bluuebunny/crossref_metadata_2025_split huggingface dataset:
A boundary integral equation method for Navier‐Stokes equations—application to flow in annulus of eccentric cylinders
Authors: Ramesh P. S. , Lean M. H. 
Published: November 2005

AbstractA novel Navier‐Stokes solver based on the boundary integral equation method is presented. The solver can be used to obtain flow solutions in arbitrary 2D geometries with modest computational effort. The vorticity transport equation is modelled as a modified Helmholtz equation with the wave number dependent on the flow Reynolds number. The non‐linear inertial terms partly manifest themselves as volume vorticity sources which are computed iteratively by tracking flow trajectories. The integral equation representations of the Helmholtz equation for vorticity and Poisson equation for streamfunction are solved directly for the unknown vorticity boundary conditions. Rapid computation of the flow and vorticity field in the volume at each iteration level is achieved by precomputing the influence coefficient matrices. The pressure field can be extracted from the converged streamfunction and vorticity fields. The solver is validated by considering flow in a converging channel (Hamel flow). The solver is then applied to flow in the annulus of eccentric cylinders. Results are presented for various Reynolds numbers and compared with the literature.
Numerical solution of 2D and 3D turbulent internal flow problems
Authors: Naixing Chen , Yanji Xu 
Published: November 2005

AbstractThe paper describes a method for solving numerically two‐dimensional or axisymmetric, and three‐dimensional turbulent internal flow problems. The method is based on an implicit upwinding relaxation scheme with an arbitrarily shaped conservative control volume. The compressible Reynolds‐averaged Navier‐Stokes equations are solved with a two‐equation turbulence model. All these equations are expressed by using a non‐orthogonal curvilinear co‐ordinate system. The method is applied to study the compressible internal flow in modern power installations. It has been observed that predictions for two‐dimensional and three‐dimensional channels show very good agreement with experimental results.
Stability analysis of finite difference schemes for two‐dimensional advection‐diffusion problems
Authors: Rigal Alain 
Published: November 2005

AbstractThis paper develops a stability analysis of second‐order, two‐ and three‐time‐level difference schemes for the 2D linear diffusion‐convection model problem. The corresponding 1D schemes have been extensively analysed in two previous papers by the same author. Most of these 2D schemes obviously generalize 1D schemes, i.e. their stencil only uses the nearest points and defines ‘product difference schemes’; however, the stability results are not always the exact generalization of the 1D stability properties. Moreover, the 1D nonviscous MFTCS scheme may only be generalized if one uses a nine‐point scheme. Numerical experiments for different values of the cell Reynolds number allow a comparison to be made between the theoretical and numerical stability limits.
Finite difference representations of non‐linear waves
Authors: Pedersen Geir 
Published: November 2005

AbstractThe work concerns cnoidal and solitary wave solutions of the Boussinesq equations in the context of finite difference methods. The existence of permanent wave‐forms is discussed and approximate solutions are found for one particular discrete formulation by perturbation techniques. These techniques can be applied to most difference and regular element discretizations of equations describing weakly non‐linear and dispersive waves. No proof of convergence of the perturbation expansions is established, but the appropriateness of the solutions is confirmed through comparison with the results of computer simulations. From the perturbation series it is found that the phase speed of solitons is useless for the evaluation of numerical methods and that asymmetries in the discrete equations may ruin the soliton solution. The availability of a discrete closed‐form solution is especially important for discussions concerning the existence and accuracy of permanent wave‐forms with oblique orientations relative to the grid.
Lagrangian finite element method for free surface Navier‐Stokes flow using fractional step methods
Authors: Hayashi Masahiro , Hatanaka Katsumori , Kawahara Mutsuto 
Published: November 2005

AbstractThis paper presents a finite element analysis based on the Lagrangian description for unsteady incompressible viscous fluid flow with a free surface. The behaviour of the fluid is expressed by the unsteady Navier‐Stokes equation. For numerical integration in time the fractional step method is used. This method is useful because one can use the same linear interpolation functions for both velocity and pressure. In this paper, four variations of the fractional step method are presented and the numerical results are compared. To confirm the effectiveness of these methods, solitary wave propagation is analysed.
Computation of normal impinging jets in cross‐flow and comparison with experiment
Authors: Knowles K. , Bray D. 
Published: November 2005

AbstractThe PHOENICS code has been used to model the flow field surrounding subsonic and underexpanded jets impinging on a ground plane in the presence of a cross‐flow, for cases with both a fixed ground plane and a ‘rolling road’. The standard k‐ε turbulence model is used, without correction factors. It is confirmed that this overpredicts the free jet entrainment rate; the wall jet spreading rate is slightly underpredicted but the initial thickness is too high. Agreement with experiment is, nevertheless, much better than for previous calculations, showing the importance of the extent of the grid used. The ground vortex formed in cross‐flow is shown to move with varying effective velocity ratio and with rolling road operation in the same manner as experimentally observed. Ground vortex self‐similarity is also accurately predicted with the numerical modelling.
Navier‐Stokes computations of horseshoe vortex flows
Authors: Deng G. B. , Piquet J. 
Published: November 2005

AbstractThe computation of the incompressible three‐dimensional turbulent viscous flow about an aerofoil/flat plate junction is investigated. An iterative, fully decoupled technique is applied to the Reynolds‐averaged Navier‐Stokes equations (RANSEs) written in a non‐orthogonal curvilinear body‐fitted co‐ordinate system. The results of the computations are compared with well‐documented experiments.
A simple numerical technique for turbulent flows with free surfaces
Authors: Lemos C. M. 
Published: November 2005

AbstractA simple technique is presented for the numerical solution of two‐dimensional time‐dependent flows, either laminar or turbulent, involving multiple free surfaces of arbitrary configuration. The governing equations are the Reynolds equations for incompressible fluids with Boussinesq closure, the k‐ and ϵ‐equations and an additional equation describing the fluid configuration. This technique can potentially describe the propagation, deformation and overturning of pre‐breaking waves and the mean flow, surface configuration and turbulence field after breaking. The properties of the method are illustrated by several calculational examples. The main parts of the algorithm are optimized for vector processing in a form suitable for installation in supercomputer facilities.
Preconditioned conjugate gradient methods for the incompressible Navier‐Stokes equations
Authors: Chin P. , D'Azevedo E. F. , Forsyth P. A. , Tang W.‐P. 
Published: November 2005

AbstractA robust technique for solving primitive variable formulations of the incompressible Navier‐Stokes equations is to use Newton iteration for the fully implicit non‐linear equations. A direct sparse matrix method can be used to solve the Jacobian but is costly for large problems; an alternative is to use an iterative matrix method. This paper investigates effective ways of using a conjugate‐gradient‐type method with an incomplete LU factorization preconditioner for two‐dimensional incompressible viscous flow problems. Special attention is paid to the ordering of unknowns, with emphasis on a minimum updating matrix (MUM) ordering. Numerical results are given for several test problems.
Enhancing control of grid distribution in algebraic grid generation
Authors: Steinthorsson E. , Shih T. I.‐P. , Roelke R. J. 
Published: November 2005

AbstractThree techniques are presented to enhance the control of grid‐point distribution for a class of algebraic grid generation methods known as the two‐, four‐ and six‐boundary methods. First, multidimensional stretching functions are presented, and a technique is devised to construct them based on the desired distribution of grid points along certain boundaries. Second, a normalization procedure is proposed which allows more effective control over orthogonality of grid lines at boundaries and curvature of grid lines near boundaries. And third, interpolating functions based on tension splines are introduced to control curvature of grid lines in the interior of the spatial domain. In addition to these three techniques, consistency conditions are derived which must be satisfied by all user‐specified data employed in the grid generation process to control grid‐point distribution. The usefulness of the techniques developed in this study was demonstrated by using them in conjunction with the two‐ and four‐boundary methods to generate several grid systems, including a three‐dimensional grid system in the coolant passage of a radial turbine blade with serpentine channels and pin fins.
Flow characteristics in the downstream region of a conical diffuser
Authors: Prinos P. , Goulas A. 
Published: November 2005

AbstractUsing the Navier‐Stokes equations in conjunction with the k‐ϵ model of turbulence, the characteristics of flow in the region downstream of a conical diffuser with 5° angle of inclination are calculated. Two representative stations 1D2 and 10D2 after the diffuser exit are selected for comparison against experimental results. The calculations indicate an underestimation of mean velocity and turbulence kinetic energy at the first station, while satisfactory agreement is obtained for the mean velocity at the second station. The use of a modified k‐ϵ model sensitive to adverse pressure conditions improves the predictions considerably. The effect of inlet properties and Reynolds number on the flow characteristics at the above stations is studied using various inlet profiles and a range of Reynolds numbers based on the inlet diameter from 50 000 to 280 000.
Complex turbulent compressible flow computation using a two‐layer approach
Authors: Mohammadi Bijan 
Published: November 2005

AbstractA two‐layer approach is proposed to compute complex flows including separations. For high‐ and low‐Reynolds‐number regions we use a two‐equation k‐ϵ model and a one‐equation k‐L model respectively. A robust algorithm is proposed for the treatment of the convective part of the turbulence equations. Several complex configurations including separations are computed.
Influence of trailing‐edge grid structure on Navier‐Stokes computation of turbomachinery cascade flow
Authors: Chung Hee‐Taeg , Baek Je‐Hyun 
Published: November 2005

AbstractThree kinds of grid system based on C‐type grid are examined in order to reveal their relative flow characteristics of the turbomachinery cascade, especially near the trailing edge and wake. Here, a semi‐conservative interpolation technique to treat the discontinuous boundary condition along the periodic boundary is proposed and is applied on the patched‐type grid structure. Computational results are presented to see the influence of trailing‐edge grid structure on the Navier‐Stokes solutions for the high‐turning transonic turbine cascade.
Analysis of fluid flow in constricted tubes and ducts using body‐fitted non‐staggered grids
Authors: Melaaen M. C. 
Published: November 2005

AbstractA finite volume method for the calculation of laminar and turbulent fluid flows inside constricted tubes and ducts is described. The selected finite volume method is based on curvilinear non‐orthogonal co‐ordinates (body‐fitted co‐ordinates) and a non‐staggered grid arrangement. The grids are either generated by transfinite interpolation or an elliptic grid generator. The method is employed for calculation of laminar flows through a tube, a converging‐diverging duct and different constricted tubes by both a two‐ and a three‐dimensional computer program. In addition, turbulent flow through an axisymmetric constricted tube is calculated. Both the power law scheme and the second‐order upwind scheme are used. The calculated results are compared with the experimental data and with other numerical solutions.
Automatic mesh generation method for shallow water flow analysis
Authors: Kashiyama Kazuo , Okada Tsuyoshi 
Published: November 2005

AbstractThis paper presents a new automatic mesh generation method for the finite element analysis of shallow water flow. The key feature of this method is that the finite element mesh can be generated so that the element Courant number is nearly constant in the whole domain. It follows that the numerical stability and accuracy improve automatically. Moreover, the finite element mesh data, including the data of water depth, can be prepared automatically. The three‐node triangular element is used for the finite element. In order to show the efficiency of the method presented, the mesh obtained by this method is applied to some shallow water flow analyses. This method is shown to be a useful and powerful tool for the preparation of optimal finite element mesh data for shallow water flow analysis.
Boundary integral/spectral element approaches to the Navier‐Stokes equations
Authors: Occhialini J. M. , Muldowney G. P. , Higdon J. J. L. 
Published: November 2005

AbstractNumerical algorithms are presented which combine spectral expansions on elemental subdomains with boundary integral formulations for solving viscous flow problems. Three distinct algorithms are described. The first demonstrates the use of spectral elements for the classic boundary integral method for steady Stokes flow. The second extends this algorithm to include domain integrals for solution of the unsteady Navier‐Stokes equations. The third algorithm explores the use of boundary integrals as a means of consolidating uncoupled elemental solutions in a domain decomposition approach. Numerical results demonstrating high‐order convergence are presented in each case.
Numerical solutions of a non‐linear density current: A benchmark solution and comparisons
Authors: Straka J. M. , Wilhelmson Robert B. , Wicker Louis J. , Anderson John R. , Droegemeier Kelvin K. 
Published: November 2005

AbstractA comparison between solutions from simulations of a non‐linear density current test problem was made in order to study the behaviour of a variety of numerical methods. The test problem was diffusion‐limited so that a grid‐converged reference solution could be generated using high spatial resolution. Solutions of the test problem using several different resolutions were computed by the participants of the ‘Workshop on Numerical Methods for Solving Nonlinear Flow Problems’, which was held on 11–13 September 1990 at the National Center for Supercomputing Applications (NCSA). In general, it was found that when the flow was adequately resolved, all of the numerical schemes produced solutions that contained the basic physics as well as most of the flow detail of the reference solution. However, when the flow was marginally resolved, there were significant differences between the solutions produced by the various models. Finally, when the flow was poorly resolved, none of the models performed very well. While higher‐order and spectral‐type schemes performed best for adequately and marginally resolved flow, solutions made with these schemes were virtually unusable for poorly resolved flow. In contrast, the monotonic schemes provided the most coherent and smooth solutions for poorly resolved flow, however with noticeable amplitude and phase speed errors, even at finer resolutions.
A kinetic theory solution method for the Navier–Stokes equations
Authors: Macrossan M. N. , Oliver R. I. 
Published: November 2005

AbstractThe kinetic‐theory‐based solution methods for the Euler equations proposed by Pullin and Reitz are here extended to provide new finite volume numerical methods for the solution of the unsteady Navier–Stokes equations. Two approaches have been taken. In the first, the equilibrium interface method (EIM), the forward‐ and backward‐flowing molecular fluxes between two cells are assumed to come into kinetic equilibrium at the interface between the cells. Once the resulting equilibrium states at all cell interfaces are known, the evaluation of the Navier–Stokes fluxes is straightforward. In the second method, standard kinetic theory is used to evaluate the artificial dissipation terms which appear in Pullin's Euler solver. These terms are subtracted from the fluxes and the Navier–Stokes dissipative fluxes are added in. The new methods have been tested in a 1D steady flow to yield a solution for the interior structure of a shock wave and in a 2D unsteady boundary layer flow. The 1D solutions are shown to be remarkably accurate for cell sizes large compared to the length scale of the gradients in the flow and to converge to the exact solutions as the cell size is decreased. The steady‐state solutions obtained with EIM agree with those of other methods, yet require a considerably reduced computational effort.
Three‐dimensional mesh embedding for the Navier–Stokes equations using upwind control volumes
Authors: Lapworth B. L. 
Published: November 2005

AbstractA numerical model for the compressible Navier–Stokes equations using local mesh embedding is presented. The model solves for three‐dimensional turbulent flow using an algebraic mixing length model of turbulence. The technique of control volume upwinding is used to produce a novel treatment, whereby the hanging nodes on the mesh interfaces are left with null control volumes. This yields an efficient discretization scheme which ensures second‐order accuracy, flux conservation and stability at the mesh interfaces, whilst retaining a simple interpolative treatment for the hanging nodes. The discrete flow equations are solved using the semi‐implicit pressure correction method. The accuracy of the embedded mesh solver is demonstrated by modelling the three‐dimensional flow through a cascade of turbine vanes at design and off‐design conditions. Mesh embedding gives a saving of 48% in the number of nodes. The embedded mesh solutions compare well with fine structured mesh solutions and experimental measurements. The capability of the embedded mesh solver to perform solution adaptive calculations is demonstrated using a two‐dimensional mid‐height section of the cascade at the off‐design flow conditions.
A parabolic numerical procedure for three‐dimensional viscous rotating flows
Authors: Shi Qingping , Ribando R. J. 
Published: November 2005

AbstractThis paper presents the development of a parabolic numerical procedure for rotating flows and its applications to three‐dimensional viscous rotating flows. The formulation is based on the Navier–Stokes equations in general co‐ordinates fixed on a rotating frame, so that the rotation effect is included in the guess‐correct process. The use of body‐fitted curvilinear co‐ordinates makes it easier to handle the complex geometries of turbomachinery components. In the present work a k–ϵ turbulence model was used for the three‐dimensional numerical tests. The algorithm is equally applicable to incompressible and compressible flows. Comparisons of the predicted results with the experimental data were reasonably good, and the solutions were stable to rotational speeds up to at least 14 000 rpm.
Finite element analysis of lift build‐up due to aerofoil indicial motion
Authors: Shi Jun , Hitchings Dennis 
Published: November 2005

AbstractIn this paper the problem of impulsively started aerofoil or suden change of incidence of an aerofoil in incompressible potential flow is investigated. The essence of solution lies in the representation of a timely and spatially varying wake in a largely irrotational potential flow field. This is achieved by representing the wake through velocity potential difference, which seems to be the only way of imposing a velocity difference condition in the finite element context with velocity potentials as the basic unknowns. Superposition is employed to meet various boundary conditions, which is justified by the linearity of the problem. The finite element solutions are compared with those from singularity method.
On finite element approximation and stabilization methods for compressible viscous flows
Authors: Fortin M. , Manouzi H. , Soulaimani A. 
Published: November 2005

AbstractThis work is devoted to the numerical solution of the Navier–Stokes equations for compressible viscous fluids. Finite element approximations and stabilization techniques are addressed. We present methods to implement discontinuous approximations for the pressure and the density. An upwinding methodology is being investigated which combines the ideas behind the stream line Petrov–Galerkin method and the flux limiter methods aiming to introduce numerical diffusion only where it is necessary.
A comparison of numerical methods applied to non‐linear adsorption columns
Authors: Poulain Christophe A. , Finlayson Bruce A. 
Published: November 2005

AbstractEight numerical schemes (first‐order upstream finite difference, MacCormack, explicit Taylor–Galerkin, random choice, flux‐corrected transport, ENO, TVD, and Euler–Lagrange methods) are compared on the basis of their computational efficiency for one‐dimensional non‐linear convection–diffusion problems. For the ideal chromatographic equation for which an exact solution exists, errors plotted against computational times show that the best methods are the random choice, Euler–Lagrange and flux‐corrected MacCormack methods. Even when significant diffusion is added to the model, steep gradients are possible because of non‐linearities. In such an instance, the random choice and flux‐corrected transport methods give the best performance. One can now tackle more complicated problems and refer to this comparative study in order to choose an adequate numerical method which will provide sufficiently accurate results at a reasonable cost.
Steady flows of non‐Newtonian fluids past a porous plate with suction or injection
Authors: Mansutti D. , Pontrelli G. , Rajagopal K. R. 
Published: November 2005

AbstractThe problem of the steady flow of three classes of non‐linear fluids of the differential type past a porous plate with uniform suction or injection is studied. The flow which is studied is the counterpart of the classical ‘asymptotic suction’ problem, within the context of the non‐Newtonian fluid models. The non‐linear differential equations resulting from the balance of momentum and mass, coupled with suitable boundary conditions, are solved numerically either by a finite difference method or by a collocation method with a B‐spline function basis. The manner in which the various material parameters affect the structure of the boundary layer is delineated. The issue of paucity of boundary conditions for general non‐linear fluids of the differential type, and a method for augmenting the boundary conditions for a certain class of flow problems, is illustrated. A comparison is made of the numerical solutions with the solutions from a regular perturbation approach, as well as a singular perturbation.