damping terms, due to coupling between pressure and velocity. A spatially variable time step is used with a fixed Courant number.
An algorithm for the global volume conservation constraint in lake circulation
Authors: Dhatt Gouri , Leclerc Michel 
Published: August 2005

AbstractWe present an algorithm for introducing a global constraint of volume conservation in lake circulation problems. The algorithm is described for linear problems, and is then generalized to non‐linear cases. Numerical examples are presented to show the influence of water‐level conditions on convergence and to demonstrate the practical superiority of the global constraint algorithm for obtaining reliable convergent solutions.