bluuebunny/crossref_metadata_2025_split huggingface dataset:
Numerical simulation of the miscible displacement of radionuclides in a heterogeneous porous medium
Authors: Bruneau C.‐H. , Marpeau F. , Saad M. 
Published: August 2005

AbstractThe aim of this paper is to model and simulate the displacement of radioactive elements in a saturated heterogeneous porous medium. New schemes are proposed to solve accurately the convection–diffusion–reaction equations including nonlinear terms in the time derivative. Numerical tests show the stability and robustness of these schemes through strong heterogeneities of the medium. Finally the COUPLEX1 benchmark concerning the far field simulation of a polluted flow by a leak of a nuclear waste disposal is performed and compared with the results available in the literature. Copyright © 2005 John Wiley & Sons, Ltd.
A combined vortex and panel method for numerical simulations of viscous flows: a comparative study of a vortex particle method and a finite volume method
Authors: Kim Kwang‐Soo , Lee Seung‐Jae , Suh Jung‐Chun 
Published: August 2005

AbstractThis paper describes and compares two vorticity‐based integral approaches for the solution of the incompressible Navier–Stokes equations. Either a Lagrangian vortex particle method or an Eulerian finite volume scheme is implemented to solve the vorticity transport equation with a vorticity boundary condition. The Biot–Savart integral is used to compute the velocity field from a vorticity distribution over a fluid domain. The vorticity boundary condition is improved by the use of an iteration scheme connected with the well‐established panel method. In the early stages of development of flows around an impulsively started circular cylinder, and past an impulsively started foil with varying angles of attack, the computational results obtained by the Lagrangian vortex method are compared with those obtained by the Eulerian finite volume method. The comparison is performed separately for the pressure fields as well. The results obtained by the two methods are in good agreement, and give a better understanding of the vorticity‐based methods. Copyright © 2005 John Wiley & Sons, Ltd.
A vector upstream differencing scheme for problems in fluid flow involving significant source terms in steady‐state linear systems
Authors: Lillington J. N. 
Published: August 2005

AbstractThis paper considers a finite difference scheme for modelling the convection/diffusion equation in strongly convective flow regimes including circumstances in which significant source terms are present.The main objective is to provide an alternative approach to central and/or upwind difference methods which for various reasons are unsatisfactory. To illustrate the main features of the scheme, an assessment of its accuracy is made by means of a Taylor expansion analysis and a study of its performance in two model problems. As a demonstration of its generality for use in large‐scale practical problems, some numerical results are presented for the prediction of the temperature distribution in a flow through a partially blocked heated rod bundle.The main conclusions are that in almost all practical circumstances results obtained using the scheme are not susceptible to false diffusion or spatial oscillations, which are, respectively, the inherent weaknesses in many upwind and central difference scheme formulations, and in general its use results in improved overall accuracy.
The cause and cure (?) of the spurious pressures generated by certain FEM solutions of the incompressible Navier‐Stokes equations: Part 1
Authors: Sani R. L. , Gresho P. M. , Lee R. L. , Griffiths D. F. 
Published: August 2005

AbstractThe spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier–Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of both mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two‐dimensions and one element in three‐dimensions. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.
On higher order multigrid methods with application to a geothermal reservoir model
Authors: Gary John 
Published: August 2005

AbstractThis paper considers the multigrid iterative method applied to the solution of finite difference approximations to a linear second‐order self‐adjoint elliptic equation. It represents an extension of work by Dinar and Brandt. We compare two methods to obtain fourth‐order convergence. The first is local error extrapolation developed by Brandt, the second is iterative improvement developed by Lindberg. This work considers non‐separable problems, but only on a rectangular domain with Dirichlet boundary conditions. We consider test cases with non‐smooth (i.e. discontinuous second derivatives) as well as smooth solutions. We also apply the multigrid method to an elliptic equation with non‐separable coefficients which occurs in a geothermal model. In this case an analysis of the error fails to show any advantage in a fourth‐order difference scheme over a second‐order scheme. However, we do demonstrate that the multigrid iteration performs well on this problem. Also, this example shows that the multigrid iteration can be combined with iterative improvement to create an efficient fourth‐order method for a non‐separable elliptic equation which is coupled with a marching equation. Other work has found an advantage in this fourth‐order scheme for a similar geothermal model.
Selective lumping finite element method for shallow water flow
Authors: Kawahara Mutsuto , Hirano Hirokazu , Tsubota Khoji , Inagaki Kazuo 
Published: August 2005

AbstractA finite element method for solving shallow water flow problems is presented. The standard Galerkin method is employed for spatial discretization. The numerical integration scheme for the time variation is the explicit two step scheme, which was originated by the authors and their co‐workers. However, the original scheme has been improved to remove the erroneous artifical damping effect. Since the improved scheme employs a combination of lumped and unlumped coefficients, the scheme is referred to as a selective lumping scheme. Stability conditions and accuracy are investigated by considering several numerical examples. The method has been applied to the tidal flow in Osaka Bay and Yatsushiro Bay.
General considerations of numerical stability and accuracy in inviscid, compressible flow calculations employing primitive variables
Authors: Bosman C. , Ahrabian D. , Kahrom M. 
Published: August 2005

AbstractThe numerical stability of a number of computation schemes currently used for three‐dimensional, inviscid, compressible flow is analysed using one‐dimensional Fourier analysis. Whereas Reference 1 analysed schemes which were modified to render them amenable to simple analysis, the present work analyses the stability of schemes as actually used by Highton,3 Ahrabian,1 Denton2 and Spalding.6 The use of current values of the variables as they become available is shown to bring a general improvement to stability margin. The manner of damping introduced by the time marching formulation is shown to be deleterious to modifications which reduce truncation error. Staggered grid schemes can be formulated to second order accuracy with better stability margin than the corresponding first order scheme. While unstaggered grid schemes can be formulated to second order error and remain stable, their stability margin becomes very small. Agreement of the theory with numerical experiments continues to be of a high order for both one and three‐dimensional disturbances.
On penalty function methods in the finite‐element analysis of flow problems
Authors: Reddy J. N. 
Published: August 2005

AbstractIn this paper the penalty function method is reviewed in the general context of solving constrained minimization problems. Mathematical properties, such as the existence of a solution to the penalty problem and convergence of the solution of a penalty problem to the solution of the original problem, are studied for the general case. Then the results are extended to a penalty function formulation of the Stokes and Navier‐Stokes equations. Conditions for the equivalence of two penalty‐finite element models of fluid flow are established, and the theoretical error estimates are verified in the case of Stokes's problem.
Conditions along the boundaries of bladed zones within the flow tracts of turbines
Authors: Lurie K. A. , Fedorov A. V. , Klimovich V. I. 
Published: August 2005

AbstractHamilton's variational principle is applied to derive a system of conditions which expresses the balance of momentum and energy of an ideal gas across the selvadgesThe reviewer of this paper confesses to be unfamiliar with the term 'selvadge(s)' which appears frequently herein. Clearly, however, it (variously) means 'boundary', 'edge', 'projection of edge line' (meridional or axial), 'locus of leading edges', etc.
of bladed zones within the flow tracts of turbines. This system provides the background for a correct formulation of optimal design problems for turbines and compressors. The exposition follows the model of a large number of blades when the basic equations can be averaged over the azimuthal co‐ordinate.An analysis is given of the obtained conditions and a computational algorithm described.
The simulation of secondary flow effects in turbulent non‐circular passage flows
Authors: Rapley C. W. 
Published: August 2005

AbstractA finite difference method has been developed to predict the overall features of the local mean flow in fully developed turbulent non‐circular passage flows. The main transport effects of secondary flow have been identified and simulated with diffusion transport in a simple way which eliminates solution of the cross‐plane momentum and continuity equations and produces a compact calculation method. Predictions are presented for four different passage shapes and are discussed in relation to experimental measurements and predictions from other more complex methods. Although some minor details were not predicted, the main effects of secondary flow on the mean flow were found to have been quite well simulated, yielding predictions that are in reasonable overall agreement with experiment.
General hyperbolic difference formulas for linear and quasilinear hyperbolic equations
Authors: Cushman John H. , Huang Chi‐Hua 
Published: August 2005

AbstractThe method of non‐standard finite elements was used to develop multilevel difference schemes for linear and quasilinear hyperbolic equations with Dirichlet boundary conditions. A closed form equation of kth‐order accuracy in space and time (O(Δtk, Δxk)) was developed for one‐dimensional systems of linear hyperbolic equations with Dirichlet boundary conditions. This same equation is also applied to quasilinear systems. For the quasilinear systems a simple iteration technique was used to maintain the kth‐order accuracy.Numerical results are presented for the linear and non‐linear inviscid Burger's equation and a system of shallow water equations with Dirichlet boundary conditions.
Numerical analysis of a moving boundary problem in coastal hydrodynamics
Authors: Gopalakrishnan T. C. , Tung C. C. 
Published: August 2005

AbstractA finite element model to tackle the moving boundary problem of wave run‐up on moderately steep slopes is developed. The special aspects considered in this study are (1) the modification of shallow water equations to accommodate the effect of vertical accelerations and (2) the use of Lagrangian acceleration coupled with an element that adapts itself to the moving boundary closely. The pressure term in the one‐dimensional momentum equation is derived using the Eulerian equation in the vertical direction. This takes care of the vertical accelerations which are significant during the motion of a wave on moderately steep slopes. The element near the boundary is allowed to change its dimension so that the fluid boundary is closely followed. Such a flexible element precludes the need for approximation of the variables with regard to the indefinite position of the boundary. This element is split into two when its dimension becomes unduly large compared to the unchanging elements. The need for such a splitting is shown by an examination of the entries in the global matrix. Results of water profile as a wave runs up a structure are given. A brief history of the work on similar problems is outlined.
A comparative study of central and upwind difference schemes using the primitive variables
Authors: Timin Tsai , Esmail M. Nabil 
Published: August 2005

AbstractThe use of the velocity‐pressure formulation of the Navier‐Stokes equations for the numerical solution of fluid flow problems is favoured for free‐surface problems, more involved flow configurations, and three‐dimensional flows. Many engineering problems involve such features in addition to strong inertial effects. The computational instabilities arising from central‐difference schemes for the convective terms of the governing equations impose serious limitations on the range of Reynolds numbers that can be investigated by the numerical method. Solutions for higher Reynolds numbers Re > 1000 could be reached using upwind‐difference schemes. A comparative study of both schemes using a method based on the primitive variables is presented. The comparison is made for the model problem of the driven flow in a square cavity. Using a central scheme stable solutions of the pressure and velocity fields were obtained for Reynolds numbers up to 5000. The streamfunction and vorticity fields were calculated from the resulting velocity field and compared with previous solutions. It is concluded that total upwind differencing results in a considerable change in the flow pattern due to the false diffusion. For practical calculations, by a proper choice of a small amount of partial upwind differencing the vorticity diffusion near the walls and the global features of the solutions are not sigificantly altered.
Fundamental solutions and numerical methods for flow problems
Authors: Wu J. C. 
Published: August 2005

AbstractAn approach for the numerical solution of flow problems based on the concept of fundamental solutions of differential equations is described. This approach uses the finite element methodology but does not rely on the concept of variational principle or that of residuals. The approach is shown to be well‐suited for many types of flow problems. Various applications of this approach are discussed in this paper, with particular emphasis placed on the solution of potential flows and viscous flows containing appreciable regions of separation.
A Dorodnitsyn finite element formulation for laminar boundary layer flow
Authors: Fletcher C. A. J. , Fleet R. W. 
Published: August 2005

AbstractThe Dorodnitsyn boundary later formulation is given a finite element interpretation and found to generate very accurate and economical solutions when combined with an implicit, non‐iterative marching scheme in the downstream direction. The algorithm is of order (Δ2u, Δx) whether linear or quadratic elements are used across the boundary layer. Solutions are compared with a Dorodnitsyn spectral formulation and a conventional finite difference formulation for three Falkner‐Skan pressure gradient cases and the flow over a circular cylinder. With quadratic elements the Dorodnitsyn finite element formulation is approximately five times more efficient than the conventional finite difference formulation.
A method for computing three dimensional flows using non‐orthogonal boundary‐fitted co‐ordinates
Authors: Maliska C. R. , Raithby G. D. 
Published: August 2005

AbstractFor three‐dimensional fluid flows in complex geometries, it is convenient to make predictions using a non‐orthogonal boundary‐fitted mesh. The present paper describes an economical method of solving the equations of motion for two and three dimensional problems using such meshes. The locations on the mesh at which the depenent variables are calculated, and the methods used to solve the equations, are key issues in the development of a successful algorithm; these are discussed in the present paper. Results obtained when the proposed method is applied to several problems are also described. The method is intended for flows in which compressibility effects do not dominate.
A single cell high order scheme for the convection‐diffusion equation with variable coefficients
Authors: Gupta Murli M. , Manohar Ram P. , Stephenson John W. 
Published: August 2005

AbstractA new finite difference scheme for the convection‐diffusion equation with variable coefficients is proposed. The difference scheme is defined on a single square cell of size 2h over a 9‐point stencil and has a truncation error of order h4. The resulting system of equations can be solved by iterative methods. Numerical results of some test problems are given.
Numerical predictions of flows over backward‐facing steps
Authors: Hackman L. P. , Raithby G. D. , Strong A. B. 
Published: August 2005

AbstractPredictions are reported for two‐dimensional, steady, incompressible flows over rearward‐facing steps for both laminar and turbulent conditions. The standard k‐ϵ turbulence model was used for the turbulent flow. Attention was focused on obtaining accurate solutions to the differential equations. It is concluded that some of the serious discrepancies that have occurred between prediction and observation, and attributed in earlier studies to the inadequacy of the turbulence model, may have been due to the inaccuracy of the solution.
A mixed algorithm for the calculation of rapidly varying fluid flows: The impulsively started circular cylinder
Authors: Rinaldo Andrea , Giorgini Aldo 
Published: August 2005

AbstractA mixed discrete Fourier transform‐Finite difference algorithm is developed and used for the calculation of rapidly changing viscous fluid flows past a circular cylinder. The numerical approach has been designed to overcome certain difficulties arising for high Reynolds number simulations. The foremost advantage of the technique lies in its fast calculations of the convolution sums portraying the convective terms of the governing equations. Third‐order spatial discretizations and fourth‐order time marching are implemented.New schemes are proposed for the boundary conditions at the solid wall and at large distances. The techniques are tested on a case study with other schemes (summarized by Roache1) in order to obtain an optimal choice. Definite indications on the stability and accuracy of boundary condition schemes are achieved. Support for the statement of dominant importance of boundary conditions is also given.A comparison of computational results with experimental data is presented for the case study of the flow past an impulsively started cylinder at Reynolds number 20.The time development of the symmetrical zone of recirculation, which is formed at an early stage of the flow, has been studied for 300 ≤ Re ≤ 9500 by means of the proposed algorithm. Computational results, comparisons with experimental data2 and discussion of upper limits of validity of the procedure will be presented in a companion paper.
Stream function finite element solution of Stokes flow with penalties
Authors: Carey Graham F. , Utku Mehmet 
Published: August 2005

AbstractA finite element method for solution of the stream function formulation of Stokes flow is developed. The method involves complete cubic non‐conforming (C0) triangular Hermite elements. This element fails the patch test. To correct the element and produce a convergent method we employ a penalty method to weakly enforce the desired continuity constraint on the normal derivative across the inter‐element boundaries. Successful use of the method is demonstrated to require reduced integration of the inter‐element penalty with a 1‐point Gauss rule. Error estimates relate the optimal choice of penalty parameter to mesh size and are corroborated by numerical convergence studies. The need for reduced integration is interpreted using rank relations for an associated hybrid method.
On the critical problem of F. D. pressure treatment for laminar flows confined by permeable walls
Authors: Albanese R. , Grasso F. , Meola C. 
Published: August 2005

AbstractIn the present work the viscous (low Reynolds) flow in plane ducts confined by permeable walls has been studied. A simple model of the filtrating walls has been used, with the normal velocity component proportional to the pressure jump across the wall, resulting in a non‐standard boundary value Navier‐Stokes problem.A critical analysis of the appropriate boundary condition and pressure problem has led to the conclusions of employing a simple explicit finite volume approach, and of avoiding the use of higher order finite difference schemes. In this paper a special emphasis on the structure of the involved computational matrices has been given to illustrate the chosen algorithm. The latter yields a steady state solution that is second order accurate in space, and it has an accuracy in time of order ≤ Δt (the time step), due to the explicit treatment of the velocity boundary conditions along the membrane. The model has been tested to study the effects of the inlet/outlet conditions, Reynolds number and filtrating wall constant.
A numerical technique for three‐dimensional compressible boundary layers
Authors: Wadia Aspi Rustom 
Published: August 2005

AbstractThe non‐linear two‐point boundary value problem for three‐dimensional compressible boundary layers is solved through the application of a boundary value technique for a range of parameters characterizing the nature of stagnation point flows. The analytical boundary conditions, at infinity, are applied at the edge of the computational mesh with iterations on the size of the domain. The solutions obtained show excellent agreement with the established similarity solutions for three‐dimensional flows. The present method has the potential advantage of yielding the wall values of f″w, g″w and θ′w as a part of the solution, contrary to the previously used ‘shooting’ methods. The algorithm is computationally simple and numerically stable and extremely suitable for engineering design applications.
The group velocity of some numerical schemes
Authors: Cathers B. , O'Connor B. A. 
Published: August 2005

AbstractThe performances of various numerical schemes used to model hyperbolic/parabolic equations have been studied by the calculation of their numerical group velocities. Numerical experiments conducted with one dimensional linear and quadratic Lagrangian finite elements with a Crank‐Nicolson finite differencing in time confirm the results of the analysis. The group velocity analysis supplements the well‐known amplitude and phase portraits introduced by Leendertse1 and helps explain the occurrence and behaviour of numerical oscillations in both finite difference and finite element schemes.
Application of the two‐equation k‐ϵ turbulence model to a two‐dimensional, steady, free surface flow problem with separation
Authors: Chapman Raymond S. , Kuo Chin Y. 
Published: August 2005

AbstractAn application of the depth‐integrated k‐ϵ turbulence model is presented for separated flow in a wide, shallow, rectangular channel with an abrupt expansion in width. The well‐known numerical problems associated with the use of upwind and central finite differences for convection are overcome by the adoption of the spatially third‐order accurate QUICK finite difference technique. Results show that modification of the depth‐integrated k‐ϵ turbulence closure model for streamline curvature leads to significant improvement in the agreement between model predictions and experimental measurements.