bluuebunny/crossref_metadata_2025 huggingface dataset:
Examination of pressure oscillations arising in the computation of cascade flow using a boundary‐fitted co‐ordinate system
Authors: Lapworth B. L.
Published: August 2005

The incompressible flow through a two‐dimensional cascade is computed using the SIMPLE algorithm in a boundary‐fitted co‐ordinate system. With the standard staggered grid arrangement the numerical solution was found to allow localized pressure oscillations to persist adjacent to the periodic boundaries. These oscillations were found to be a consequence of the extended momentum control volumes which are required in this region of the cascade. Such control volumes may be removed by the use of appropriately non‐staggered velocity storage locations, which are also desirable in the boundary‐fitted system since the Cartesian velocity components are no longer related to the grid line orientations. However, this storage permits the propagation of global pressure oscillations, which were previously suppressed by the staggered grid arrangement. This paper attempts to define a solution procedure which uses non‐staggered velocity locations and is able to eliminate the consequent global pressure oscillations. To achieve this aim, two forms of pressure correction scheme were considered. The first implemented the scheme proposed by Vanka et al. but was found to be inadequate in the open part of the cascade, whereas the second employed a modification of the scheme proposed by Rhie and Chow and was found to be successful in all regions of the flow. The results computed using this scheme were compared with the available experiment results.
A multigrid method for recirculating flows
Authors: Sivaloganathan S. , Shaw G. J.
Published: August 2005

The use of multigrid methods in complex fluid flow problems is recent and still under development. In this paper we present a multigrid method for the incompressible Navier‐Stokes equations. The distinctive features of the method are the use of a pressure‐correction method as a smoother and a novel continuity‐preserving manner of grid coarsening. The shear‐driven cavity problem is used as a test case to demonstrate the efficiency of the method.
Computation of complex fluid flows using an adaptive grid method
Authors: Shyy Wei
Published: August 2005

Recently the concept of adaptive grid computation has received much attention in the computational fluid dynamics research community. This paper continues the previous efforts of multiple one‐dimensional procedures in developing and asessing the ideas of adaptive grid computation. The focus points here are the issue of numerical stability induced by the grid distribution and the accuracy comparison with previously reported work. Two two‐dimensional problems with complicated characteristics—namely, flow in a channel with a sudden expansion and natural convection in an enclosed square cavity—are used to demonstrate some salient features of the adaptive grid method. For the channel flow, by appropriate distribution of the grid points the numerical algorithm can more effectively dampen out the instabilities, especially those related to artificial boundary treatments, and hence can converge to a steady‐state solution more rapidly. For a more accurate finite difference operator, which contains less undesirable numerical diffusion, the present adaptive grid method can yield a steady‐state and convergent solution, while uniform grids produce non‐convergent and numerically oscillating solutions. Furthermore, the grid distribution resulting from the adaptive procedure is very responsive to the different characteristics of laminar and turbulent flows. For the problem of natural convection, a combination of a multiple one‐dimensional adaptive procedure and a variational formulation is found very useful. Comparisons of the solutions on uniform and adaptive grids with the reported benchmark calculations demonstrate the important role that the adaptive grid computation can play in resolving complicated flow characteristics.
Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm
Authors: Gaskell P. H. , Lau A. K. C.
Published: August 2005

The paper describes a new approach to approximating the convection term found in typical steady‐state transport equations. A polynomial‐based discretization scheme is constructed around a technique called ‘curvature compensation’; the resultant curvature‐compensated convective transport approximation is essentially third‐order accurate in regions of the solution domain where the concept of order is meaningful. In addition, in linear scalar transport problems it preserves the boundedness of solutions. Sharp changes in gradient in the dependent variable are handled particularly well. But above all, the scheme, when used in conjunction with an ADI pentadiagonal solver, is easy to implement with relatively low computational cost, representing an effective algorithm for the simulation of multi‐dimensional fluid flows. Two linear test problems, for the case of transport by pure convection, are employed in order to assess the merit of the method.
On variable grids for modelling flow in reciprocating engines
Authors: Shah P. , Markatos N. C. , Glynn D. R.
Published: August 2005

The moving boundary (i.e. the piston) within a reciprocating engine poses the problem that as it moves towards the cylinder head it compresses the computational grid lines. Control cells that started with reasonable aspect ratios become so compressed that aspect ratios of 1000 are not unusual in some cases. This, of course, adversely affects numerical accuracy and convergence. It is the purpose of this paper to present a conservative scheme that allows for the removal and addition of grid cells, during simulation, so as to restore reasonable aspect ratios. Results of the computations are presented and compared with experimental data. It is concluded that with the proposed scheme convergence is obtained within fewer iterations, CPU time is reduced and the results are generally in better agreement with experimental data.
A simple numerical technique for transient creep flows with free surfaces
Authors: Golafshani Mehdi
Published: August 2005

A simple, but powerful iterative technique is presented for the numerical solution of the time‐dependent flow of an incompressible viscous fluid with or without a free surface. The usual numerical stability restrictions related to the viscous acceleration terms are avoided using standard implicit differencing techniques. The properties and accuracy of the method are illustrated by several calculational examples.
Unsteady viscous flow over a grooved wall: A comparison of two numerical methods
Authors: Hung S. C. , Kinney R. B.
Published: August 2005

A numerical study is made of the unsteady two‐dimensional laminar flow of an incompressible fluid over a periodically grooved wall. Two independent finite difference techniques are employed. One is based on the vorticity‐stream function and the other on the vorticity‐velocity (i.e. induction law) formulation. The fluid motion is initiated impulsively from rest and is assumed to be spatially periodic in the streamwise direction. The numerical formulations are derived in detail. The generation of vorticity at the solid surface is modelled differently in the two approaches, and this is found to play an important role in determining the surface pressure distribution and the drag coefficient. The flow field is examined during the early transient phase of development, during which the greatest changes occur. Results are presented for a moderate Reynolds number (based on groove depth) equal to 100. It is found that the vorticity‐stream function approach does not produce a spatially periodic wall pressure distribution, and therefore global conservation of total vorticity is not achieved. This results in substantial errors in the predictions for the drag coefficient. These deficiencies are not found in the results obtained by the vorticity‐velocity formulation.
Accuracy of a deterministic particle method for Navier‐Stokes equations
Authors: Choquin J. P. , Lucquin‐Desreux B.
Published: August 2005

The accuracy of a deterministic particle method in approximating the solution of the Navier‐Stokes equations is investigated. The convective part is solved using a classical vortex method for inviscid fluids, and an iterative procedure is added to improve the interpolation of the vorticity function. In our examples the vorticity is radially symmetric. For a regular initial data, a discrete quadratic error on the velocity and the vorticity is considered. Otherwise, for a singular initial data, the exact and computed angular moments of the vorticity are compared.
The analysis of glass melting processes using three‐dimensional finite elements
Authors: Murnane R. A. , Johnson W. W. , Moreland N. J.
Published: August 2005

Traditionally glass process problems have been studied using laboratory and two‐dimensional computer simulation techniques to quantify the melting, cooling and distribution of the molten glass and its quality. Although these approaches are adequate for a large number of simple glass systems, there are processes with asymmetric geometries and operating conditions which cannot neglect the effect of the third dimension. During the past few years, with the advent of commercial parallel processors and corresponding software, extensive progress has been made with the implementation of full three‐dimensional glass flow simulations. Several development applications using FIDAP will be illustrated for electric melters, circular refiners and contoured forehearths. The discussion will cover the problem set‐ups, mesh generation, solution strategy, post‐processing and results. The advantages and developmental needs of FIDAP will be highlighted from the point of view of applied glass process engineering.
Finite element simulation of 3D turbulent free shear flows
Authors: Pelletier Dominique , Camareo Ricardo
Published: August 2005

This paper reviews past and current efforts in developing a simple but robust turbulence model for free shear flows. Much of this work has been published previously and this paper is a rearrangement aimed at the conference. The model is presented and is interfaced with FIDAP to solve three‐dimensional flows and a pusher—prop configuration. The eight‐node brick, the penalty formulation and the Broyden method are used to solve the Navier‐Stokes equations. The propeller is modelled as an actuator disc and the direct simulation of a given propeller is considered in detail. Good results are obtained for the square jet. For propeller cases detailed comparison with wind tunnel measurements shows excellent prediction of the velocity and pressure for flows of this complexity.
Comparison with experiment for TVD calculations of blast waves from a shock tube
Authors: Cooke Charlie H. , Fansler Kevin S.
Published: August 2005

Harten's second‐order‐accurate total‐variation‐diminishing (TVD) scheme is applied to calculation of flow from the open end of a shock tube. Comparison of numerical results with available experimental data for overpressure at selected points around the shock tube exit shows good agreement. Numerically indicated positions of the moving shock front and Mach stem also compare well with flow shadowgraph data. Where the problem geometry is sufficiently simple and rectangular gridding can be used, Harten's method affords a good choice for blast wave calculations.
Momentum transport in a turbulent mixing layer
Authors: Chein Reiyu , Chung J. N. , Troutt T. R.
Published: August 2005

The turbulent momentum transport phenomena in a two‐dimensional mixing layer are investigated numerically by a discrete vortex method. The numerical model and calculations are verified through a comparison with existing numerical simulations and experimental measurements. The main emphasis is placed on the exploration of the detailed time‐dependent instantaneous local momentum fluctuations and on the comparison of numerical results with available experimental measurements. The current simulations confirm qualitatively the various trends in the turbulent momentum flux and fluctuating components of the velocity in the mixing layer found with several experimental results. The study shows that similarity exists in turbulent momentum quantities along the axial direction of the mixing layer. The calculations also show a definite correlation between the passage of a large‐scale structure and a burst in the turbulent momentum flux. The probability density functions of the fluctuating quantities are shown to be mostly Gaussian‐like, with only a few exceptions.
Finite difference methods for solving the two‐dimensional advection–diffusion equation
Authors: Noye B. J. , Tan H. H.
Published: August 2005

Using weighted discretization with the modified equivalent partial differential equation approach, several accurate finite difference methods are developed to solve the two‐dimensional advection–diffusion equation following the success of its application to the one‐dimensional case. These new methods are compared with the conventional finite difference methods in terms of stability and accuracy. The new methods are more accurate and often more stable than the conventional schemes.
Numerical analysis of the developing fluid flow in a circular duct rotating steadily about a parallel axis
Authors: Gethin D. T. , Johnson A. R.
Published: August 2005

A numerical analysis of the flow pattern in the inlet region of a circular pipe rotating steadily about an axis parallel to its own is presented. Both finite cell and finite element methods are used to analyse the problem and they give qualitatively similar results which show that a swirling fluid motion is induced in the pipe inlet region. The analyses show that the direction of swirl is opposite to that of the pipe rotation when viewed along the flow axis and that its magnitude depends on the speed of pipe rotation and throughflow Reynolds number. Neither numerical analysis predicts the marked upturn in friction factor (or pressure drop) which has been observed experimentally. However, a dependence on the pipe inlet boundary conditions is demonstrated.
Effects of grid staggering on numerical schemes
Authors: Shih T. M. , Tan C. H. , Hwang B. C.
Published: August 2005

Nine finite difference schemes using primitive variables on various grid arrangements were systematically tested on a benchmark problem of two‐dimensional incompressible Navier–Stokes flows. The chosen problem is similar to the classical lid‐driven cavity flow, but has a known exact solution. Also, it offers the reader an opportunity to thoroughly evaluate accuracies of various conceptual grid arrangements.

Compared to the exact solution, the non‐staggered grid scheme with higher‐order accuracy was found to yield an accuracy significantly better than others. In terms of ‘overall performance’, the so‐called 4/1 staggered grid scheme proved to be the best. The simplicity of this scheme is the primary benefit. Furthermore, the scheme can be changed into a non‐staggered grid if the pressure is replaced by the pressure gradient as a field variable.

Finally, the conventional staggered grid scheme developed by Harlow and Welch also yields relatively high accuracy and demonstrates satisfactory overall performance.
Conjugate gradient methods and ILU preconditioning of non‐symmetric matrix systems with arbitrary sparsity patterns
Authors: Langtangen Hans Petter
Published: August 2005

Preconditioning techniques based on incomplete Gaussian elimination for large, sparse, non‐symmetric matrix systems are described. A certain level of fill‐in may be specified in the incomplete factorizations. All methods considered may be applied to matrices with arbitrary sparsity patterns, for instance those associated with the general preprocessor algorithms or adaptive mesh techniques. The preconditioners have been combined with five conjugate gradient‐like methods and tested on finite element discretized scalar convection‐diffusion equations in 2D and 3D. It is found from numerical experiments that an amount of fill‐in corresponding to about 50% of the number of original non‐zero matrix entries is the optimal choice for this class of preconditioners. The preconditioners show almost no sensitivity to grid distortion. In problems with significantly variable coefficients or anisotropy the preconditioners stabilize the basic iterative schemes in addition to reducing the computational work substantially, mostly by more than 90%. The modified preconditioning technique, where fill‐in is added on the main diagonal, performs in general better than the standard incomplete LU factorization, but is inferior to the latter in 3D problems and for matrix systems with complicated sparsity patterns.
A finite element analysis of the steady laminar entrance flow in a 90° curved tube
Authors: Van De Vosse F. N. , Van Steenhoven A. A. , Segal A. , Janssen J. D.
Published: August 2005

A standard Galerkin finite element penalty function method is used to approximate the solution of the three‐dimensional Navier–Stokes equations for steady incompressible Newtonian entrance flow in a 90° curved tube (curvature ratio δ = 1/6) for a triple of Dean numbers (κ = 41, 122 and 204). The computational results for the intermediate Dean number (κ = 122) are compared with the results of laser–Doppler velocity measurements in an equivalent experimental model. For both the axial and secondary velocity components, fair agreement between the computational and experimental results is found.
Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady euler equations
Authors: Bruneau Charles‐Henri , Laminie Jacques , Chattot Jean‐Jacques
Published: August 2005

A variational method for solving directly the full steady Euler equations is presented. This method is based on both Newton's linearization and a least squares formulation. The validity of the Euler model and boundary conditions to capture the vortex sheet is discussed. A finite element approximation of the groups of conservative variables is described and results are given for 3D subsonic flows as well as supersonic flows past a flat plate at high angle of attack.
Robust semidirect finite difference methods for solving the Navier–Stokes and energy equations
Authors: Macarthur J. Ward , Patankar Suhas V.
Published: August 2005

Semidirect solution techniques can be an effective alternative to the more conventional iterative approaches used in many finite difference methods. This paper summarizes several semidirect techniques which generally have not been applied to the Navier–Stokes and energy equations in finite difference form. The methods presented use both successive substitution and Jacobian‐based updates as well as two variations of Broyden's full matrix update. A hybrid method is also presented, as is a norm‐reducing search technique that can be used to enhance the convergence characteristics of any semidirect approach. These methods have been compared with the well known iterative methods SIMPLE and SIMPLER. The comparison was performed on the natural convection and driven cavity problems. The semidirect methods proved to be reliably convergent without the need for a priori specification of variable under‐relaxation factors, which was necessary with the iterative methods. Natural convection and driven cavity solutions have been readily obtained with the proposed methods for Rayleigh and Reynolds numbers up to 109 and 106 respectively. Of the semidirect techniques, the hybrid approach was the most robust. From an arbitrary zero initial guess this method was able to obtain a solution to the natural convection problem for Rayleigh numbers three orders of magnitude larger than was possible with the Newton‐Raphson update. The computational effort required by the semidirect methods is comparable to that required by the iterative methods; however, the memory requirements can be significantly greater.
Numerical study of the axially symmetric motion of an incompressible viscous fluid in an annulus between two concentric rotating spheres
Authors: Yang Jen‐Kang , Nigro Nicholas J. , Elkouh Abdel F. , Gagliardi John C.
Published: August 2005

The research reported herein involved the study of the transient motion of a system consisting of an incompressible Newtonian fluid in an annulus between two concentric, rotating, rigid spheres. The primary purpose of the research was to study the use of a numerical method for analysing the transient motion that results from the interaction between the fluid in the annulus and the spheres which are started suddenly by the action of prescribed torques. The problems considered in this research included cases where: (a) one or both spheres rotate with prescribed constant angular velocities and (b) one sphere rotates due to the action of an applied constant or impulsive t̀orque.

In this research the coupled solid and fluid equations were solved numerically by employing the finite difference technique. With the approach adopted in this research, only the derivatives with respect to spatial variables were approximated with the use of the finite difference formulae. The steady state problem was also solved as a separate problem (for verification purposes), and the results were compared with those obtained from the solution of the transient problem. Newton's algorithm was employed to solve the algebraic equations which resulted from the steady state problem, and the Adams fourth‐order predictor–corrector method was employed to solve the ordinary differential equations for the transient problem. Results were obtained for the streamfunction, circumferential function, angular velocity of the spheres and viscous torques acting on the spheres as a function of time for various values of the system dimensionless parameters.
Comparison of k–ϵ and algebraic Reynolds stress models for swirling diffuser flow
Authors: Armfield S. W. , Fletcher C. A. J.
Published: August 2005

A brief overview of classes of turbulent swirling flow in conical diffusers is given, together with a description of appropriate numerical schemes for each class. Numerical results obtained for the class of moderate swirl in a 20° diffuser and for the class of no swirl in an 8° diffuser are compared with experimental results. The results are obtained using a multi‐sweep scheme solving the full steady state time‐averaged Navier–Stokes equations. Turbulence quantities are approximated using two types of algebraic Reynolds stress model and two types of k–ϵ model. One of the algebraic Reynolds stress models includes extra production terms associated with the Christoffel symbols in cylindrical co‐ordinates, and one of the k–ϵ models includes a swirl‐related modification to the ϵ equation. It is demonstrated that the standard k–ϵmodel gives poor prediction of the mean flow, and it is necessary to at least use the modified form or one of the two algebraic Reynolds stress models.
On TVD difference schemes for the three‐dimensional Euler equations in general co‐ordinates
Authors: Takakura Yoko , Ishiguro Tomiko , Ogawa Satoru
Published: August 2005

An improved treatment for the Harten–Yee and Chakravarthy–Osher TVD numerical flux functions in general co‐ordinates is presented. The proposed formulation is demonstrated by a series of numerical experiments for three‐dimensional flows around the ONERA‐M6 wing. The numerical results indicate that it is important to use a suitable artificial compression parameter in order to obtain more accurate solutions around the leading edge of the wing. The two TVD numerical fluxes give excellent results: they capture the shock wave without numerical oscillations, they capture the rapid expansion around the leading edge sharply, they have self‐adjusting mechanisms regarding numerical viscosity and they also have robustness.
An investigation of pressure transients in pipelines with two‐phase bubbly flow
Authors: Ng K. C. , Yap C.
Published: August 2005

This paper presents a two‐dimensional model for the analysis of the pressure transient of a two‐phase homogeneous bubbly mixture flowing in a pipeline and the numerical integration using the centre implicit method (CIM). Experiments were conducted to confirm the proposed sonic speed equation of an air–water mixture for an air concentration of less than 1%. The 2D CIM model is compared with the method of characteristics (MoC) for a two‐phase bubbly flow in a pipeline. The comparisons show that the proposed 2D CIM model generally gives good agreement with the method of characteristics.
The simple layer potential method of fundamental solutions for certain biharmonic problems
Authors: Karageorghis Andreas , Fairweather Graeme
Published: August 2005

A novel formulation of the method of fundamental solutions for the numerical solution of plane biharmonic problems, based on the simple layer potential representation of Fichera, is presented. The applicability and accuracy of the method are demonstrated by examining its performance on a set of practical problems arising in Stokes fluid flow.
Vorticity—velocity formulation in the computation of flows in multiconnected domains
Authors: Stella F. , Guj G.
Published: August 2005

The thermofluid dynamic fields in two‐dimensional multiconnected domains are analysed by solving the Navier–Stokes equations with the Boussinesq approximation in the vorticity–velocity formulation. The need of an integral condition for the pressure to be single‐valued on each independent irreducible loop, in analogy with the ω–Ψ formulation, is demonstrated. The field equations are discretized by a finite difference technique and solved at the steady state via an alternating direction implicit method of a scalar type. Two test cases at low Reynolds and Rayleigh numbers are considered: the multiconnected driven cavity and an annulus with isothermal walls and stationary or rotating inner cylinder.
Numerical studies of slow viscous rotating flow past a sphere. III
Authors: Raghavarao C. V. , Pramadavalli K.
Published: August 2005

The flow of steady incompressible viscous fluid rotating about the z‐axis with angular velocity ω and moving with velocity u past a sphere of radius a which is kept fixed at the origin is investigated by means of a numerical method for small values of the Reynolds number Reω. The Navier–Stokes equations governing the axisymmetric flow can be written as three coupled non‐linear partial differential equations for the streamfunction, vorticity and rotational velocity component. Central differences are applied to the partial differential equations for solution by the Peaceman–Rachford ADI method, and the resulting algebraic equations are solved by the ‘method of sweeps’.

The results obtained by solving the non‐linear partial differential equations are compared with the results obtained by linearizing the equations for very small values of Reω. Streamlines are plotted for Ψ = 0·05, 0·2, 0·5 for both linear and non‐linear cases. The magnitude of the vorticity vector near the body, i.e. at z = 0·2, is plotted for Reω = 0·05, 0·24, 0·5. The correction to the Stokes drag as a result of rotation of the fluid is calculated.
A singular finite element for Stokes flow: The stick–slip problem
Authors: Georgiou Georgios C. , Olson Lorraine G. , Schultz William W. , Sagan Susan
Published: August 2005

Abrupt changes in boundary conditions in viscous flow problems give rise to stress singularities. Ordinary finite element methods account effectively for the global solution but perform poorly near the singularity. In this paper we develop singular finite elements, similar in principle to the crack tip elements used in fracture mechanics, to improve the solution accuracy in the vicinity of the singular point and to speed up the rate of convergence. These special elements surround the singular point, and the corresponding field shape functions embody the form of the singularity. Because the pressure is singular, there is no pressure node at the singular point. The method performs well when applied to the stick–slip problem and gives more accurate results than those from refined ordinary finite element meshes.
Convergence properties of high‐Reynolds‐number separated flow calculations
Authors: Rubin S. G. , Himansu A.
Published: August 2005

The convergence properties of an iterative solution technique for the Reduced Navier–Stokes equations are examined for two‐dimensional steady subsonic flow over bump and trough geometries. Techniques for decreasing the sensitivity to the initial pressure approximation, for fine meshes in particular, are investigated. They are shown to improve the robustness of the relaxation process and to decrease the computational work required to obtain a converged solution. A semi‐coarsening multigrid technique that has previously been found to be particularly advantageous for high‐Reynolds‐number (Re) flows with flow separation and with highly stretched surface‐normal grids is applied herein to further accelerate convergence. Solutions are obtained for the laminar flow over a trough that is more severe than has been considered to date. Sufficient axial grid refinement in this case leads to a shock‐like reattachment and, for sufficiently large Re, to a local ‘divergence’ of the numerical computations. This ‘laminar flow breakdown’ appears to be related to an instability associated with high‐frequency fine‐grid modes that are not resolvable with the present modelling. This behaviour may be indicative of dynamic stall or of incipient transition. The breakdown or instability is shown to be controllable by suitable introduction of transition turbulence models or by laminar flow control, i.e. small amounts of wall suction. This lends further support to the hypothesis that the instability is of a physical rather than numerical character and suggests that full three‐dimensional analysis is required to properly capture the flow behaviour. Another inference drawn from this investigation is that there is a need for careful grid refinement studies in high‐Re flow computations, since coarser grids may yield oscillation‐free solutions that cannot be obtained on finer grids.
Variations on Fourier wave theory
Authors: Sobey Rodney J.
Published: August 2005

A review of the analytical and numerical background of Fourier wave theory establishes the commonality of existing formulations and identifies a number of analytical and numerical assumptions that are unnecessary. Some formulations in particular lack flexibility in excluding the possibility of Stokes' second definition of phase speed. A generalized formulation is introduced for comparative purposes and it is shown that published solutions differ only in the approach to the limit wave. Detailed consideration of truncation order confirms that it is the crucial parameter, especially at extreme wave heights. All formulations considered are shown to provide acceptable solutions for small to moderately extreme waves.
A Newton's method scheme for solving free‐surface flow problems
Authors: Dandy David S. , Leal L. Gary
Published: August 2005

A Newton's method scheme is described for solving the system of non‐linear algebraic equations arising when finite difference approximations are applied to the Navier–Stokes equations and their associated boundary conditions. The problem studied here is the steady, buoyancy‐driven motion of a deformable bubble, assumed to consist of an inviscid, incompressible gas. The linear Newton system is solved using both direct and iterative equation solvers. The numerical results are in excellent agreement with previous work, and the method achieves quadratic convergence.
A finite element analysis of laminar unsteady flow of viscoelastic fluids through channels with non‐uniform cross‐sections
Authors: Ponnalagarsamy R. , Kawahara M.
Published: August 2005

The effects of non‐Newtonian behaviour of a fluid and unsteadiness on flow in a channel with non‐uniform cross‐section have been investigated. The rheological behaviour of the fluid is assumed to be described by the constitutive equation of a viscoelastic fluid obeying the Oldroyd‐B model. The finite element method is used to analyse the flow. The novel features of the present method are the adoption of the velocity correction technique for the momentum equations and of the two‐step explicit scheme for the extra stress equations. This approach makes the computational scheme simple in algorithmic structure, which therefore implies that the present technique is capable of handling large‐scale problems. The scheme is completed by the introduction of balancing tensor diffusivity (wherever necessary) in the momentum equations. It is important to mention that the proper boundary condition for pressure (at the outlet) has been developed to solve the pressure Poisson equation, and then the results for velocity, pressure and extra stress fields have been computed for different values of the Weissenberg number, viscosity due to elasticity, etc. Finally, it is pertinent to point out that the present numerical scheme, along with the proper boundary condition for pressure developed here, demonstrates its versatility and suitability for analysing the unsteady flow of viscoelastic fluid through a channel with non‐uniform cross‐section.
Least‐squares finite element methods for compressible Euler equations
Authors: Jiang Bo‐Nan , Carey G. F.
Published: August 2005

A method based on backward finite differencing in time and a least‐squares finite element scheme for first‐order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L2‐norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high‐order elements, computed solutions based on the L2‐method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1‐norm of the residual is proposed and leads to a successful scheme with high‐degree elements. Finally, a conservative least‐squares finite element method is also developed. Numerical results for two‐dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.
A least‐squares procedure for the solution of transport problems
Authors: Bensabat J. , Zeitoun D. G.
Published: August 2005

In this paper a least‐squares formulation associated with a conjugate gradient algorithm is proposed for the solution of transport problems. In this procedure the advection–diffusion equation is first discretized in time using an implicit scheme. At each time step the resulting partial differential equation is replaced by an optimal control problem. This minimization problem involves the minimization of a functional defined via a state equation. This functional is chosen in order to force the numerical solution of the advection–diffusion equation to be equal to the hyperbolic advective part of this equation. The effectiveness of the method is shown through a one‐dimensional example involving advective and diffusive transport. No oscillation and high accuracy have been obtained for the entire range of Peclet numbers with a Courant number well in excess of unity.
Application of a vortex lattice numerical model in the calculation of inviscid incompressible flow around delta wings
Authors: Bandyopadhyay G.
Published: August 2005

The flow over a flat plate delta wing at incidence and in sideslip is studied using vortex lattice models based on streamwise penelling. For the attached flow problem the effect of sideslip is simulated by modifying the standard vortex lattice model for zero sideslip by aligning the trailing vortices aft of the wing along the resultant flow direction. For the separated flow problem a non‐linear vortex lattice model is developed for both zero and non‐zero sideslip angles in which the shape and position of the leading edge separation vortices are calculated by an iterative procedure starting from an assumed initial shape. The theoretical values are compared with available theoretical and experimental results.
A scheme for automatic generation of boundary‐fitted depth‐ and depth‐gradient‐ dependent grids in arbitrary two‐dimensional regions
Authors: Nielsen Per , Skovgaard Ove
Published: August 2005

In this paper we present a scheme for the numerical generation of boundary‐fitted grids that adapt to both water depth and depth gradient. The scheme can be used in arbitrary two‐dimensional regions and is based on the application of the well‐known control function approach to generate adaptive grids. The method includes the evaluation of water depths at the grid points from a known distribution of depth points and their associated depths plus a procedure for the numerical evaluation of depth gradients. It is demonstrated that the smoothness of the grid can be enhanced by introducing a suitable filtering technique.
A moving finite element method for the population balance equation
Authors: Tsang T. H. , Rao A.
Published: August 2005

A moving finite element algorithm has been compared against the upwind‐differencing and Smolarkiewicz methods for the population balance equation of multicomponent particle growth processes. Analytical solutions and an error function have been used to test the numerical methods. The moving finite elements technique is much more accurate than other methods for a wide range of parameters. Since this method uses moving grids, it is able to model very narrow particle size distributions. It is also shown that the method can be extended to solve condensational growth problems which include particle curvature and non‐continuum mass transfer effects.
Boundary element calculation of shallow water waves
Authors: Kaneko N. , Utagawa N. , Kawahara M.
Published: August 2005

A boundary element method is proposed for studying periodic shallow water problems. The numerical model is based on the shallow water equation. The key feature of this method is that the boundary integral equations are derived using the weighted residual method and the fundamental solutions for shallow water wave problems are obtained by solving the simultaneous singular equations. The accuracy of this method is studied for the wave reflection problem in a rectangular tank. As a result of this test, it has been shown that the number of element divisions and the distribution of nodes are significant to the accuracy. For numerical examples of external problems, the wave diffraction problems due to single cylindrical, double cylindrical and plate obstructions are analysed and compared with the exact and other numerical solutions. Relatively accurate solutions are obtained.
Global pressure relaxation for laminar two‐dimensional internal flow
Authors: Rosenbaum D. , Rubin S. G.
Published: August 2005

This study extends the reduced Navier–Stokes (RNS) global pressure relaxation procedure developed by Rubin and co‐workers for external flow to internal flow applications. The streamwise pressure gradient is split into a backward‐differenced or initial value component, as in boundary layer marching, and a forward‐differenced or boundary value component that represents the elliptic downstream effects. The streamwise convection terms are upwind‐differenced and all other streamwise derivatives are backward‐differenced. We thus obtain a standard boundary layer marching technique imbedded in a conventional line relaxation technique. For compressible flow the pressure iteration determines the interior flow interation as well as the inlet mass flux that is consistent with the outflow pressure boundary condition. Results have been computed for incompressible flow in both rectangular and curved channels, and for subsonic compressible flow in the simulation of an aerofoil in a wind tunnel. Converged solutions were obtained over a range of Reynolds numbers generating small to moderately large separation bubbles.
Thermocapillary flow and natural convection in a melt column with an unknown melt/solid interface
Authors: Lan C. W. , Kou Sindo
Published: August 2005

A vertical melt column set up between an upper heating rod and a lower sample rod, i.e. the so‐called halfzone system, is a convenient experimental tool for studying convection in the melt in floating‐zone crystal growth. In order to help understand the convection observed in the melt column, a computer model has been developed to describe steady state, axisymmetrical thermocapillary flow and natural convection in the melt. The governing equations and boundary conditions are expressed in general non‐orthogonal curvilinear co‐ordinates in order to accurately treat the unknown melt/solid interface as well as all other physical boundaries in the system. The effects of key dimensionless variables on the following items are discussed: (1)convection and temperature distribution in the melt; (2) the shape of the melt/solid interface; (3) the height of the melt column. These dimensionless variables are the Grashof, Marangoni and Prandtl numbers.
A computational method for the hydrodynamics of fractured‐porous media
Authors: Grandi G. M. , Ferreri J. C.
Published: August 2005

A numerical method based on the boundary‐fitted finite difference method (BFDM) is presented in this paper. The boundaries are external (the boundary of the physical domain) and internal (which corresponds to the fracture network). The difference between this approach and the usual one lies in the inclusion of discrete fractures in the volume that represents the porous medium. The numerical model has been used in the prediction of the flow pattern in several internationally recognized verification cases and applied to the solution of hypothetical problems of interest to us in the field of nuclear waste repository modelling. The results obtained show that the numerical approach considered gives accurate and reliable predictions of the hydrodynamics of fractured‐porous media, thus justifying its use for the above‐mentioned studies.
Numerical solutions for impulsively started and decelerated viscous flow past a circular cylinder
Authors: Wang Xuegeng , Dalton Charles
Published: August 2005

A finite difference study of the unsteady two‐dimensional flow past a circular cylinder has been conducted using vorticity and streamfunction as the dependent variables. The two cases considered were impulsively started and decelerated flows. The impulsively started problem was considered to validate the method and has yielded results which agree quite closely with existing results from both calculations and experiments. The decelerated flow analysis produced results which can be explained in terms of induced velocity effects from existing wake vortices for both suddenly stopped and uniformly decelerated flows.
Higher‐order difference approximations of the Navier‐Stokes equations
Authors: Luchini Paolo
Published: August 2005

A discretization scheme is presented which, unlike the standard higher‐order finite difference and spline methods, does not give rise to unphysical solution modes and boundary conditions. Practical application of this scheme is achieved via the DCMG algorithm recently developed by the same author, which turns out to be able to find a converged solution of the ψ‐ζ Navier‐Stokes equations in about the same time for highorder as for low‐order discretization schemes. Examples are presented for the driven cavity problem to explore the accuracy of the new method. Finally, a local analysis is performed of the corner singularities which exist in driven cavity flow, and their effect on the overall accuracy of the solutions obtained by polynomial interpolation methods is investigated.
Three‐dimensional hydrodynamics on finite elements. Part II: Non‐linear time‐stepping model
Authors: Lynch Daniel R. , Werner Francisco E.
Published: August 2005

The development and application of a non‐linear 3D hydrodynamic model are described. The model is based on the wave equation rearrangement of the primitive 3D shallow water equations with a general eddy viscosity formulation for the vertical shear. A Galerkin procedure is used to discretize these on simple sixnode elements: linear triangles in the horizontal with linear variations in the vertical. Resolution of surface, bottom and interfacial boundary layers is facilitated and total flexibility is preserved for specifying spatial and temporal variations in the vertical viscosity and density fields. A semi‐implicit time‐stepping algorithm allows the solutions for elevation and velocity to be uncoupled during each time step. The elevation solution is essentially a 2D wave equation calculation with a stationary sparse matrix representing the gravity waves. With nodal quadrature the subsequent velocity calculation is achieved by factoring only a tridiagonal diffusion matrix representing the vertical viscous terms. As a result the overall calculation scales computationally as only a 2D problem but provides the full 3D solution. Application to field‐scale problems is illustrated for the English Channel/Southern Bight system and the Lake Maracaibo system.
Dynamical eigenfunction decomposition of turbulent channel flow
Authors: Ball K. S. , Sirovich L. , Keefe L. R.
Published: August 2005

The results of an analysis of low‐Reynolds‐number turbulent channel flow based on the Karhunen‐Loéve(K‐L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier‐Stokes equations at a Reynolds number Re,= 80 (based on the wall shear velocity and channel half‐width). The K‐L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K‐L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90% of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, posses viscous boundary layers at the walls and are much richer in harmonics than the original basis functions. Chaotic temporal behaviour is observed in all modes and increases for higher‐order eigenfunctions. The structure and dynamical behaviour of the eigenmodes are discussed as well as their use in the representation of the turbulent flow.
Examination of wall damping for the k‐ε turbulence model using direct simulations of turbulent channel flow
Authors: Miner E. Wade , Swean Thomas F. , Handler Robert A. , Leighton Richard I.
Published: August 2005

Handler, Hendricks and Leighton have recently reported results for the direct numerical simulation (DNS) of a turbulent channel flow at moderate Reynolds number. These data are used to evaluate the terms in the exact and modelled transport equations for the turbulence kinetic energy k and the isotropic dissipation function ε. Both modelled transport equations show significant imbalances in the high‐shear region near the channel walls. The model for the eddy viscosity is found to yield distributions for the production terms which do not agree well with the distributions calculated from the DNS data. The source of the imbalance is attributed to the wall‐damping function required in eddy viscosity models for turbulent flows near walls. Several models for the damping function are examined, and it is found that the models do not vary across the channel as does the damping when evaluated from the DNS data. The Lam‐Bremhorst model and the standard van Driest model are found to give reasonable agreement with the DNS data. Modification of the van Driest model to include an effective origin yields very good agreement between the modelled production and the production calculated from the DNS data, and the imbalance in the modelled transport equations is significantly reduced.