bluuebunny/crossref_metadata_2025_split huggingface dataset:
A practical implementation of spectral methods resistant to the generation of spurious eigenvalues
Authors: Lindsay K. A. , Ogden R. R. 
Published: November 2005

AbstractThis work describes a practical way of constructing a spectral representation of linear boundary value problems (BVPs) using a tau method. All BVPs are treated as first‐order systems, unlike most implementations which tend to view the problem in terms of a single high‐order differential equation. For most applications this formulation will adhere more closely to the natural derivation of the original equations from, for example, a series of conservation laws. The technique is exemplified for Chebyshev polynomials in a variety of real applications, although detailed results are provided for any polynomial basis.
Computation of flow of viscoelastic fluids by parameter differentiation
Authors: Ariel P. D. 
Published: November 2005

AbstractA technique combining the features of parameter differentiation and finite differences is presented to compute the flow of viscoelastic fluids. Two flow problems are considered: (i) three‐dimensional flow near a stagnation point and (ii) axisymmetric flow due to stretching of a sheet. Both flows are characterized by a boundary value problem in which the order of the differential equation exceeds the number of boundary conditions. The exact numerical solutions are obtained using the technique described in the paper. Also, the first‐order perturbation solutions (in terms of the viscoelastic fluid parameter) are derived. A comparison of the results shows that the perturbation method is inadequate in predicting some of the vital characteristic features of the flows, which can possibly be revealed only by the exact numerical solution.
Turbulent flow through bifurcated nozzles
Authors: Hershey Donald E. , Thomas Brian G. , Najjar Fady M. 
Published: November 2005

AbstractA finite‐element model has been used to study steady‐state turbulent flow through bifurcated submerged‐entry nozzles with oversized ports typical of those used in the continuous casting of steel. Both 2D and 3D simulations have been performed with the commercial code FIDAP, using the standard K–ϵ turbulence model. Predicted velocities from 3D simulations compare reasonably with experimental measurements using a hot‐wire anemometer conducted in a physical water model, where severe turbulent fluctuations are present. Results show that a 2D simulation can also capture the main flow characteristics of the jet existing the nozzle and requires two orders of magnitude less computer time than the 3D simulation. A model combining the nozzle and mould was set up to study the effect of the outlet boundary conditions of the nozzle on the jet characteristics. This modelling technique will assist in the design of submerged‐entry nozzles, especially as applied to enhance steel quality in the continuous casting process. Further, the model will provide appropriate inlet boundary conditions for a separate numerical model of the mould.
Spectral methods for the viscoelastic time‐dependent flow equations with applications to Taylor–Couette flow
Authors: Avgousti Marios , Liu Baichen , Beris Antony N. 
Published: November 2005

AbstractThe time evolution of finite amplitude axisymmetric perturbations (Taylor cells) to the purely azimuthal, viscoelastic, cylindrical Couette flow was numerically simulated. Two time integration numerical methods were developed, both based on a pseudospectral spatial approximation of the variables, efficiently implemented using fast Poisson solvers and optimal filtering routines. The first method, applicable for finite Re numbers, is based on a time‐splitting integration with the divergence‐free condition enforced through an influence matrix technique. The second one, is based on a semi‐implicit time integration of the constitutive equation with both the continuity and the momentum equations enforced as constraints. Stability results for an upper convected Maxwell fluid were obtained for the supercritical bifurcations, either steady or time‐periodic, developed after the onset of instabilities in the primary flow. At small elasticity values, ϵ ≡ De/Re, the time integration of finite amplitude disturbances confirms the stability of the single branch of steady Taylor cells. At intermediate ϵ values the rotating wave family of time‐periodic solutions developed at the onset of instability is stable, whereas the standing wave is found to be unstable. At high ϵ values, and in particular for the limit of creeping flow (ϵ = ∞), the present study shows that the rotating wave family is unstable and the standing (radial) wave is stable, in agreement with previous finite‐element investigations. It is thus shown that spectral techniques provide a robust and computationally efficient method for the simulation of complex, non‐linear, time‐dependent viscoelastic flows.
Segregated finite element algorithms for the numerical solution of large‐scale incompressible flow problems
Authors: Haroutunian Vahé , Engelman Michael S. , Hasbani Isaac 
Published: November 2005

AbstractThis paper presents results of an ongoing research program directed towards developing fast and efficient finite element solution algorithms for the simulation of large‐scale flow problems. Two main steps were taken towards achieving this goal. The first step was to employ segregated solution schemes as opposed to the fully coupled solution approach traditionally used in many finite element solution algorithms. The second step was to replace the direct Gaussian elimination linear equation solvers used in the first step with iterative solvers of the conjugate gradient and conjugate residual type. The three segregated solution algorithms developed in step one are first presented and their integrity and relative performance demonstrated by way of a few examples. Next, the four types of iterative solvers (i.e. two options for solving the symmetric pressure type equations and two options for solving the non‐symmetric advection–diffusion type equations resulting from the segregated algorithms) together with the two preconditioning strategies employed in our study are presented. Finally, using examples of practical relevance the paper documents the large gains which result in computational efficiency, over fully coupled solution algorithms, as each of the above two main steps are introduced. It is shown that these gains become increasingly more dramatic as the complexity and size of the problem is increased.
A new method for accelerating the rate of convergence of the simple‐like algorithm
Authors: Wen X. , Ingham D. B. 
Published: November 2005

AbstractA pressure correction formula is proposed for the SIMPLE‐like algorithm in order to improve the rate of the convergence when solving laminar Navier–Stokes equations when there is rapidly varying pressure. Based on global mass conservation, a line average pressure correction is derived by integration of the momentum equation for approximate one‐dimensional flow. The use of this formula with the SIMPLE‐like algorithm can rapidly build up the pressure distribution in the region where the pressure undergoes a very large change, which normally causes the rate of convergence of the SIMPLE or the SIMPLEC schemes to be slow. In order to illustrate the technique, the performances of SIMPLE and of SIMPLEC with the average pressur correction are investigated for axisymmetric flow past and through a sampler. A comparison of these two techniques shows that the average pressure correction proposed in this paper significantly accelerates the rate of convergence.
Methods for extending high‐resolution schemes to non‐linear systems of hyperbolic conservation laws
Authors: Rider William J. 
Published: November 2005

AbstractIn extending high‐resolution methods from the scalar case to systems of equations there are a number of options available. These options include working with either conservative or primitive variables, characteristic decomposition, two‐step methods, or component‐wise extension. In this paper, several of these options are presented and compared in terms of economy and solution accuracy. The characteristic extension with either conservative or primitive variables produces excellent results with all the problems solved. Using primitive variables, the two‐step formulation produces high‐quality results in a more economical manner. This method can also be extended to multiple dimensions without resorting to dimensional splitting. Proper selection of limiters is also important in non‐characteristic extension to systems.
A multigrid procedure for three‐dimensional flows on non‐orthogonal collocated grids
Authors: Smith K. M. , Cope W. K. , Vanka S. P. 
Published: November 2005

AbstractThe development of a multigrid solution algorithm for the computation of three‐dimensional laminar fully‐elliptic incompressible flows is presented. The procedure utilizes a non‐orthogonal collocated arrangement of the primitive variables in generalized curvilinear co‐ordinates. The momentum and continuity equations are solved in a decoupled manner and a pressure‐correction equation is used to update the pressures such that the fluxes at the cell faces satisfy local mass continuity. The convergence of the numerical solution is accelerated by the use of a Full Approximation Storage (FAS) multigrid technique. Numerical computations of the laminar flow in a 90° strongly curved pipe are performed for several finite‐volume grids and Reynolds numbers to demonstrate the efficiency of the present numerical scheme. The rates of convergence, computational times, and multigrid performance indicators are reported for each case. Despite the additional computational overhead required in the restriction and prolongation phases of the multigrid cycling, the superior convergence of the present algorithm is shown to result in significantly reduced overall CPU times.
Accuracy and convergence of element‐by‐element iterative solvers for incompressible fluid flows using penalty finite element model
Authors: Reddy M. P. , Reifschneider L. G. , Reddy J. N. , Akay H. U. 
Published: November 2005

AbstractThe ability of two types of Conjugate Gradient like iterative solvers (GMRES and ORTHOMIN) to resolve large‐scale phenomena as a function of mesh density and convergence tolerance limit is investigated. The flow of an incompressible fluid inside a sudden expansion channel is analysed using three meshes of 400, 1600 and 6400 bilinear elements. The iterative solvers utilize the element‐by‐element data structure of the finite element technique to store and maintain the data at the element level. Both the mesh density and the penalty parameter are found to influence the choice of the convergence tolerance limit needed to obtain accurate results. An empirical relationship between the element size, the penalty parameter, and the convergence tolerance is presented. This relationship can be used to predict the proper choice of the convergence tolerance for a given penalty parameter and element size.
Entrance flow in elliptical ducts
Authors: Velusamy K. , Garg Vijay K. 
Published: November 2005

AbstractA control volume‐based solution of the complete set of Navier–Stokes equations for the laminar, three dimensional developing flow in elliptical cross‐section ducts is described. Numerical results for velocity and pressure development, pressure defect and entrance lengths are presented for a wide range of aspect ratios from 0·1 to 0·999. The present results match very well with earlier numerical solutions for developing flow in a circular duct and the fully developed flow in elliptical ducts. A comparison with earlier numerical and experimental data for developing flow in elliptical ducts is also satisfactory for pressure development but not so good for the velocity profiles. The relative growth rate of boundary layer thickness along the major axis is slower than that along the minor axis which is contrary to the assumption used in earlier numerical analyses. The present results show no transverse recirculation contrary to the speculation based on earlier experimental data. The ratio of entry length in an elliptical duct to that in a circular duct with radius equal to the semi‐major axis of the elliptical duct is nearly equal to the aspect ratio of the duct. In conformity with the previous work, the present results find the total pressure defect to be independent of the aspect ratio, with a value of 1·234.
The calculation of separated flows using a distributed memory mimd computer
Authors: Hardy N. , Murray B. A. , Downie M. J. , Bettess P. 
Published: November 2005

AbstractA brief description of distributed memory MIMD computers, and in particular, a transputer based computing surface, is presented. The factors to be considered in their application to computationally intensive CFD problems are discussed with reference to the discrete vortex method used for the solution of separated flow about bluff bodies. Three parallel algorithms for its implementation are presented, and the results are discussed in the context of the speed‐ups obtained using up to sixty‐four parallel processors.
Stability of a numerical algorithm for gas bubble modelling
Authors: Barkhudarov M. R. , Chin S. B. 
Published: November 2005

AbstractA free‐surface‐tracking algorithm based on the SOLA‐VOF method is analysed for numerical stability when modelling gas bubble evolution in a fluid. It is shown that an instability can arise from the fact that the bubble pressure varies with its volume. A time step stability criterion is introduced which is a function of the natural oscillation period but does not depend on the mesh size. This dependence suggests that the instability is likely to arise in the case of a general motion of a bubble, especially if break‐up occurs. The effect is shown using linear Fourier analysis of the discretized equation for radial bubble oscillation and demonstrated numerically using a CFD code FLOW‐3D. One‐ and three‐dimensional situations are considered: a bubble in a fluid bounded by two concentric surfaces and a bubble floating in a fluid chamber with and without gravity. In cases where no analytical solution is available, a numerical method for the stability time step limit calculation is suggested based on finding the natural oscillation frequency.The nature of the instability suggests that it can be a feature of any numerical algorithm which models transient fluid flow with a free surface.
Fully coupled finite volume solutions of the incompressible Navier–Stokes and energy equations using an inexact Newton method
Authors: McHugh Paul R. , Knoll Dana A. 
Published: November 2005

AbstractAn inexact Newton method is used to solve the steady, incompressible Navier–Stokes and energy equation. Finite volume differencing is employed on a staggered grid using the power law scheme of Patankar. Natural convection in an enclosed cavity is studied as the model problem. Two conjugate‐gradient ‐like algorithms based upon the Lanczos biorthogonalization procedure are used to solve the linear systems arising on each Newton iteration. The first conjugate‐gradient‐like algorithm is the transpose‐free quasi‐minimal residual algorithm (TFQMR) and the second is the conjugate gradients squared algorithm (CGS). Incomplete lower‐upper (ILU) factorization of the Jacobian matrix is used as a right preconditioner. The performance of the Newton‐ TFQMR algorithm is studied with regard to different choices for the TFQMR convergence criteria and the amount of fill‐in allowed in the ILU factorization. Performance data are compared with results using the Newton‐CGS algorithm and previous results using LINPACK banded Gaussian elimination (direct‐Newton). The inexact Newton algorithms were found to be CPU competetive with the direct‐Newton algorithm for the model problem considered. Among the inexact Newton algorithms, Newton‐CGS outperformed Newton‐ TFQMR with regard to CPU time but was less robust because of the sometimes erratic CGS convergence behaviour.
Finite element solution of the streamfunction‐vorticity equations for incompressible two‐dimensional flows
Authors: Comini G. , Manzan M. , Nonino C. 
Published: November 2005

AbstractThe streamfunction‐vorticity equations for incompressible two‐dimensional flows are uncoupled and solved in sequence by the finite element method. The vorticity at no‐slip boundaries is evaluated in the framework of the streamfunction equation. The resulting scheme achieves convergence, even for very high values of the Reynolds number, without the traditional need for upwinding. The stability and accuracy of the approach are demonstrated by the solution of two well‐known benchmark problems: flow in a lid‐driven cavity at Re ⩽ 10,000 and flow over a backward‐facing step at Re = 800.
A numerical approach to model non‐isothermal viscous flow through fibrous media with free surfaces
Authors: Bruschke M. V. , Advani S. G. 
Published: November 2005

AbstractA numerical simulation is presented to predict the free surface and its interactions with heat transfer and cure for flow of a shear‐thinning resin through the fibre preform the flow part of the simulation is based on the finite element/control volume method. Since the traditional control volume approach produces an error associated with a mass balance inconsistency, a new method which overcomes this issue is proposed, the element control volume method.The heat transfer and cure analysis in the simulation are based on the finite difference/control volume method. Since heat conduction is dominant in the through‐thickness direction and most of the heat convection is in‐plane, heat transfer and cure are solved in fully three‐dimensional form. A simple concept of the boundary condition constant is introduced which models a realistic mould configuration with a heating element located at a distance behind the mould wall. The varying viscosity throughout the mould associated with the strain rate, temperature and degree of cure distribution may be accounted for in calculating the mould‐filling pattern. This introduces a two‐way coupling between momentum and energy transport in fibrous media during mould filling.
Grid adaptation using a distribution of sources applied to inviscid compressible flow simulations
Authors: Weatherill N. P. , Marchant M. J. , Hassan O. , Marcum D. L. 
Published: November 2005

AbstractUnstructured tetrahedral grids are generated using a new, very efficient procedure based upon the Delaunay triangulation. The generation procedure is extremely fast, having the capability to generate large grids in minutes on workstations. To maximize this computational performance, a new form of adaptivity has been developed involving the use of sources placed within regions of the domain which require further grid point resolution. A source has a position and a specified grid point density. An error indicator is used to find the elements within the grid which require refinement. Within such elements sources are placed with specified grid point densities which are proportional to the amount of refinement required. The grid generation procedure is then invoked and a grid generated whose grid point density is controlled by the sources. The resulting grid is thus refined in the regions identified by the error indicator as requiring greater resolution. The paper discusses the generation process and emphasizes the new solution adaptation capability. Several examples of the approach are given, including aerospace compressible flow simulations over realistic configurations.
Simulation of supersonic flows with detached shocks using a property convection method
Authors: Milthorpe J. F. 
Published: November 2005

AbstractAn algorithm based on the convection of fundamental flow quantities, i.e. mass, momentum and energy, has been described by the author previously.1 Computer codes to implement the algorithm have been developed for two‐dimensional and axisymmetric flows. This algorithm has been further developed to improve the accuracy and stability of the calculations. In this paper the algorithm is used to calculate the flows about two‐dimensional and axisymmetric bluff bodies. Bodies of practical interest in supersonic and hypersonic flows are often sufficiently bluff for a detached shock to develop, and correct prediction of the shock stand‐off distance and the position of the sonic line is a useful test of numerical methods.The programme is used to calculate flows with a detached shock around three standard shapes: a sphere, a body of revolution with a flat nose and a plate with a flat nose. The Mach number range for the flows described is from 1.177 to 6.0. Comparisons are given with standard experimental results for the steady state stand‐off.
Simultaneous solution of the Navier‐Stokes and elastic membrane equations by a finite element method
Authors: Rast Mark Peter 
Published: November 2005

AbstractFluid flow through a significantly compressed elastic tube occurs in a variety of physiological situations. Laboratory experiments investigating such flows through finite lengths of tube mounted between rigid supports have demonstrated that the system is one of great dynamical complexity, displaying a rich variety of self‐excited oscillations. The physical mechanisms responsible for the onset of such oscillations are not yet fully understood, but simplified models indicate that energy loss by flow separation, variation in longitudinal wall tension and propagation of fluid elastic pressure waves may all be important. Direct numerical solution of the highly non‐linear equations governing even the most simplified two‐dimensional models aimed at capturing these basic features requires that both the flow field and the domain shape be determined as part of the solution, since neither is known a priori. To accomplish this, previous algorithms have decoupled the solid and fluid mechanics, solving for each separately and converging iteratively on a solution which satisfies both. This paper describes a finite element technique which solves the incompressible Navier‐Stokes equatikons simultaneously with the elastic membrane equations on the flexible boundary. The elastic boundary position is parametized in terms of distances along spines in a manner similar to that which has been used successfully in studies of viscous free surface flows, but here the membrane curvature equation rather than the kinematic boundary condition of vanishing normal velocity is used to determine these diatances and the membrane tension varies with the shear stresses exerted on it by the fluid motions. Bothy the grid and the spine positions adjust in response to membrane deformation, and the coupled fluid and elastic equations are solved by a Newton‐Raphson scheme which displays quadratic convergence down to low membrane tensions and extreme states of collapse. Solutions to the steady problem are discussed, along with an indication of how the time‐dependent problem might be approached.
A numerical study of vortex shedding around a heated/cooled circular cylinder by the three‐step Taylor‐Galerkin method
Authors: Hatanaka Katsumori , Kawahara Mutsuto 
Published: November 2005

AbstractIn this paper the vortex shedding around a heated/cooled circular cylinder is numerically simulated by solving the time‐dependent Navier‐Stokes and energy equations. A finite element method that is referred to as the three‐step Taylor‐Galerkin method is used to compute these equations. The attention of this study is directed to the investigation of the effect of buoyancy on the vortex street behind the cylinder at constant Reynolds number. The present paper shows the suppression or generation of the von Kármán vortex street behind the cylinder when the cylinder surface is heated or cooled respectively. The relationship between the temperature‐induced buoyancy force and the vortex shedding is also discussed through several numerical examples.