bluuebunny/crossref_metadata_2025_split huggingface dataset:
Modelling flow over a backward–facing step using the F.E.M. and the two‐equation model of turbulence
Authors: Taylor C. , Thomas C. E. , Morgan K. 
Published: August 2005

AbstractFlow over a downstream‐facing step is predicted using the F.E.M. A two‐equation model of turbulence is employed where the transport of turbulence kinetic energy and dissipation rate are depicted using transport‐type equations, i.e. the two‐equation model of turbulence. The results obtained are compared with other models and experimental results. Generally, the model was found to be under‐predictive with regard to the reattachment length when previous empirical data was used in the transport equations.
A generalized variational formulation for convective heat transfer
Authors: Keramidas George A. 
Published: August 2005

AbstractThe Scope of this paper is to develop the basic equations for a variational formulation which can be used to solve problems related to convection and/or diffusion dominated flows. The formulation is based on the introduction of a generalized quantity defined as the hear displacement. The governing equation is expressed in terms of this quantity and a variational formulation is developed which leads to a system of equations similar in form to Lagrange's equations of mechanics. These equations can be used for obtaining approximate solutions, though they are of particular interest for application of the finite element method.As an example of the formulation two finite element models are derived for solving convectiondiffusion boundary value problems. The performance of the two models is investigated and numerical results are given for different cases of convection and diffusion with two types of boundary conditions. The applications of the developed formulations are not limited to convection‐diffusion problems but can also be applied to other types of problems such as mass transfer, hydrodynamics and wave propagation.
An approximately divergence‐free 9‐node velocity element (with variations) for incompressible flows
Authors: Griffiths D. F. 
Published: August 2005

AbstractExplicit basis functions are constructed for 9‐node biquadratic velocity fields which guarantee that a weak form of the continuity equation is satisfied. The corresponding pressure approximations are either piecewise constant, piecewise linear or piecewise bilinear. These results are extended to give bases for bilinear velocity/piecewise constant pressure elements and also to some three‐dimensional brick elements.
Old and new finite elements for incompressible flows
Authors: Fortin Michel 
Published: August 2005

AbstractThis paper presents some seemingly new elements for the computation of two and three‐dimensional incompressible flow. We want to obtain elements satisfying the Babǔska‐Brezzi condition for mixed methods and thus introducing no spurious pressure modes (cf. Sani et al.1). In order to present clearly the advantages and disadvantages of our new elements we compare them on a qualitative basis with more standard ones. Of particular importance for incompressible flow is the size and shape of vortices that can be produced by the elements. We shall try to describe this as precisely as possible. The conclusion is that the elements introduced here should be quite competitive on a cost/precision scale.
The Lagrangian approach of advective term treatment and its application to the solution of Navier—Stokes equations
Authors: Huffenus J. P. , Khaletzky D. 
Published: August 2005

AbstractA one‐dimensional transport test applied to some conventional advective Eulerian schemes shows that linear stability analyses do not guarantee the actual performances of these schemes. When adopting the Lagrangian approach, the main problem raised in the numerical treatment of advective terms is a problem of interpolation or restitution of the transported function shape from discrete data. Several interpolation methods are tested. Some of them give excellent results and these methods are then extended to multi‐dimensional cases.The Lagrangian formulation of the advection term permits an easy solution to the Navier‐Stokes equations in primitive variables V, p, by a finite difference scheme, explicit in advection and implicit in diffusion.As an illustration steady state laminar flow behind a sudden enlargement is analysed using an upwind differencing scheme and a Lagrangian scheme. The importance of the choice of the advective scheme in computer programs for industrial application is clearly apparent in this example.
Numerical predictions of the laminar flow over a normal flat plate
Authors: Castro I. P. , Cliffe K. A. , Norgett M. J. 
Published: August 2005

AbstractFinite‐difference and finite‐element techniques have been used to calculate the steady laminar flow over a flat plate normal to an air stream, up to a Reynolds number, Re, based on the plate half‐width, of 100. The boundary conditions simulate a central splitter plate downstream of the body, to prevent vortex shedding, so the flow is characterized by a closed recirculation region which grows with increasing Re but at Re = O(100) is very similar in size to the turbulent recirculating region that occurs in the corresponding high Reynolds‐number flow. Motivation came, in part, from the increasing efforts of turbulence modellers to calculate complex turbulent flows (containing elliptic regions) and our belief that the numerical methods commonly employed for such work can be inaccurate. The predictions are compared with each other and with some expectations based on classic solutions of the Navier‐Stokes equations, and the nature of the numerical errors is demonstrated. It is concluded that effort comparable with that expended in developing turbulence models should be directed to developing higher‐order numerical methods, before the numerical accuracy of predictions of, for example, bluff‐body flows can be made sufficiently high to sustain detailed discussion of the adequacy of turbulence models in such situations.
Investigation of solution of Navier–Stokes equations using a variational formulation
Authors: Ecer A. , Rout R. K. , Ward P. 
Published: August 2005

AbstractA variational formulation for the solution of two dimensional, incompressible viscous flows has been developed by one of the authors.1 The main objective of the present paper is to demonstrate the applicability of this approach for the solution of practical problems and in particular to investigate the introduction of boundary conditions to the Navier‐Stokes equations through a variational formulation. The application of boundary conditions for typical internal and external flow problems is presented. Sample cases include flow around a cylinder and flow through a stepped channel.Quadrilateral, bilinear isoparametric elements are utilized in the formulation. A single‐step, implicit, and fully coupled numerical integration scheme based on the variational principle is employed. Presented results include sample cases with different Reynolds numbers for laminar and turbulent flows. Turbulence is modelled using a simple mixing length model. Numerical results show good agreement with existing solutions.
Formulation of a linear three‐dimensional hydrodynamic sea model using a Galerkin‐eigenfunction method
Authors: Davies A. M. 
Published: August 2005

AbstractThe three dimensional linear hydrodynamic equations which describe wind induced flow in a sea are solved using the Galerkin method. A basis set of eigenfunctions is used in the calculation. These eigenfunctions are determined numerically using an expansion of B‐splines.Using the Galerkin method the problem of wind induced flow in a rectangular basin is examined in detail. A no‐slip bottom boundary condition with a vertically varying eddy viscosity distribution is employed in the calculation. With a low (of order 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s near the sea bed together with high current shear in this region are physically realistic and have been observed in the sea.In order to accurately compute the eigenfunctions associated with large (of order 2000 cm2/s at the sea surface to 1 cm2/s at the sea bed) vertical variation of viscosity, an expansion of the order of thirty‐five B‐splines has to be used. The spline functions are distributed through the vertical so as to give the maximum resolution in the high shear region near the sea bed.Calculations show that in the case of a no‐slip bottom boundary condition, with an associated region of high current shear near the sea bed, the Galerkin method with a basis set of the order of ten eigenfunctions (a Galerkin‐eigenfunction method) yields an accurate solution of the hydrodynamic equations. However, solving the same problem using the Galerkin method with a basis set of B‐splines, requires an expansion of the order of thirty‐five spline functions in order to obtain the same accuracy.Comparisons of current profiles and time series of sea surface elevation computed using a model with a slip bottom boundary condition and a model with a no‐slip boundary condition have been made. These comparisions show that consistent solutions are obtained from the two models when a physically relistic coefficient of bottom friction is used in the slip model, and a physically realistic bottom roughness length and thickness of the bottom boundary layer are employed in the no‐slip model.
Evaluation of tidal residual currents in a wide estuary, using a finite element method
Authors: Jenkins A. D. 
Published: August 2005

AbstractFrom the linearized, time‐independent, constant depth, shallow water tidal equations in an f‐plane for a two‐layer estuary, two independent modal Helmholtz equations are derived. These modal equations are solved using a fifth‐degree finite element technique. The first and second space derivatives of the complex modal tidal elevations, and thus the modal currents and their first derivatives, are evaluated directly from the solution at each node of the finite element mesh.The Stokes drift, which is the major part of the residual tidal flow, is evaluated from these nodal values of the currents and their derivatives. Good agreement is obtained with the exact analytical solution for a wedge‐shaped estuary with a wedge angle of π/3, using a mesh of 64 equilateral triangles with sides approximately 1/10 of the wavelength 2πC2/σ of a Kelvin wave solution for the short‐wavelength mode.
Numerical solution of viscous flows using integral equation methods
Authors: Bush M. B. , Tanner R. I. 
Published: August 2005

AbstractA formulation of the boundary element method for the solution of non‐zero Reynolds number incompressible flows in which the non‐linear terms are lumped together to form a forcing function is presented. Solutions can be obtained at low to moderate Reynolds numbers. The method was tested using the flow of a fluid in a two‐dimensional converging channel (Hamel flow) for which an exact solution is available. An axisymmetric formulation is demonstrated by examining the drag experienced by a sphere held stationary in uniform flow. Performance of the method was satisfactory. New results for an axisymmetric free jet at zero Reynolds number obtained using the boundary element method are also included. The method is ideal for this type of free‐surface problem.
Numerical solutions for solute transport in unconfined aquifers
Authors: Guvanasen V. , Volker R. E. 
Published: August 2005

AbstractTwo numerical methods for solving the problem of solute transport in unsteady flow in unconfined aquifers are studied. They are the method of characteristics (MOC) based on the finite difference method (FDM), and the finite element method (FEM). The FEM is further subdivided into four schemes: moving mesh, pseudo‐Lagrangian (FEM1); stationary mesh, pseudo‐Lagrangian (FEM2); pseudo saturated‐unsaturated, Eulerian (FEM3); and non‐stationary element, Eulerian (FEM4).Experiments on a one‐dimensional flow case are performed to illustrate the schemes and to determine the effect of discretization on accuracy. In two‐dimensional flow the above methods are compared with experimental results from a sand box model. Results indicate that for a similar degree of accuracy, the FEM requires less computational effort than the MOC. Among the four FEM schemes, FEM4 appears to be most attractive as it is the most efficient and most convenient to apply.
Noise problems with ephemeral streams in aquifer models
Authors: Connorton B. J. , Wood W. L. 
Published: August 2005

AbstractPrevious papers12 have drawn attention to the sustained oscillations (‘noise’) in the solution by successive over‐relaxation of the equations from the finite difference approximation of regional groundwater flow including ephemeral streams. This paper shows that the trouble can be avoided by introducing an averaging step in the algorithm; the trouble can also be avoided by ‘under‐relaxation’ but this is far less efficient than averaging.
Natural convection of air in a square cavity: A bench mark numerical solution
Authors: De Vahl Davis G. 
Published: August 2005

AbstractDetails are given of the computational method used to obtain an accurate solution of the equations describing two‐dimensional natural convection in a square cavity with differentially heated side walls. Second‐order, central difference approximations were used. Mesh refnement and extrapolation led to solutions for 103⩽Ra⩽10 6 which are believed to be accurate to better than 1 per cent at the highest Rayleigh number and down to one‐tenth of that at the lowest value.
Angled jet flow model for a diesel engine intake process—random vortex method
Authors: Sung Nak Won , Laitone Jonathan A. , Patterson Donald J. 
Published: August 2005

AbstractA numerical model is developed to study the interactions of multiple angled jet flows in the inlet port plane of the Detroit Diesel 6V‐92 two‐stroke engine cylinder. The random vortex method is used in two dimensions.Results show axisymmetric swirl initially. As flow develops, the centre of the swirl moves to the mid‐radius region and begins to precess about the cylinder centre. The flow becomes progressively more chaotic as time progresses.
A method for solving the factorized vorticity‐stream function equations by finite elements
Authors: Quartapelle L. , Napolitano M. 
Published: August 2005

AbstractA new finite element method for solving the time‐dependent incompressible Navier‐Stokes equations with general boundary conditions is presented. The two second‐order partial differential equations for the vorticity and the stream function are factorized, apart from the non‐linear advection term, by eliminating the coupling due to the double specification on the stream function at (a part of) the boundary. This is achieved by reducing the no‐slip boundary conditions to projection integral conditions for the vorticity field and by evaluating the relevant quantities involved according to an extension of the method of Glowinski and Pironneau for the biharmonic problem. Time integration schemes and iterative algorithms are introduced which require the solution only of banded linear systems of symmetric type. The proposed finite element formulation is compared with its finite difference equivalent by means of a few numerical examples. The results obtained using 4‐noded bilinear elements provide an illustration of the superiority of the finite element based spatial discretization.
A finite‐element study of the bénard problem using parameter‐stepping and bifurcation search
Authors: Jackson C. P. , Winters K. H. 
Published: August 2005

AbstractThe problem of fluid motion in a cavity with rigid sidewalls that is heated uniformly from below is studied by the finite‐element method. The techniques of parameter‐stepping and monitoring the determinant of the Jacobian matrix to find bifurcations are used. Results are presented for width‐to‐height ratios in the range 1 to 4, and for three different boundary conditions on the horizontal surfaces, namely both rigid, both free, and rigid bottom with free top. The non‐linear branches above the critical Rayleigh number are examined. Extensions to non‐Boussinesq flow are trivial.
Simulation of polymeric flows in the injection moulding process
Authors: Shen Shan‐Fu 
Published: August 2005

AbstractRecent progress in the simulation of polymeric flows of two key problems in the injection moulding process, carried out by a team at Cornell University, is briefly described. For the filling of cooled thin cavities, the fluid is characterized by a power‐law viscosity with exponential temperature dependence, and interaction between the transient thermal boundary‐layer and the core flow in a domain with moving boundary is essential. The earlier procedure of Hieber and Shen is modified in two aspects: a boundary‐integral formulation replaces the finite‐element treatment of the pressure, and an ‘energy integral’ approach is used for the transient temperature. The second problem is the steady visco‐elastic flow in the juncture region where sudden changes of the geometry and large strain rates occur. The constitutive equation is postulated according to the Leonov model. The main features in the numerical implementation are: integration along a streamline to determine the elastic deformation tensors for a given velocity field, and finite‐element treatment (in time‐dependent form) of the pressure and fields for given stresses. In an example where the contraction ratio is 7:1, results for nominal Deborah number exceeding 100 show no numerical instability. (However, for this problem, the true Weissenberg number, i.e. the ratio of local first‐normal‐stress difference to shear stress turns out to be generally O(10).) The predictions also correlate very well with experimental birefringence measurements.
Finite element solutions for laminar and turbulent compressible flow
Authors: Srinivas K. , Fletcher C. A. J. 
Published: August 2005

AbstractThe time‐split finite element method is extended to compute laminar and turbulent flows with and without separation. The examples considered are the flows past trailing edges of a flat plate and a backward‐facing step. Eddy viscosity models are used to represent effects of turbulence. It is found that the time‐split method produces results in agreement with previous experimental and computational results. The eddy viscosity models employed are found to give accurate predictions in all regions of flow except downstream of reattachment.
Finite element simulation of dip coating, I: Newtonian fluids
Authors: Tanguy P. , Fortin M. , Choplin L. 
Published: August 2005

AbstractA finite element simulation of the dip coating process based on a discretization of the continuum with discontinuous pressure elements is presented. The algorithm computes the flow field from natural boundary conditions while an extra condition provided by the existence of free surface is employed to displace the meniscus location towards the actual position. The process is iterative and uses a pseudo‐time stepping technique coupled to a cubic spline fitting of the free surface. Numerical predictions exhibit good agreement with experimental data for Newtonian fluids in the case of flat plate dip coating as well as in the case of wire dip coating.
A modified finite element method for solving the time‐dependent, incompressible Navier‐Stokes equations. Part 2: Applications
Authors: Gresho Philip M. , Chan Stevens T. , Lee Robert L. , Upson Craig D. 
Published: August 2005

AbstractThree examples will be presented to demonstrate the performance of the scheme described in Part 1 of this paper.1 Two are isothermal (T = 0) and two‐dimensional, and one of these is steady and the other time‐dependent. The third example involves buoyancy effects, is time‐dependent and three‐dimensional, and is presented in less detail. The paper concludes with a short discussion and some conclusions from both Parts 1 and 2.
A new, reliable family of split‐operator methods for computing reacting flows
Authors: Greenberg J. B. 
Published: August 2005

AbstractA new, reliable family of split‐operator methods is presented for the computation of reacting flows. The methods may be inconsistent or consistent depending upon their applicability. Analyses are carried out for flow combusting according to general multicomponent, multireaction linear or non‐linear chemical kinetic models, and conditions for guaranteed stability/convergence are established. A special chemical splitting parameter can also be embedded in the methods enabling accelerated convergence of an iterative finite‐difference solution. Computed results highlight the capabilities and properties of the methods.
On a family of Stokes flows
Authors: Zaturska M. B. , Banks W. H. H. 
Published: August 2005

AbstractA family of simple Stokes flows involving sliding surfaces adjacent to surfaces at rest is considered. Principally, two specific flow configurations are investigated: (i) that arising when parts of the boundary of an infinitely long circular cylinder are rotating about the axis while other parts of the boundary are at rest, and (ii) the flow produced when a cap of a sphere is held at rest while the remainder of the sphere rotates about the symmetry axis. In each case computer plots of streamlines or constant velocity lines are presented to give a general impression of the resulting flow pattern.
Pressure method for the numerical solution of transient, compressible fluid flows
Authors: Casulli V. , Greenspan D. 
Published: August 2005

AbstractIn this paper the pressure method for incompressible fluid flow simulation is extended and applied to the numerical simulation of compressible fluid flow. The governing equations, obtained from the physical principles of conservation of momentum, mass and energy, are first studied from a characteristic point of view. Then they are discretized with a semi‐implicit finite difference technique in such a fashion that stability is achieved independently of the speed of sound. The resulting algorithm is fast, accurate and particularly efficient in subsonic flow calculations. As an example, the computer simulation of the von Kármán vortex street is described and discussed.
A comparison of mixed methods for solving the flow of a Maxwell fluid
Authors: Van Schaftingen J. J. , Crochet M. J. 
Published: August 2005

AbstractThe proficiency of available mixed methods for solving the flow of a Maxwell fluid is evaluated through their application to the same problem. The reasons for the usual degeneracy of the numerical results beyond some level of elasticity are investigated. The best‐performing technique is applied to the flow through an abrupt 4/1 contraction.
On the consistency of four different control surfaces used for finite area blade‐to‐blade flow calculations
Authors: Arts T. 
Published: August 2005

AbstractThe aim of this contribution is to investigate the consistency and order of accuracy of different control surfaces used for finite area blade‐to‐blade flow calculations. The following cases will be treated: a hexagonal element, a trapezoidal element, a bitrapezoidal element and a quadrilateral element. Finally, the consistency conditions will be discussed and compared with respect to a cascade flow application.
Towards generalization and optimization of implicit methods
Authors: Lin Avi 
Published: August 2005

AbstractA general implicit (GI) method for solving iteratively the algebraic system arising from a finite difference approximation of an elliptic partial differential equation is formulated. Under certain assumptions this method can be reduced to the already known implicit techniques. It is shown that the GI method has a very special physical meaning when solving fluid flow problems. It is shown also how this method can be optimized to achieve the maximum rate of convergence. Finally it is shown how this new strategy is applied by solving some classical numerical fluid dynamics problems.