bluuebunny/crossref_metadata_2025 huggingface dataset:
Finite element solution of an enclosed turbulent diffusion flame
Authors: Benim A. C.
Published: August 2005

A finite element formulation of enclosed turbulent diffusion flames is presented. A primitive variables approach is preferred in the analysis. A mixed interpolation is employed for the velocity and pressure. In the solution of the Navier‐Stokes equations, a segregated formulation is adopted, where the pressure discretization equation is obtained directly from the discretized continuity equation, considering the velocity‐pressure relationships in the discretized momentum equations. The state of turbulence is defined by a κ–ϵ model. Near solid boundaries, a wall function approach is employed. The combustion rates are estimated using the eddy dissipation concept. The expensive direct treatment of the integrodifferential equations of radiation is avoided by employing the moment method, which allows the derivation of an approximate local field equation for the radiation intensity. The proposed finite element model is verified by investigating a technical turbulent diffusion flame of semi‐industrial size, and comparing the results with experiments and finite difference predictions.
Numerical simulation of silencers
Authors: Cooke Charlie H. , Fansler Kevin S.
Published: August 2005

The problem of attenuating the noise from weapons firing is studied experimentally and numerically. As a possible method of attenuating the noise significantly, a silencer with no internal baffles is attached to the M242 cannon. The internal pressures inside the muffler are measured. The near‐field overpressures outside the muffler at various polar angles are also measured. A numerical simulation of the flow through the muffler is performed, using Harten's shock‐capturing method to solve the Euler equations of ideal compressible flow. The numerical simulation yields a detailed picture of the flow field as displayed by the pressure and Mach contours. Pressure–time curves at selected locations are obtained and compared with experimental data. There is good agreement, except that the numerical simulation generates more vigorous oscillations.
Quantum phenomena in numerical wave propagation
Authors: Vichnevetsky Robert
Published: August 2005

The analysis of wave propagation in computing domains where hyperbolic equations are approximated with finite differences has revealed surprising analogies between this subject and quantum mechanics. The first part of this paper consists of a review of the corresponding phenomena and of their description with known results from numerical analysis and wave propagation theory. We then introduce a new formalism, containing a finite difference analogue of the classical Schrodinger equation, which describes the ensemble of those phenomena. The validity of the new formalism is verified by its agreement with known theoretical results in numerical wave propagation (it contains in fact many of those results) as well as with new data obtained in numerical experiments with monochromatic waves which display properties similar to those of Schrödinger's wavefunction for the quantum mechanics description of the equivalent experiments with physical particles. While the results of this paper are derived in the context of wave propagation in computing domains, they remain applicable to similar aspects of wave propagation in other (physical) periodic structures.
Low Reynolds number hydrodynamic interaction of a solid particle with a planar wall
Authors: Ascoli E. P. , Dandy D. S. , Leal L. G.
Published: August 2005

The slow viscous flow problem of an arbitrary solid particle in motion near a planar wall is recast into a boundary integral formulation. The present formulation employs the Green function appropriate to the planar wall problem and is developed in sufficient generality to allow calculations for arbitrary particles in any base flow which satisfies Stokes equations and no‐slip on the wall. The resulting integral equations are easily discretized and solved for the particle surface tractions. Calculations are performed for axisymmetric motions of a variety of ellipsǫids near the planar wall. Agreement with existing theory is excellent.
Coupled heat transfer and viscous flow, and magnetic effects in weld pool analysis
Authors: McLay R. , Carey G. F.
Published: August 2005

A finite element formulation and analysis is developed to study coupled heat transfer and viscous flow in a weld pool. The thermal effects generate not only buoyancy forces but also a variation in the surface tension which acts to drive the viscous flow in the molten weld pool. A moving phase boundary separates molten and solid material. Numerical experiments reveal the nature of the highly convective flow in the weld pool and the associated thermal profiles. The relative importance of buoyancy, surface tension, phase change, convection, etc. are examined. We also consider the sensitivity of the solution to the finite element mesh and related non‐linear numerical instabilities. Of particular interest is the coupling of the thermal and viscous flow fields for the case when radial flow is inward or outward.
Numerical simulation and hydrodynamic visualization of transient viscous flow around an oscillating aerofoil
Authors: Daube O. , Phuoc L. Ta , Dulieu A. , Coutanceau M. , Ohmi K. , Texier A.
Published: August 2005

Unsteady viscous flow around a large‐amplitude and high‐frequency oscillating aerofoil is examined in this paper by numerical simulation and experimental visualization. The numerical method is based on the combination of a fourth‐order Hermitian finite difference scheme for the stream function equation and a classical second‐order scheme to solve the vorticity transport equation. Experiments are carried out by a traditional visualization method using solid tracers suspended in water. The comparison between numerical and experimental results is found to be satisfactory. Time evolutions of the flow structure are presented for Reynolds numbers of 3 × 103 and 104. The influence of the amplitude and frequency of the oscillating motion on the dynamic stall is analysed.
Second‐moment closure and its use in modelling turbulent industrial flows
Authors: Launder B. E.
Published: August 2005

Second‐moment turbulence models focus directly on the transport equations for the Reynolds stresses rather than supposing the stress and strain fields to be directly linked via an eddy viscosity. This elaboration enables the effects of complex strains and force fields on the turbulence structure to be better captured. The paper summarizes the principal modelling strategies adopted for the unknown processes in these equations and presents the forms that have been found most useful in engineering calculations. Methods adopted for overcoming significant problems of numerical instability and lack of convergence compared with eddy‐viscosity‐based schemes are also presented. Applications involving momentum and heat transfer in complex flows are drawn from the advanced technology sectors of the power generation and aircraft industries.
On the application of pseudospectral FFT techniques to non‐periodic problems
Authors: Biringen S. , Kao K. H.
Published: August 2005

The reduction‐to‐periodicity method using the pseudospectral fast Fourier transform (FFT) technique is applied to the solution of non‐periodic problems, including the two‐dimensional incompressible Navier–Stokes equations. The accuracy of the method is explored by calculating the derivatives of given functions, one‐ and two‐dimensional convective‐diffusive problems, and by comparing the relative errors due to the FFT method with a second‐order finite difference (FD) method. Finally, the two‐dimensional Navier–Stokes equations are solved by a fractional step procedure using both the FFT and the FD methods for the driven cavity flow and the backward‐facing step problems. Comparisons of these solutions provide a realistic assessment of the FFT method.
Comment on ‘generalized potential flow theory and direct calculation of velocities applied to the numerical solution of the Navier–Stokes and the Boussinesq equations’
Authors: Abdallah S. , Deutsch S.
Published: August 2005

In a recent paper a generalized potential flow theory and its application to the solution of the Navier–Stokes equation are developed.1 The purpose of this comment is to show that the analysis presented in that paper is in general not correct. We note that the theoretical development of Reference 1 is in fact an extension—although not cited—of some work first done by Hawthorne for steady inviscid flow.2 Hawthorne's solution is correct, and his analysis, which we briefly describe, provides a useful introduction to this note.
Numerical studies of slow viscous rotating flow past a sphere. II
Authors: Raghavarao C. V. , Pramadavalli K.
Published: August 2005

The Navier–Stokes equations, which are the governing equations for a steady, viscous, incompressible fluid rotating about the z‐axis with angular velocity ω, are linearized using the Oseen approximation. Two parameters, namely the Reynolds number Re = Ua/v and Reω = 2ωa2/v (the Reynolds number w.r.t. rotation), enter the linearized equations. These equations are solved by the Peaceman–Rachford ADI method and the resulting algebraic equations are solved by the SOR method. Streamlines are plotted and compared with the Oseen solution for the non‐rotating case. The magnitude of the vorticity vector with increasing θ is also plotted.
Two‐dimensional subcritical and supercritical open channel flow calculation using a time‐marching method
Authors: Soulis Johannes Vassiliou
Published: August 2005

A time‐marching method is presented for the calculation of two‐dimensional, high‐speed channel flow, including the usually neglected terms of slope and bottom friction. Time‐marching methods are potentially the most flexible means of calculating flow through geometrically complex channel passages, since they can readily deal with subcritical and supercritical flows. The adopted numerical scheme comes straight from gas flow computations in turbomachines. The flow is assumed to be fully mixed in the vertical direction, so that vertical variations may be neglected. Comparisons with other numerical solutions for various open channel configurations show that the proposed approach is a comparatively accurate, reliable and fast technique. It can be utilized for open channel designs.
Numerical simulation of an impinging jet on a flat plate
Authors: Chuang Shu‐Hao
Published: August 2005

Two‐dimensional normal impinging jet flowfields, with or without an upper plate, were analysed by employing an implicit bidiagonal numerical method developed by Lavante and Thompkins Jr. The Jones–Launder K–ϵ two‐equation turbulent model was employed to study the turbulent effects of the impinging jet flowfield. The upper plate surface pressure, the ground plane pressure and other physical parameters of the momentum flowfield were calculated at various jet exit height and jet inlet Reynolds numbers. These results were compared with those of Beam and Warming's numerical method, Hsiao and Chuang, and others, along with experimental data. The potential core length of the impinging jet without an upper plate is longer than that of the free jet because of the effects of the ground plane, while the potential core length of the impinging jet with an upper plate is shorter than that of the free jet because of the effects of the upper plate. This phenomenon in the present analysis provides a fundamental numerical study of an impinging jet and a basis for further analysis of impinging jet flowfields on a variable angle plate.
Marangoni convection in weld pools with a free surface
Authors: Tsai M. C. , Kou Sindo
Published: August 2005

A steady‐state two‐dimensional model of heat transfer and fluid flow was developed to describe Marangoni convection in the weld pool. Both the pool surface and the fusion boundary were calculated. The validity of the model was verified against an asymptotic solution for Marangoni‐convection‐induced free surface geometry. Two different cases were studied, i.e. a negative surface tension temperature coefficient ∂γ/∂T a positive one, and the resultant shapes of the weld pool surface were compared.
Spectral simulations of oscillatory convection at low Prandtl number
Authors: Pulicani J. P. , Del Arco E. Crespo , Randriamampianina A. , Bontoux P. , Peyret R.
Published: August 2005

Pseudospectral methods are used for the computation of the time‐dependent convective flows which arise in shallow cavities filled with low‐Prandtí‐number liquids when submitted to a horizontal temperature gradient. In similar situations several former numerical results have been shown to disagree about the determination of the threshold of oscillations and about the subsequent supercritical regimes. Two different tau–Chebyshev methods based on the vorticity–streamfunction formulation and using multistep time schemes are considered. Their results are discussed to assess the validity of the solutions. The physical problems concern rectangular cavities which involve either a rigid or a stress‐free top wall and either conducting or insulating horizontal walls. Aside from the prediction of the onset of oscillations, which is discussed in the various situations with respect to the results of linear and non‐linear analyses and to other computational results, the present study exhibits some bifurcation sequences and a hysteresis cycle at moderate Grashof numbers which are associated to the occurrence of multiple solutions.
Fluid flow in curved ducts
Authors: Jayanti S. , Hewitt G. F. , Kightley J. R.
Published: August 2005

The advent of standard algorithms for the numerical solution of partial differential equations has given researchers a new tool for fluid flow calculations. In this paper, single‐phase flow in curved ducts is numerically simulated by imposing a spatially varying centrifugal force on a fluid flowing in a straight tube. The resulting set of partial differential equations is solved using the HARWELL‐FLOW3D computer program. Comparison with other numerical and experimental results shows that this simplified formulation gives accurate results. The model neglects certain geometric terms of the order d/D, the duct‐to‐coil diameter ratio. The effect of these terms is investigated by considering the flow in a 90° bend for large d/D. It is shown that while there may be significant error in the prediction of the local variables for large d/D, the circumference‐averaged quantities are well predicted.
An improved SIP scheme for numerical solutions of transonic streamfunction equations
Authors: Bao‐Guo Wang , Nai‐Xing Chen
Published: August 2005

A new improved strongly implicit procedure (SIP) is presented for solving large sets of transonic streamfunction equations with matrix of coefficients [B]. This algorithm has several advantages over those now in use. First, Stone's auxiliary matrix [B′] is non‐symmetric, while in the present scheme the auxiliary matrix [B′] is symmetric and the matrix [B + B′] is positive definite and symmetric when [B] is a symmetric matrix. This ensures the numerical stability of the iterative algorithms. Secondly, for an appropriate choice of iterative parameter ω, the rate of convergence of the new iterative procedure should be faster than the original SIP scheme.

Numerical results of the blade‐to‐blade flows are given with the present scheme. It is shown that the algorithm is efficient and robust.
Simulation of planar converging flow of a Leonov viscoelastic fluid
Authors: Tseng Hsieng‐Cheng , Lin Gwo‐Geng
Published: August 2005

An efficient finite element algorithm is presented to simulate the planar converging flow for the viscoelastic fluid of the Leonov model. The governing equation set, composed of the continuity, momentum and constitutive equations for the Leonov fluid flow, is conveniently decoupled and a two‐stage cyclic iteration technique is employed to solve the velocity and elastic strain fields separately. Artificial viscosity terms are imposed on the momentum equations to relax the elastic force and data smoothing is performed on the iterative calculations for velocities to further stabilize the numerical computations. The calculated stresses agree qualitatively with the experimental measurements and other numerically simulated results available in the literature. Computations were successful to moderately high values of Deborah number of about 27·5.
Implicit finite element methods for two‐phase flow in oil reservoirs
Authors: Langtangen Hans Petter
Published: August 2005

The equations governing immiscible, incompressible, two‐phase, porous media flow are discretized by generalized streamline diffusion Petrov–Galerkin methods in space and by implicit differences in time. Systems of non‐linear algebraic equations are solved by Newton–Raphson iteration employing ILU‐preconditioned conjugate‐gradient‐like methods to the non‐symmetric matrix system in each iteration. The resulting solution methods are robust, enable complex grids with irregular nodal orderings and allow capillary effects.

Several numerical formulations are tested and compared for one‐, two‐ and three‐dimensional flow cases, with emphasis on problems involving saturation shocks, heterogeneous media and curved boundaries. For reservoirs consisting of multiple rock types with differing capillary pressure properties, it is shown that traditional Bubnov‐Galerkin methods give poor results and the new Petrov–Galerkin formulations are required. Investigations regarding the behaviour of several preconditioned conjugate‐gradient‐like methods in these type of problems are also reported.
Dynamic simulation of the hydrodynamic interaction among immersed particles in Stokes flow
Authors: Ingber Marc S.
Published: August 2005

A numerical method for the dynamic simulation of the hydrodynamic interaction among particles in Stokes flow is developed. The method couples the quasi‐static Stokes equations for the fluid with the equilibrium equations for the particles. The boundary element method is used to represent the velocity at a general field point in terms of surface velocities and stresses. However, neither the stresses nor the velocities are assumed to be known on the surface of the particles. Kinematic equations relating the linear and angular velocities at the centroids of the particles to the surface velocities are combined with the discretized boundary element equations and the equilibrium equations to generate a system of linear equations. The associated coefficient matrix is correspondent to the grand resistance matrix which relates the velocities of the particles to a given geometry.
On the numerical solution of the turbulence energy equations for wave and tidal flows
Authors: Davies A. M. , Jones J. E.
Published: August 2005

This paper deals with the numerical solution, using finite difference methods, of the hydrodynamic and turbulence energy equations which describe wind wave and tidally induced flow.

Calculations are performed using staggered and non‐staggered finite difference grids in the vertical, with various time discretizations of the production and dissipation terms in the turbulence energy equations. It is shown that the time discretization of these terms can significantly influence the stability of the solution. The effect of time filtering on the numerical stability of the solution is also considered. The form of the mixing length is shown to significantly influence the bed stress in wind wave problems.

A no‐slip condition is applied at the sea bed, and the associated high‐shear bottom boundary layer is resolved by transforming the equations onto a logarithmic or log‐linear co‐ordinate system before applying the finite difference scheme.

A computationally economic method is developed which remains stable even when a very fine vertical grid (over 200 points) is used with a time step of up to 30 min.
Using a segregated finite element scheme to solve the incompressible Navier‐Stokes equations
Authors: Shaw C. T.
Published: August 2005

In this paper, a segregated finite element scheme for the solution of the incompressible Navier‐Stokes equations is proposed which is simpler in form than previously reported formulations. A pressure correction equation is derived from the momentum and continuity equations, and equal‐order interpolation is used for both the velocity components and pressure. Algorithms such as this have been known to lead to checkerboard pressure oscillations; however, the pressure correction equation of this scheme should not produce these oscillations. The method is applied to several laminar flow situations, and details of the methods used to achieve converged solutions are given.
On the use of the reach‐back characteristics method for calculation of dispersion
Authors: Yang Jinn‐Chuang , Hsu Euan‐Lung
Published: August 2005

The Holly‐Preissmann two‐point finite difference scheme (HP method) has been popularly used for solving the advection equation. The key idea of this scheme is to solve the dependent variable (i.e. the concentration for the pollutant transport problem) by the method of characteristics with the use of cubic interpolation on the spatial axis. The interpolating polynomials of higher order are constructed by use of the dependent variable and its derivatives at two adjacent grid points. In this paper a new interpolating technique is introduced for incorporation with the Holly‐Preissmann two‐point method. The new method is denoted herein as the Holly‐Preissmann reach‐back method (HPRB) and allows the characteristics to project back several time steps beyond the present time level. Through stability analyses it has been observed that the increase of the reach‐back time step numbers for the characteristics indeed reduces the numerical damping and dispersive phenomena. A schematic model has been constructed to demonstrate the merits of this new technique for the calculation of the pure advection and dispersion equations. Numerical experiments and comparisons with analytical solutions which support and demonstrate this new technique are presented.
Vorticity‐streamfunction formulation of unsteady incompressible flow past a cylinder: Sensitivity of the computed flow field to the location of the outflow boundary
Authors: Behr M. , Liou J. , Shih R. , Tezduyar T. E.
Published: August 2005

The influence of the location of the outflow computational boundary on the unsteady incompressible flow past a circular cylinder at Reynolds number 100 is examined. The vorticity‐streamfunction formulation of the Navier‐Stokes equations is used in all computations. Two types of outflow boundary conditions are subjected to a series of tests in which the domain length is gradually reduced. The traction‐free condition performs well in most cases and allows the outflow boundary to be located as close as 6.5 cylinder diameters from the body. The other boundary condition type is not as forgiving, but has the advantage of being simpler to implement and can still provide reasonably accurate solutions. It is also observed that both condition types can influence the flow field strongly and globally when the boundary is brought closer than 2.5 diameters from the body. In such cases the temporal periodicity of the solution is lost.
A hybrid k‐ε turbulence model of recirculating flow
Authors: Chang K. C. , Chen C. S. , Uang C. I.
Published: August 2005

This investigation deals with the modification of streamline curvature effects in the k‐ε turbulence model for the case of recirculating flows. Based upon an idea that the modification of curvature effects in C2 should not be made in regions where the streamline curvature is small, a hybrid k‐ε model extended from the modification originally proposed by Srinivasan and Mongia is developed. A satisfactory agreement of model predictions with experimental data reveals that the hybrid k‐ε model can perform better simulation of recirculating turbulent flows.
A globally well‐posed finite element algorithm for aerodynamics applications
Authors: Iannelli G. S. , Baker A. J.
Published: August 2005

A finite element CFD algorithm is developed for Euler and Navier‐Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second‐order‐accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion‐error control mechanisms; (2) a stiffly stable second‐order‐accurate implicit Rosenbrock‐Runge‐Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large‐matrix statement. Thorough analyses are presented regarding well‐posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi‐one‐ and two‐dimensional Euler and Navier‐Stokes benchmark test problems. Of critical importance, essentially non‐oscillatory solutions are uniformly attained for a range of supercritical flow situations with shocks.
Shedding patterns of the near‐wake vortices behind a circular cylinder
Authors: Sa Jong‐Youb , Chang Keun‐Shik
Published: August 2005

The unsteady incompressible Navier‐Stokes equations have been accurately solved for the laminar flow past a circular cylinder in the Reynolds number range 50–200. A direct elliptic solver called the SEVP is used to rapidly advance the streamfunction in time, facilitating the overall convergence to the fully periodic or quasi‐steady state. A new integral‐series method is developed for the far‐field streamfunction condition on a finite two‐dimensional computational domain. The use of fourth‐order Hermitian relations for the convection terms in the conservation‐form vorticity transport equation has also contributed to the good comparison of the present results with the earlier experimental data. The vortex‐shedding patterns visualized by the experimentalist are numerically reproduced here in the given Reynolds number range. Discussions that may be helpful in interpreting the behaviour of the shedding frequency are presented in the main text.
Stabilization of a time integrator for the 3D shallow water equations by smoothing techniques
Authors: de Goede E. D.
Published: August 2005

A smoothing technique is applied to improve the stability of a semi‐implicit time integrator for the three‐dimensional shallow water equations. In this method the terms involving the vertical direction are treated implicitly. The stability condition on the time step depends only on the horizontal mesh sizes; therefore in the horizontal‐direction a smoothing operator is added. Owing to the smoothing, the maximally stable time step increases considerably while the accuracy is hardly affected. Moreover, it turns out that the smoothing operator is efficient on vector and parallel computers.
Calculation of laminar recirculating flows using a local non‐staggered grid refinement system
Authors: Coelho P. , Pereira J. C. F. , Carvalho M. G.
Published: August 2005

A grid‐embedding technique for the solution of two‐dimensional incompressible flows governed by the Navier‐Stokes equations is presented. A finite volume method with collocated primitive variables is employed to ensure conservation at the interfaces of embedding grids as well as global conservation. The discretized equations are solved simultaneously for the whole domain, providing a strong coupling between regions of different refinement. The formulation presented herein is applicable to uniform or non‐uniform Cartesian meshes. The method was applied to the solution of two scalar transport equations, to cavity flows driven by body and shear forces and to a sudden plane contraction flow. The numerical predictions are compared with the exact solutions when available and with experimental data. The results show that neither the convergence rate nor the stability of the method is affected by the presence of embedded grids. Embedded grids provide a better distribution of grid nodes over the computational domain and consequently the solution accuracy was improved. The grid‐embedding technique proved also that significant savings in computing time could be achieved.
Euler analysis of transonic stator‐rotor interaction using a finite volume method
Authors: Kang In‐Mo , Chang Keun‐Shik
Published: August 2005

A generalized finite volume method that can solve the Euler equations for the stator and rotor parts of stage flow in similar formulations is presented. The method consists of a new moving grid finite volume formulation applied to the rotor region and the existing fixed grid finite volume method used in the stator region, with the data transfer made by an interpolation procedure at the sliding surface in between. The accuracy of the method has been demonstrated on a simple cascade flow before the time‐dependent compressor stage flow is fully investigated. The transonic stator‐rotor flow interaction is elucidated within the inviscid and rotational flow limit.
A Helmholtz pressure equation method for the calculation of unsteady incompressibl eviscous flows
Authors: Williams Morgan
Published: August 2005

A time‐implicit numerical method for solving unsteady incompressible viscous flow problems is introduced. The method is based on introducing intermediate compressibility into a projection scheme to obtain a Helmholtz equation for a pressure‐type variable. The intermediate compressibility increases the diagonal dominance of the discretized pressure equation so that the Helmholtz pressure equation is relatively easy to solve numerically. The Helmholtz pressure equation provides an iterative method for satisfying the continuity equation for time‐implicit Navier–Stokes algorithms. An iterative scheme is used to simultaneously satisfy, within a given tolerance, the velocity divergence‐free condition and momentum equations at each time step. Collocated primitive variables on a non‐staggered finite difference mesh are used. The method is applied to an unsteady Taylor problem and unsteady laminar flow past a circular cylinder.
Iterative methods for stabilized mixed velocity–pressure finite elements
Authors: Atanga John , Silvester David
Published: August 2005

This paper is concerned with iterative techniques for the solution of the linear system of equations arising from a finite element approximation of an elliptic partial differential equation by a mixed method. Three types of iterative algorithms are investigated. Applications to the Stokes equations are discussed and the results of numerical experiments given.
Parallel algorithms for panel methods
Authors: David Tim , Blyth Graham
Published: August 2005

A parallel algorithm for the solution of potential flow problems using the panel method of Hess and Smith and conjugate and bi‐conjugate gradient techniques is presented. Analysis of the parallelism for the matrix. solvers shows the algorithms to have scalable properties as the problem size grows indefinitely large. Speed‐up and efficiency values are presented along with experimental and theoretical values for the optimum number of processors for maximum speed‐up. It is envisaged that the parallel techniques presented here have applications using other boundary integral methods for solving engineering problems of a more complex nature.
Towards the numerical simulation of the horizontal slug front
Authors: Yacoub N. , Maron D. Moalem , Naot D.
Published: August 2005

Steps towards the numerical simulation of the flow behind the slug front in horizontal slug flow performed with a streamfunction‐vorticity representation of the mean flow and an energy dissipation model for the turbulence are discussed. The flow field consists of two vortices, one saddle point and four stagnation regions. Attention is focused on the following boundary conditions: moving wall jet, moving wall, free jet velocity discontinuity and vertical liquid‐gas open surface. A dissipation flux boundary condition is suggested to simulate the interaction of the turbulent eddies with the open surface. A method to assess the necessity to use a transport model equation for the dissipation rather than a geometric specification of a length is suggested. Three different ways to characterize the mixing zone length are proposed.
Hot flow analysis of swirling sudden‐expansion dump combustor
Authors: Chuang Shu‐Hao , Lin Hsun‐Cheng , Tai Fang‐Mei , Sung Hong‐Ming
Published: August 2005

Hot flow of a sudden‐expansion dump combustor with swirling is analysed by employing an infinite chemical reaction rate. Turbulence properties are closed using one type of algebraic Reynolds stress model and two types of κ–ϵ model. One of the κ–ϵ models includes a swirling effect modification to the ε‐equation. Computations have been performed by the SIMPLE‐C algorithm with a power‐law scheme. The calculated results of the momentum fields and turbulence quantities for swirling flow are compared with the available experimental data. It is shown that the standard κ–ϵ model gives poor prediction of the mean velocity, particularly the tangential velocity. For the hot flow analysis of a sudden‐expansion dump combustor with swirling flow it is suggested that it is necessary to use the modified κ–ϵ model or algebraic Reynolds stress model.
Computation of axisymmetric confined jets in a diffuser
Authors: Zhu J. , Rodi W.
Published: August 2005

The paper reports on a numerical study of turbulent confined jets in a conical duct with a 5° divergence. The flow has a large ratio of jet to ambient velocities at the entrance so that it gives rise to strong recirculation. The calculations are carried out with a general finite volume method designed for calculating incompressible elliptic flows with complex boundaries. Turbulence is simulated by the standard κ–ϵ model. The sensitivity of the solution to numerical discretization errors is examined using three convection schemes, i.e. hybrid central/upwind differencing, QUICK and SOUCUP, on two grids consisting of 68 × 50 and 102 × 82 points respectively. An examination is also made of the influence of inlet boundary conditions on the predicted flow field. The computed results are compared with experimental data for mean axial velocity, turbulent shear stress and turbulent kinetic energy profiles. It is shown that the calculations reproduce the essential features of the flow observed in the experiments.
Simulation of supersonic and hypersonic flows
Authors: Milthorpe J. F.
Published: August 2005

A simple convection algorithm for simulation of time‐dependent supersonic and hypersonic flows of a perfect but viscous gas is described. The algorithm is based on conservation and convection of mass, momentum and energy in a grid of rectangular cells. Examples are given for starting flow in a shock tube and oblique shocks generated by a wedge at Mach numbers up to 30·4. Good comparisons are achieved with well‐known perfect gas flows.
Transient finite element method for calculating steady state three‐dimensional free surfaces
Authors: Wambersie O. , Crochet M. J.
Published: August 2005

In order to reduce the cost of large three‐dimensional calculations of steady state free surfaces, we have combined a time‐dependent approach, a decoupling algorithm and a conjugate gradient solver along the lines introduced earlier by Gresho and Chan. The free surface is calculated separately by applying the kinematic condition to a number of faces defined on the undeformed surface. For the pseudo‐time‐marching technique we show that it is economical to adopt different time steps for the free surface calculation and the other fields. The accuracy of the method is tested on the well‐known circular die problem; the method is then used to reveal the effects of inertia and shear thinning on square and rectangular dies.
A least‐squares method for solving the mixed form of the groundwater flow equations
Authors: Bentley L. R. , Pinder G. F.
Published: August 2005

The mixed form of the areal groundwater flow equations is solved with a least‐squares finite element procedure (LESFEM). Hydraulic head and x‐ and y‐directed fluxes are state variables. Physical parameters and state variables are approximated using a bilinear basis. Grid refinements and irregular domain boundaries are implemented on rectangular meshes.

Residuals are constructed at collocation points for conservation of mass and Darcy's law. Boundary condition residuals are constructed at discrete points along the boundary. The residuals are weighted, squared and summed. A set of algebraic equations is formed by taking the derivatives of the weighted sum of the squares of the residuals with respect to each unknown parameter in the approximation for the state variable and setting them to zero.

Proper choice of a potential scaling parameter and residual weights is essential for the effective application of the algorithm. Test problem results demonstrate that the method is effective for both transient and steady state cases.

The LESFEM algorithm generates a C°‐continuous velocity field. The continuous velocity field and the rectangular mesh simplify the implementation of algorithms that require tracking. In addition, rectangular meshes simplify mesh and boundary generation.
A least‐squares finite element method for incompressible Navier‐Stokes problems
Authors: Jiang Bo‐Nan
Published: August 2005

A least‐squares finite element method based on the velocity–pressure–vorticity formulation was proposed for solving steady incompressible Navier‐Stokes problems. This method leads to a minimization problem rather than to the saddle point problem of the classic mixed method and can thus accommodate equal‐order interpolations. The method has no parameter to tune. The associated algebraic system is symmetric and positive definite. In order to show the validity of the method for high‐Reynolds‐number problems, this paper provides numerical results for cavity flow at Reynolds number up to 10 000 and backward‐facing step flow at Reynolds number up to 900.
The double von Mises transformation in the study of two‐phase fluid flow over curved boundaries: Theory and analysis
Authors: Barron R. M. , Hamdan M. H.
Published: August 2005

A numerical method to handle the flow of a two‐phase fluid over curved boundaries is proposed. The method is based on the double von Mises transformation which is derived in this work and is expected to be applicable to a variety of flow situations while utilizing the finite difference technique. In order to illustrate the numerical implementation of the method, dusty fluid flow through a porous channel possessing curved boundaries and the flow through a semi‐infinite porous layer overlying a curved lower boundary are considered. The flow is assumed to be governed by model equations based on Brinkman's equation and reflecting boundary conditions are employed in the study based on a uniform dust particle distribution. Results indicate that an increase in the permeability results in decreasing the tangential velocity component in regions close to the curved boundary, and increasing the dust parameters decreases this component. The effects of the grid size and the extent of the computational domain are discussed. The results also shed some light on the applicability of the dusty fluid flow model and suggest that the model is best employed when the permeability is high, a conclusion that is consistent with the validity of Brinkman's equation.
A prediction of the pressure field in a plane turbulent jet using an algebraic stress model
Authors: Bergstrom Donald J.
Published: August 2005

A numerical prediction is obtained for the mean pressure field in the similarity region of a plane turbulent jet. An algebraic stress model, which introduces non‐isotropic relations for the Reynolds stress components, is used to close the mean momentum equation. The full two‐dimensional form of the transport equations is retained and the resultant equation set solved elliptically. The numerical prediction simulates many of the characteristics of the pressure field measured by experimental studies. However, the overall level of the predicted field is lower than the experimental values. The level obtained for the mean pressure field depends strongly on the prediction for the transverse normal Reynolds stress component 〈u2u2〉. The pressure field is shown to represent a small negative contribution to the net strearnwise momentum balance.
Numerical simulation of fully non‐linear steady free surface flow
Authors: Lalli F. , Campana E. , Bulgarelli U.
Published: August 2005

The fully non‐linear free surface potential flow past a 2D non‐lifting body is computed. The numerical method is based on the simple layer integral formulation; the non‐linear solution is obtained by means of an iterative procedure. Under some hypotheses, viscosity effects at the free surface are considered. All the numerical results obtained have been tested against analytical solutions and experimental results.
Two‐dimensional wave run‐up analysis by selective lumping finite element method
Authors: Okamoto Takashi , Kawahara Mutsuto , Ioki Nobuhiro , Nagaoka Hiroaki
Published: August 2005

A new finite element technique for the analysis of wave run‐up is presented in this paper. In this finite element approach, the movement of the shoreline is expressed by that of the nodal points at the wave front, and an auto mesh generation technique is effectively used. The present method is tested by the comparison with the experimental result of a channel with uniform slope, and two numerical examples are reported to show the efficiency of this method. As a final example, the tsunami run‐up caused by the 1983 Nihonkai‐Chubu earthquake is analysed and compared with actual records of the flooded area.
Conservative monotone streamline upwind formulation using simplex elements
Authors: Shemirani F. , Jambunathan K.
Published: August 2005

A streamline upwind formulation is presented for the treatment of the advection terms in the general transport equation. The formulation is monotone and conservative and is based on the discontinuous nature of the advection mechanism. The results of there benchmark test cases for the full range of flow Peclet numbers are presented. The new formulation is shown to accurately model the advection phenomenon with significantly smaller numerical diffusion than the existing methods. The results are also free of all spatial oscillations. Considerable savings in computer storage and execution time have been achieved by employing the three‐noded triangular element for which exact integrations exist. The formulation is straightforward and can be readily incorporated into any finite element code using the conventional Galerkin approach.
Die design: An implicit formulation for the inverse problem
Authors: Legat Vincent , Marchal Jean‐Marie
Published: August 2005

Let us call a direct extrusion problem (DEP) the problem of finding the shape of the extrudate coming out of a die of prescribed shape. An implicit finite element formulation of the DEP which is geometrically general and for which a Newton‐Raphson technique can be implemented has recently been proposed by Legat and Marchal. However, the problem posed to the die designer is frequently the inverse extrusion problem (IEP), i.e. finding the die shape which produces an extrudate of prescribed shape. This paper presents an extension of our original method for solving the IEP which avoids the ‘trial‐and‐error’ iteration on the die geometry itself.

The advantage of the formulation lies in its capability to handle complex geometrics and in its low cost, because the CPU time and memory required to solve the IEP are almost identical to those of the DEP. We present benchmark results for squares and rectangles and new results obtained for geometries involving multiple corners. For an octagonal shape we also consider the case of a power‐law fluid.

For all results presented in this paper, surface tension has not been included.
A probabilistic method for field solutions in two‐phase flows
Authors: Zhang J. , Roco M. C.
Published: August 2005

Solid‐particle motion and related transport phenomena in two‐phase flow are fluctuating processes in space and time. A deterministic method can describe only partially the intrinsic physics of these processes. In this paper, the fluctuations of the flow parameters are modelled by considering the spatial correlations, and a probabilistic computational method for two‐phase flow is presented. The probabilistic governing equations have been discretized in space using a finite volume method, and then solved by applying the Neumann expansion method. This last method is time efficient, and its convergence can be guaranteed even for large fluctuations. A liquid‐solid particle mixture flow in a circular pipe is taken as an example. Computational results illustrate the merit of the probabilistic approach for the prediction of two‐phase flow phenomena.
An assessment of the finite termination property of the defect correction method
Authors: Shaw G. J. , Crumpton P. I.
Published: August 2005

This paper investigates the use of defect correction procedures for the solution of finite volume approximations to systems of conservation laws. Particular emphasis is laid on the order of accuracy obtained after a fixed finite number of iterations. It is shown that a high order of accuracy may be achieved after only one defect correction iteration, involving two inversions of a stable lower‐order‐accurate operator. However, this result is found to be critically dependent on the consistency of the lower‐order operator, a property which does not always hold for conservative finite volume discretizations. Through numerical experiments, the lack of consistency of these schemes is found to inhibit severely the finite termination property of the defect correction process. Results are presented for linear advection, Poisson's equation, and the Euler equations.
Computer simulation of moist atmospheric convection with finite elements
Authors: Mann Kenneth J.
Published: August 2005

A computer simulation is made of cellular convection in a moist atmosphere in an endeavour to obtain a computer model which more closely approximates the observed modes of convection. A finite element Galerkin technique, with Taylor approximation and Crank‐Nicolson, is employed and comparisons are made with the author's earlier finite element models of convection in an absolutely unstable atmosphere and with finite difference models. It is found that the inclusion of the moisture effects alters the structure of a cell to that of a narrow ascending region and a wider descending region with the former of larger velocities than the latter, and also alters the preferred mode of convection by increasing the aspect ratio. This more closely resembles that which is observed in the atmosphere.
A remark on the projection‐3 method
Authors: Shen Jie
Published: August 2005

We show that the continuous (in time) form of the projection‐3 scheme proposed in Reference 2 is not a proper approximation of the unsteady Navier‐Stokes equations. Hence, the projection‐3 scheme and its variants are not appropriate for the numerical computation of the Navier‐Stokes equations.
Solution of the discretized incompressible Navier‐Stokes equations with the GMRES method
Authors: Vuik C.
Published: August 2005

We describe some experiences using interative solution methods of GMRES type to solve the discretized Navier‐Stokes equations. The discretization combined with a pressure correction scheme leads to two different systems of equations: the momentum equations and the pressure equation. It appears that a fast solution method for the pressure equation is obtained by applying the recently proposed GMRESR method, or GMRES combined with a MILU preconditioner. The diagonally scaled momentum equations are solved by GMRES(m), a restarted version of GMRES.