bluuebunny/crossref_metadata_2025 huggingface dataset:
Waves generated by an inclined‐plate wave generator
Authors: Wu Yung‐Chao
Published: August 2005

This paper describes the characteristics of small‐amplitude waves generated by a sinusoidally oscillating, inclined paddle‐type wavemaker operating in a constant‐depth channel. Two‐dimensional, linearized potential flow is assumed. A semi‐analytical method, the boundary collocation method, is used to establish the relationship between wave amplitude and paddle stroke. The numerical results are compared with the numerical results of the boundary integral equation method. It is found that the boundary collocation method is simpler and more flexible to implement and faster to compute. In addition, the numerical results are in reasonably good agreement with the laboratory experimental data. For the vertical wavemaker, which is a special case of the inclined wavemaker, an analytical series solution can be found. By using the boundary collocation method and the boundary integral equation method to solve the vertical wavemaker problem and comparing the results with the analytical series solution, it is found that the boundary collocation method yields a solution which is much more accurate than that from the boundary integral equation method. Finally, the relationships between wave amplitude and paddle stroke are established for different inclinations of the paddle‐type wavemaker, based on the boundary collocation method.
A frequency–time domain finite element model for tidal circulation based on the least‐squares harmonic analysis method
Authors: Westerink J. J. , Connor J. J. , Stolzenbach K. D.
Published: August 2005

An iterative type harmonic finite element model is developed for solving the full non‐linear form of the shallow water equations. The scheme iteratively updates time histories of the non‐linear terms which are then harmonically decomposed and used as forcing terms for the linear sets of equations which result from the harmonic separation of the shallow water equations.

A least‐squares harmonic analysis procedure is used to decompose the non‐linear forcing terms. This procedure allows for the very efficient separation of extremely closely spaced harmonics, since it is highly selective with respect to the frequencies it considers. In addition tailoring the procedure and using very specific time steps and sampling periods significantly reduces the number of time samplings points required. In conjunction with the iterative nature of our scheme, the least‐squares procedure makes the scheme entirely general, allows for the direct assessment of all tidal constituents, including compound tides, and permits the clear cut and complete investigation of their mutual interaction through the non‐linearities. In addition this procedure readily computes very‐low‐frequency or residual type circulations.

The FE formulation used shows a very low degree of spurious oscillations while remaining quite simple to implement. This control on nodal oscillations is especially important due to the energy transfer mechanisms involved in this type of iterative scheme.

In an example application the effects of the various non‐linear overtide and compound tide type interactions are examined. It is demonstrated that not only are compound tides significant relative to the overtides, but they also influence the overtides.
Comparison of two numerical methods for the solution of non‐Newtonian flow in ducts
Authors: Liu Ta‐Jo , Lin Ho‐May , Hong Chin‐Nan
Published: August 2005

Two numerical methods, the Galerkin finite element method (FEM) and the boundary‐fitted co‐ordinate transformation method (BFCTM), have been applied to solve inelastic non‐Newtonian fluid flow in ducts of irregular cross‐section. Three representative fluid models, namely the power‐law, the Ellis and the Bingham models, have been analysed. The application of the FEM is straightforward, while for the BFCTM the accurate estimation of viscosity on the duct boundary and the proper mesh adjustment appear to be critical for generating convergent solutions. A detailed comparison of the two numerical methods in terms of volumetric flow rate, axial velocity, shear rate, viscosity and CPU time is given. Both methods can generate accurate solutions of velocity over a wide range of variables, but the FEM requires much less computing time to reach the same level of accuracy. Only the BFCTM can be used to approximate shear rate and viscosity with reasonable accuracy.
Prediction of oscillating thick cambered aerofoil aerodynamics by a locally analytic method
Authors: Chiang Hsiao‐Wei D. , Fleeter Sanford
Published: August 2005

A complete first‐order model and locally analytic solution method are developed to analyse the effects of mean flow incidence and aerofoil camber and thickness on the incompressible aerodynamics of an oscillating aerofoil. This method incorporates analytic solutions, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual grid elements. The velocity potential is separated into steady and unsteady harmonic parts, with the unsteady potential further decomposed into circulatory and non‐circulatory components. These velocity potentials are individually described by Laplace equations. The steady velocity potential is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating aerofoil. A body‐fitted computational grid is then utilized. Solutions for both the steady and the coupled unsteady flow fields are obtained by a locally analytic numerical method in which locally analytic solutions in individual grid elements are determined. The complete flow field solution is obtained by assembling these locally analytic solutions. This model and solution method are shown to accurately predict the Theodorsen oscillating flat plate classical solution. Locally analytic solutions for a series of Joukowski aerofoils demonstrate the strong coupling between the aerofoil unsteady and steady flow fields, i.e. the strong dependence of the oscillating aerofoil aerodynamics on the steady flow effects of mean flow incidence angle and aerofoil camber and thickness.
A stable least‐squares finite element method for non‐linear hyperbolic problems
Authors: Jiang B. N. , Carey Graham F.
Published: August 2005

A class of stable least‐square finite element methods for non‐linear hyperbolic problems is developed and some exploratory studies made. The methods are based on modifying the L2‐norm of the. residual and a related approximation to the H1‐norm of the residual. The effect of the additional terms in these residual functionals is to introduce a dissipative effect proportional to the solution gradient. This acts to stabilize the solution for non‐linear hyperbolic problems which generate shocks. Numerical results for a one‐dimensional nozzle and shock tube problem demonstrate the accuracy and stability of the method. Results are for an implicit scheme and calculations for linear, quadratic and cubic elements are given.
Axially symmetric cavitation flow at small cavitation numbers
Authors: Dagan A.
Published: August 2005

A method for computing the drag coefficient of a body in an axially symmetric, steady‐state cavitation flow is presented. A ‘vortex ring’ distribution along the wetted body surface and along the cavity interface is assumed. Since the location of the cavitation interface is unknown a priori, an iterative procedure is used, where, for the first stage, an arbitrary cavitation interface is assumed. The flow field is then solved, and by an iterative process the location of the cavitation interface is corrected. Even though the flow field is governed by the linear Laplace equation, strong non‐linearity resulting from the kinematic boundary conditions appears along the cavitation interface. An improved numerical scheme for solving the dual Fredholm integral equations is obtained by formulating high‐order approximations to the singular integrals in order to reduce the matrix dimensions. Good agreement is found between the numerical results of the present work, experimental results and other solutions.
On the accuracy of least‐squares finite elements for a first‐order conservation equation
Authors: Wilders P.
Published: August 2005

The numerical solution of a single first‐order conservation equation by a least‐squares finite element method is considered. Isoparametric bilinear quadrilateral elements are used. The accuracy is studied numerically and it is shown that the discrete equations associated with nodal points on the boundaries should be modified in order to obtain an accurate numerical solution.
Two‐equation (k, ϵ) turbulence computations by the use of a finite element model
Authors: Utnes Torbjørn
Published: August 2005

A finite element technique is presented and applied to some one‐ and two‐dimensional turbulent flow problems. The basic equations are the Reynolds averaged momentum equations in conjunction with a two‐equation (k, ϵ) turbulence model. The equations are written in time‐dependent form and stationary problems are solved by a time iteration procedure. The advection parts of the equations are treated by the use of a method of characteristics, while the continuity requirement is satisfied by a penalty function approach. The general numerical formulation is based on Galerkin's method. Computational results are presented for one‐dimensional steady‐state and oscillatory channel flow problems and for steady‐state flow over a two‐dimensional backward‐facing step.
Improving the accuracy of the least‐squares finite element approximation of the linearized steady Euler equations by an embedding method
Authors: Wilders P.
Published: August 2005

The standard least‐squares finite element method for the linearized Euler equations turns out to be inaccurate. This method is studied in detail for a system of composite type, obtained by transformation of the linearized Euler equations. The shortcomings of the method are clarified and an embedding method is constructed. It is shown numerically that this new method is O(h2)‐accurate.
Dynamics of non‐Newtonian fluid interfaces in a porous medium: Incompressible fluids
Authors: Pascal H. , Pascal F.
Published: August 2005

This paper concerns the applications of frontal advance theory to the dynamics of a moving flat interface in a porous medium, when both displacing and displaced fluids are of power law behaviour. The rheological effects of non‐Newtonian behaviour of these fluids on the interface position and its velocity are numerically illustrated and discussed with regard to the practical implications in oil displacement mechanisms. The results obtained should be useful in finding an optimal policy of injection in order to control the dynamics of the moving interface in field projects of enhanced oil recovery floods.
A comment on the paper ‘finite difference methods for the stokes and Navier‐Stokes equations’ by J. C. Strikwerda
Authors: Roache Patrick J.
Published: August 2005

This work comments on a recent paper by J. C. Strikwerda in SIAM Journal on Scientific and Statistical Computing, in an attempt to clear up the evident confusion regarding the use of a Poisson equation for pressure in incompressible Navier‐Stokes solutions.
Evaluation of FIDAP on some classical laminar and turbulent benchmarks
Authors: Sohn J. L.
Published: August 2005

Numerical solutions of the Fluid Dynamics Analysis Package (FIDAP) for some laminar and turbulent flow problems, namely (1) two‐dimensional laminar flow inside a wall‐driven cavity, (2) two‐dimensional laminar flow over a backward‐facing step and (3) two‐dimensional turbulent flow over a backward‐facing step, are presented. The consistent integration penalty finite element method is used with Q2/P1 (nine‐node biquadratic velocity with linear discontinuous pressure) finite elements. Results of FIDAP on the above problems are compared with other numerical solutions and experimental data to evaluate its numerical accuracy. The influence of streamline upwinding is also investigated for all the test cases.
Heat exchanger analysis on a MicroVAX II/GPX
Authors: Haught Alan F.
Published: August 2005

The finite element code FIDAP was used to examine the fluid flow path within a flat plate tube/fin heat exchanger and the resulting heat transfer from the fins and tube walls. The mathematical formulation, mesh development and analysis procedure are presented, and the results obtained are compared with experimental observations of the fluid flow and measurements of the fluid heating. This problem illustrates the capabilities of finite element techniques for analysing complex three‐dimensional convection‐dominated heat transfer, and demonstrates the scope of problems which can be addressed on a Micro VAX II/GPX workstation.
Developing flows in narrow channels, containing heated obstacles
Authors: Torok Dennis , Gronseth Rosanne
Published: August 2005

The use of numerical techniques to augment experimentally collected temperature data of electrical components is illustrated. FIDAP, a finite element CFD code, is used to generate the numerical results. Comparisons of the numerical results with experimental data of HaCohen, experimentally derived correlations of Wirtz and Dykshoorn and numerical results of Heaton et al. are given. A discussion of modelling techniques, mesh refinement, numerical error and stability is presented with suggestions for improvement of flow models. The results generated by FIDAP, using 2D models, compare favourably (to within 10%) with the experimental data of HaCohen. The results indicate the possibility of augmenting experimental data collection with numerical results, at least in the regions of laminar and low turbulent flow.
Euler flow solutions for transonic shock wave–boundary layer interaction
Authors: Koren Barry
Published: August 2005

Steady 2D Euler flow computations have been performed for a wind tunnel section, designed for research on transonic shock wave–boundary layer interaction. For the discretization of the steady Euler equations, an upwind finite volume technique has been applied. The solution method used is collective, symmetric point Gauss–Seidel relaxation, accelerated by non‐linear multigrid. Initial finest grid solutions have been obtained by nested iteration. Automatic grid adaptation has been applied for obtaining sharp shocks. An indication is given of the mathematical quality of four different boundary conditions for the outlet flow. Two transonic flow solutions with shock are presented: a choked and a non‐choked flow. Both flow solutions show good shock capturing. A comparison is made with experimental results.
Are fem solutions of incompressible flows really incompressible? (or how simple flows can cause headaches!)
Authors: Pelletier Dominique , Fortin Andre , Camarero Ricardo
Published: August 2005

It is generally accepted that mixed and penalty finite element methods can routinely solve the incompressible Navier–Stokes equations. This paper shows by means of simple examples that problems can arise even for the simpler Stokes equations. The causes of the problem fall in either of two categories: round‐off and ill conditioning, or a poor choice of pressure discretization. Nonsensical solutions can be obtained. Computation of the discrete divergence of the flow field is a simple and powerful tool to diagnose such conditions. In the first part of the paper several simple techniques for minimizing the effect of round‐off are reviewed. In the second part it is shown that, for coupled flow problems, care must be exercised in the choice of the pressure approximation. A unified treatment of various observations by different workers is presented. This should prove useful for general users of the finite element method.
Numerical simulation of axisymmetric turbulent flow in combustors and diffusers
Authors: Yung Chain‐Nan , Keith Theo. G. , De Witt Kennet H. J.
Published: August 2005

Numerical studies of turbulent flow in an axisymmetric 45° expansion combustor and bifurcated diffuser are presented. The Navier‐Stokes equations incorporating a k–ϵ model were solved in a non‐orthogonal curvillinear co‐ordinate system. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass flux. Three finite differencing methods—hybrid, quadratic upwind and skew upwind—were used to represent the convection terms. Results were compared with existing experimental data. In general, good agreement between predicted and measured values was obtained.
Efficient quadrature for a boundary element method to compute three‐dimensional Stokes flow
Authors: Varnhorn Werner
Published: August 2005

A collocation‐type boundary element method based on bilinear B‐splines is used for the numerical solution of the Stokes Dirichlet problem in bounded domains D ⊂ R3. The computation of the influence matrix requires the numerical evaluation of weakly singular integrals on the domain boundary if the usual double‐layer potential ansatz is chosen. Here mostly standard methods with disjoint grids for collocation and integration are used. We develop a special integration scheme based on triangular co‐ordinates near the singularity and show its efficiency compared with the method mentioned above.
A new look at Theodorsen's method in aerofoil theory
Authors: Bera Rajendra K.
Published: August 2005

Theodorsen's method for calculating the incompressible potential flow past an aerofoil is viewed afresh. It is found that some simple modifications to the computational process make the computations relatively faster, easier and more accurate. The new modifications are applicable to the analysis of conventional aerofoils with up to moderate thickness and camber ratios. Several examples are presented to show the effectiveness of the modifications.
Numerical simulation of the hydrodynamic interaction between a sedimenting particle and a neutrally buoyant particle
Authors: Ingber Marc S.
Published: August 2005

A new method for the simulation of the translational and rotational motions of a system containing a sedimenting particle interacting with a neutrally buoyant particle has been developed. The method is based on coupling the quasi‐static Stokes equations for the fluid with the rigid body equations of motion for the particles. The Stokes equations are solved at each time step with the boundary element method. The stresses are then integrated over the surface of each particle to determine the resultant forces and moments. These forces and moments are inserted into the rigid body equations of motion to determine the translational and rotational motions of the particles. Unlike many other simulation techniques, no restrictions are placed on the shape of the particles. Superparametric boundary elements are employed to achieve accurate geometric representations of the particles. The simulation method is able to predict the local fluid velocity, resolve the forces and moments exerted on the particles, and track the particle trajectories and orientations.
Three‐dimensional unsteady flow simulations: Alternative strategies for a volume‐averaged calculation
Authors: Perng Chin‐Yuan , Street Robert L.
Published: August 2005

This work builds on a SIMPLE‐type code to produce two numerical codes of greatly improved speed and accuracy for solution of the Navier–Stokes equations. Both implicit and explicit codes employ an improved QUICK (quadratic upstream interpolation for convective kinematics) scheme to finite difference convective terms for non‐uniform grids. The PRIME (update pressure implicit, momentum explicit) algorithm is used as the computational procedure for the implicit code. Use of both the ICCG (incomplete Cholesky decomposition, conjugate gradient) method and the MG (multigrid) technique to enhance solution execution speed is illustrated. While the implicit code is first‐order in time, the explicit is second‐order accurate. Two‐ and three‐dimensional forced convection and sidewall‐heated natural convection flows in a cavity are chosen as test cases. Predictions with the new schemes show substantial computational savings and very good agreement when compared to previous simulations and experimental data.
Multifronts and transputer networks for solving fluid mechanical finite element systems
Authors: Miles R. G. , Havard S. P.
Published: August 2005

This paper is concerned with the implementation of a multifrontal solver on a network of transputers. We briefly discuss the transputer, outline the frontal and multifrontal schemes and consider the implementation of these schemes on the network. Results are presented for two test problems in fluid mechanics showing that the solver displays close to linear speed‐up.
Some uses of Green's theorem in solving the Navier–Stokes equations
Authors: Dennis S. C. R. , Quartapelle L.
Published: August 2005

This paper gives a review of methods where Green's theorem may be employed in solving numerically the Navier–Stokes equations for incompressible fluid motion. They are based on the concept of using the theorem to transform local boundary conditions given on the boundary of a closed region in the solution domain into global, or integral, conditions taken over it. Two formulations of the Navier–Stokes equations are considered: that in terms of the streamfunction and vorticity for two‐dimensional motion and that in terms of the primitive variables of the velocity components and the pressure. In the first formulation overspecification of conditions for the streamfunction is utilized to obtain conditions of integral type for the vorticity and in the second formulation integral conditions for the pressure are found. Some illustrations of the principle of the method are given in one space dimension, including some derived from two‐dimensional flows using the series truncation method. In particular, an illustration is given of the calculation of surface vorticity for two‐dimensional flow normal to a flat plate. An account is also given of the implementation of these methods for general two‐dimensional flows in both of the mentioned formulations and a numerical illustration is given.
The development of advanced computational methods for turbomachinery blade design
Authors: Stow P.
Published: August 2005

The paper describes the basic components of a turbomachinery blade design system in use within Rolls‐Royce. A number of modelling aspects of the advanced computational methods in use and under development are reviewed together with areas for future research and development.

A quasi‐3D blade design system which is used for both compressors and turbines is described covering through‐flow and blade‐to‐blade analysis. Various features of blade‐to‐blade analysis are discussed including the use of compatible design and analysis modes and coupled boundary layer analysis capable of handling attached and separated flow; examples are included to show capabilities. Advances being made in the development and application of Reynolds‐averaged Navier–Stokes models are covered showing capabilities with regard to loss and heat transfer prediction.

A fully coupled quasi‐3D through‐flow and blade‐to‐blade analysis system is described and results presented to show basic capabilities.

The need for 3D flow analysis is discussed and the elements of a 3D blade design system presented showing how this links to the traditional quasi‐3D system. Examples are given showing basic capabilities of the methods available and under development.

Finally areas for future development are presented indicating the mathematical and numerical modelling problems to be addressed.
Navier–Stokes computation of transonic vortices over a round leading edge delta wing
Authors: Müller Bernhard , Rizzi Arthur
Published: August 2005

A 3D Navier–Stokes solver has been developed to simulate laminar compressible flow over quadrilateral wings. The finite volume technique is employed for spatial discretization with a novel variant for the viscous fluxes. An explicit three‐stage Runge–Kutta scheme is used for time integration, taking local time steps according to the linear stability condition derived for application to the Navier–Stokes equations. The code is applied to compute primary and secondary separation vortices at transonic speeds over a 65° swept delta wing with round leading edges and cropped tips. The results are compared with experimental data and Euler solutions, and Reynolds number effects are investigated.
Analysis of incompressible massively separated viscous flows using unsteady Navier–Stokes equations
Authors: Ghia K. N. , Osswald G. A. , Ghia U.
Published: August 2005

The unsteady incompressible Navier–Stokes equations are formulated in terms of vorticity and stream‐function in generalized curvilinear orthogonal co‐ordinates to facilitate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the vorticity transport equation using the alternating direction implicit method, whereas the streamfunction equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a backstep in a doubly infinite channel, using clustered conformal co‐ordinates. One‐dimensional stretching functions, dependent on the Reynolds number and the asymptotic behaviour of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honour the multiple length scales of the separated flow model problem. The asymptotic behaviour of the finite differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second‐order‐accurate wiggle‐free solutions, i.e. with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem, prior to the onset of three‐dimensionality in the experiment.
Numerical solution of transonic flows on a streamfunction co‐ordinate system
Authors: Barron Ronald M. , Naeem R. K.
Published: August 2005

A new method has been developed for the computation of steady two‐dimensional full‐potential transonic flow past symmetric aerofoils. This method utilizes von Mises variables (x, ψ), where ψ is taken as the streamfunction for the flow. The flow equations and appropriate boundary conditions are formulated in terms of the von Mises variables (x, ψ) for symmetric aerofoils at zero incidence. This yields a system of two equations for unknowns ρ(x, ψ) and y(x, ψ). Finite difference solutions have been computed using SLOR at subcritical and supercritical Mach numbers. The results are compared with available data and are in excellent agreement.
A boundary element method for a non‐linear free surface problem
Authors: Campana E. , Lalli F. , Bulgarelli U.
Published: August 2005

In this paper a numerical method to compute the wave resistance of a body submerged in a free stream of finite and infinite depth is presented. Non‐linear effects on the free surface are taken into account by an iterative procedure; the solution is in the form of a single‐layer potential. For the 2D problem, results are shown for both the cases of finite and infinite depth of the fluid domain, with special emphasis on the supercritical flow in which the consistency of the scheme is pointed out. The method is also extended to the 3D case of a spheroid submerged in deep water. All the results presented are compared with experimental data and analytical solutions available in the literature.
An efficient algorithm for compressible flows with real gases
Authors: Glaister P.
Published: August 2005

An efficient algorithm is presented for the solution of the Euler equations of gas dynamics with a general convex equation of state. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only one function evaluation in each computational cell is required by using a local parametrization of the equation of state. The scheme is applied to two standard test problems in gas dynamics for some specimen equations of state.
Comments on a recent paper by W. Zijl
Authors: Greenside H. S.
Published: August 2005

A recent paper by W. Zijl, which reformulated the Navier–Stokes and Boussinesq equations in terms of Clebsch potentials, has an error that greatly reduces the generality of the results. Some other recent efforts to use such potentials in fluid and plasma dynamics are briefly discussed.
A comparison of primitive variables and streamfunction–vorticity for fem depth‐averaged modelling of steady flow
Authors: DeVantier Bruce A.
Published: August 2005

The governing equations for depth‐averaged turbulent flow are presented in both the primitive variable and streamfunction–vorticity forms. Finite element formulations are presented, with special emphasis on the handling of bottom stress terms and spatially varying eddy viscosity. The primitive variable formulation is found to be preferable because of its flexibility in handling spatial variation in viscosity, variability in water surface elevations, and inflow and outflow boundaries. The substantial reduction in computational effort afforded by the streamfunction–vorticity formulation is found not to be sufficient to recommend its use for general depth‐averaged flows. For those flows in which the surface can be approximated as a fixed level surface, the streamfunction–vorticity form can produce results equivalent to the primitive variable form as long as turbulent viscosity can be estimated as a constant.
A numerical study of heat and momentum transfer for tube bundles in crossflow
Authors: Chang Yeon , Beris Antony N. , Michaelides Efstathios E.
Published: August 2005

A numerical scheme is developed to predict the heat transfer and pressure drop coefficients in flow through rigid tube bundles. The scheme uses the Galerkin finite element technique. The conservation equations for laminar steady‐state flow are cast in the form of streamfunction and vorticity equations. A Picard iteration method is used for the solution of the resulting system of non‐linear algebraic equations. Results for the heat transfer and pressure drop coefficients are obtained for tube arrays of pitch ratios of 1·5 and 2·0. Very good agreement of the present results and experimental data obtained in the past is observed up to Reynolds numbers of 1000. It is also observed that the results of the present method show better agreement with the experimental data and that they are applicable for higher Reynolds numbers than results of other studies.
Probabilistic approach for transport of contaminants through porous media
Authors: Roco M. C. , Khadilkar J. , Zhang J.
Published: August 2005

The channels formed between individual particles in porous media have variable dimensions and orientations. The porosity, permeability and its anisotropy exhibit random spatial distributions. The probabilistic approach can effectively describe the transport of contaminants through porous media and is analysed in this paper. Numerical results are obtained by considering (I) random dispersion coefficients without and with spatial structure, (II) random time distribution of concentration at the inlet boundary, (III) random velocity distribution in the flow field without and (IV) with variable dispersion coefficient, (V) non‐linearity of the governing equation and (VI) anisotropy of the dispersion coefficient. Two methods are used for probabilistic predictions: (1) Gaussian field approach in conjunction with Monte Carlo method and (2) random walk method. The input random parameters are assumed to have normal and log‐normal distributions according to available experimental data. The probability distribution functions of the contaminant concentration at different locations within the flow domain are calculated and compared with the input distributions as a function of the mean and fluctuation Peclet numbers. The one‐dimensional case is analysed in detail and the illustrative numerical predictions are compared with analytical and experimental results. The extension to a two‐dimensional domain is discussed in the last part of this paper.
High‐order axisymmetric Navier–Stokes code: Description and evaluation of boundary conditions
Authors: Sørensen J. N. , Loc Ta Phuoc
Published: August 2005

A description is given of a high‐order solution algorithm for the solution of the unsteady axisymmetric Navier–Stokes equations. The method consists of a combination of fourth‐order and second‐order accurate finite difference schemes, where the approximated equations are solved by an alternating direction implicit (ADI) method. Special attention is paid to the boundary conditions. Results are compared with measurements for the cases of rotating flow within a closed cylinder (rotating driven cavity), developing axial flow in a stationary pipe and developing flow in a rotating pipe.
Large eddy simulation of a developing turbulent boundary layer at a low Reynolds number
Authors: Tsai H. M. , Leslie D. C.
Published: August 2005

A spectral code has been used to simulate a developing turbulent boundary layer at low Reynolds number Reθ (based on free stream velocity and momentum thickness) between 353 and 576. The starting field was generated by allowing a step change of temperature to diffuse outwards from one wall in a fully developed channel flow. The thermal boundary layer so created was conditionally sampled to convert it into a momentum boundary layer with an irrotational free stream region, a process which is justified by appeal to experiments. This initial field was allowed to develop until the momentum boundary layer thickness δ995 had grown to about 1·5 times its original thickness.

The results of the simulation have been compared with a wide range of experimental data. The outcome of this comparison is generally very satisfactory; the main trends of the experiments are well reproduced and our simulation supplements and extends the existing sets of experimental data. The simulation also gives pressure statistics which cannot be obtained experimentally. In particular, it gives the contribution of pressure diffusion to the balance equations for the Reynolds stress and indicates the error produced by omitting this term.
A stable fast marching scheme for computational fluid mechanics
Authors: Behnia M. , Wolfshtein M. , De Vahl Davis G.
Published: August 2005

A stable fast marching scheme has been developed for the solution of coupled parabolic partial differential equations such as the Navier–Stokes equations. The scheme was developed with the aid of a stability analysis. The implementation of the method in standard alternating direction implicit algorithms is straightforward. The scheme was tested on the problem of natural convection in a square cavity. The number of iterations required for convergence was significantly reduced compared to conventional methods.
A computational method for simulating transient motions of an incompressible inviscid fluid with a free surface
Authors: Nakayama Tsukasa
Published: August 2005

A new numerical method has been developed for the analysis of unsteady free surface flow problems. The problem under consideration is formulated mathematically as a two‐dimensional non‐linear initial boundary value problem with unknown quantities of a velocity potential and a free surface profile. The basic equations are discretized spacewise with a boundary element method and timewise with a truncated forward‐time Taylor series. The key feature of the present paper lies in the method used to compute the time derivatives of the unknown quantities in the Taylor series.

The use of the Taylor series expansion has enabled us to employ a variable time‐stepping method. The size of time increment is determined at each time step so that the remainders of the truncated Taylor series should be equal to a given small error limit. Such a variable time‐stepping technique has made a great contribution to numerically stable computations.

A wave‐making problem in a two‐dimensional rectangular water tank has been analysed. The computational accuracy has been verified by comparing the present numerical results with available experimental data. Good agreement is obtained.
A finite difference self‐adaptive mesh solution of flow in a sedimentation tank
Authors: Casonato Marco , Gallerano Francesco
Published: August 2005

A new numerical model has been developed to evaluate the removal efficiency of primary sedimentation clarifiers operating at neutral density condition. The velocity and concentration fields as well as the development in time and space of the settled particle bed thickness are simulated. The main difficulties in simulation of velocity and concentration fields are related to (1) numerical instabilities produced by the prevalence of convective terms in the unknown variable high‐gradient regions and (2) turbulence effects on the suspension of solid particles from the settled bed. The need to overcome the numerical instabilities without the upwind difference approximation, which introduces high numerical viscosity, suggests the use of non‐uniform grids of calculation.

The velocity field is obtained by solving the motion equations in the vorticity and streamfunction formulation by means of a new numerical method based upon a dynamically self‐adjusting calculation grid. These grids allow for a finer mesh following the evolution of the unknown quantities. A k–ϵ model is used to simulate turbulence phenomena.

The sedimentation field is found by solving the diffusion and transport equation of the solid particle concentration. Boundary conditions on the bottom line are imposed relating the amount of turbulence flux and sedimentation flux to the actual concentration and the reference concentration. Such an approach makes it possible to represent the solid particle suspension from the bottom, taking into account its dependence on (1) the characteristics and the evolution in time of the settled bed, (2) the velocity component parallel to the bottom line and (3) the turbulence structure.
Boundary node correction and superconvergence in the FEM
Authors: Yao M. , Malkus D. S.
Published: August 2005

Convergence improvement and superconvergence behaviour, obtained by the simple boundary node correction (BNC) procedure for certain stress‐like variables of smoothed FEM solutions, are reported in this paper. The effectiveness of BNC is shown through three examples of steady flow problems, and a posterior error analysis based on the multiple‐mesh extrapolation technique has been used for estimating the convergence rates.
Finite volume method for prediction of fluid flow in arbitrarily shaped domains with moving boundaries
Authors: Demirdžić I. , Perić M.
Published: August 2005

In this paper a method is presented that can be used for both the Lagrangian and the Eulerian solution of the Navier–Stokes equations in a domain of arbitrary shape, bounded by boundaries which move in any prescribed time‐varying fashion. The method uses the integral form of the governing equations for an arbitrary moving control volume, with pressure and Cartesian velocity components as dependent variables. Care is taken to also satisfy the space conservation law, which ensures a fully conservative computational procedure. Fully implicit temporal differencing makes the method stable for any time step.

A detailed description is provided for the discretization in two dimensions, with a collocated arrangement of variables. Central differences are used to evaluate both the convection and diffusion fluxes. The well known SIMPLE algorithm is employed for pressure–velocity coupling. The resulting algebraic equation systems are solved iteratively in a sequential manner. Results are presented for a flow in a channel with a moving indentation; they show favourable agreement with experimental observations.
Internal three‐dimensional viscous flow solutions using the vorticity‐potential method
Authors: Yang Herong , Camarero Ricardo
Published: August 2005

A numerical solution procedure for internal three‐dimensional viscous flow is proposed in this paper. The formulation is based on the non‐primitive variables, the vorticity and potentials, on a curvilinear grid. A new upwind difference scheme is introduced to overcome the convective instabilities arising in the central difference scheme for the vorticity transport equations, while keeping false diffusion to a minimum level. Developing flows in both straight and curved square ducts are simulated to validate the procedure. The results are compared with both experimental measurements and analytical solutions.
A higher‐order eulerian scheme for coupled advection‐diffusion transport
Authors: Yang Guolu , Belleudy Philippe , Temperville André
Published: August 2005

A new accurate high‐order numerical method is presented for the coupled transport of a passive scalar (concentration) by advection and diffusion.

Following the method of characteristics, the pure advection problem is first investigated. Interpolation of the concentration and its first derivative at the foot of the characteristic is carried out with a fifth‐degree polynomial. The latter is constructed by using as information the concentration and its first and second derivatives at computational points on current time level t in Eulerian co‐ordinates. The first derivative involved in the polynomial is transported by advection along the characteristic towards time level t + Δt in the same way as is the concentration itself. Second derivatives are obtained at the new time level t + Δt by solving a system of linear equations defined only by the concentrations and their derivatives at grid nodes, with the assumption that the third‐order derivatives are continuous. The approximation of the method is of sixth order.

The results are extended to coupled transport by advection and diffusion. Diffusion of the concentration takes place in parallel with advection along the characteristic. The applicability and precision of the method are demonstrated for the case of a Gaussian initial distribution of concentrations as well as for the case of a steep advancing concentration front. The results of the simulations are compared with analytical solutions and some existing methods.
Numerical aspects of calculation of confined swirling flows with internal recirculation
Authors: Durst F. , Wennerberg D.
Published: August 2005

Predictions were performed for two different confined swirling flows with internal recirculation zones. The convection terms in the elliptic governing equations were discretized using three different finite differencing schemes: hybrid, quadratic upwind interpolation and skew upwind differencing. For each flow case, calculations were carried out with these schemes and successively refined grids were employed. For the turbulent flow case the k‐ε turbulence model was used. The predicted cases were a laminar swirling flow investigated by Bornstein and Escudier, and a turbulent low‐swirl case studied by Roback and Johnson. In both cases an internal recirculation zone was present. The laminar case is well predicted when account is taken of the estimated radial velocity component at the chosen inlet plane. The quadratic upwind interpolation and skew upwind schemes predict the main features of the internal recirculation zone also with a coarse grid. The turbulent case is well predicted with the coarse as well as the finer grids, the skew upwind and quadratic upwind interpolation schemes yielding results very close to the measurements. It is concluded that the skew upwind scheme reaches grid independence slightly before the quadratic upwind scheme, both considerably earlier than the hybrid scheme.
Vortex simulation of the intake flow in a planar piston‐chamber device
Authors: Martins Luis‐Filipe , Ǵhoniem Ahmed F.
Published: August 2005

A numerical scheme based on the application of the vortex method to update the vorticity field and the implementation of the finite element method to satisfy the normal velocity boundary condition inside a complex time‐dependent geometry is applied to simulate the flow produced by a piston sliding out of a chamber equipped with single or multiple intakes. This unsteady confined vortex flow is of interest in many applications. We use the idealization that the flow is incompressible, two‐dimensional and planar and we analyse the results to study the flow during the intake process inside a model of an engine cylinder. The chamber top is fitted with an inlet channel, an inlet port or an inlet valve. In all cases when the intake channel axis coincides with that of the chamber, the flow in each side of the chamber consists essentially of two large counter‐rotating eddies of almost the same size. The computed structures of these flows resemble qualitatively those which have been observed experimentally. The fluid motion is also computed for the case of a chamber equipped with an intake whose axis is not aligned with the chamber axis. In this case the flow at the end of the stroke is dominated by a single large eddy produced by the merging of the two eddies forming on the sides of the port.
Acceleration of convergence by shifting the spectrum of implicit finite difference operators associated with the equations of gas dynamics
Authors: Cheer A. , Saleem M.
Published: August 2005

Eigensystem analysis techniques are applied to finite difference formulations of the Navier‐Stokes equations in one dimension. Spectra of the resulting implicit difference operators are computed. The largest eigenvalues are calculated by using a combination of the Frechet derivative of the operators and Arnoldi's method. The accuracy of Arnoldi's method is tested by comparing the rate of convergence of the iterative method with the dominant eigenvalue of the original iteration matrix.

On the basis of the pattern of eigenvalue distributions for various flow configurations, a shifting of the implicit operators in question is devised. The idea of shifting is based on the power method of linear algebra and is very simple to implement. This procedure has improved the rates of convergence of CFD codes (developed at NASA Ames Research Center) by 20%–50%. The sensitivity of the computed solution with respect to the shift is also studied. Finally, an adaptive shifting of the spectrum together with Wynn's acceleration algorithm are discussed. It turns out that the shifting process is a preconditioner for Wynn's method.
Finite element modelling of quasi‐three‐dimensional nearly horizontal flow
Authors: Utnes Torbjørn
Published: August 2005

A quasi‐three‐dimensional numerical model is presented and applied to some test problems with constant density. The numerical technique is based on a finite element formulation and the three‐dimensional problem is factorized into one‐ and two‐dimensional subproblems. The non‐linear advection is treated by use of a weak formulation of the characteristics method and the equations are transformed to ‘sigma’ coordinates.
Cavitating flows through a cascade of flat plates
Authors: Wen X. , Ingham D. B.
Published: August 2005

The purpose of this research is to consider the flow through a cascade of bluff bodies, behind which there exist cavities, by using the free streamline theory. When the wake extends to infinity, both the free surface and the velocity on the free surface are unknown and the cavitation number cannot be specified arbitrarily. Given the geometry of the cascade, a numerical method is described in which we obtain the shape of the free surface and the cavitation number. We obtain the relationship between the contraction coefficient, cavitation number and drag coefficient.