bluuebunny/crossref_metadata_2025_split huggingface dataset:
On some accurate finite‐difference methods for laminar flame calculations
Authors: Ramos J. I. 
Published: August 2005

AbstractThe ozone‐decomposition flame has been studied by means of fourth‐ and second‐order accurate schemes. The fourth‐order methods include a method of lines, a time‐linearization algorithm, and a majorant operatorsplitting technique. The second‐order schemes include two time‐linearization methods which use different temporal approximations. It is shown that the fourth‐order techniques yield comparable results to those obtained with very accurate finite element and adaptive grid finite‐difference algorithms. The results of the second‐order methods are in good agreement with second‐order explicit predictor‐corrector methods but predict a lower flame speed than that obtained by means of fourth‐order techniques. It is also shown that the temporal approximations are not as important as the spatial approximations in flame propagation problems characterized by the presence of several small time scales.
Efficient ADI and spline ADI methods for the steady‐state Navier‐Stokes equations
Authors: Napolitano Michele 
Published: August 2005

AbstractThe present paper provides an improved alternating direction implicit (ADI) technique as well as high‐order‐accurate spline ADI method for the numerical solution of steady two‐dimensional incompressible viscous flow problems. The vorticity‐stream function Navier‐Stokes equations are considered in a general curvilinear coordinate system, which maps an arbitrary two‐dimensional flow domain in the physical plane into a rectangle in the computational plane. The stream function equation is parabolized in time by means of a relaxation‐like time derivative and the steady state solution is obtained by a time‐marching ADI method requiring to solve only 2 × 2 block‐tridiagonal linear systems. The difference equations are written in incremental form; upwind differences are used for the incremental variables, for stability, whereas central differences approximate the non‐incremental terms, for accuracy, so that, at convergence, the solution is free of numerical viscosity and second‐order accurate. The high‐order‐accurate spline ADI technique proceeds in the same manner; in addition, at the end of each two‐sweep ADI cycle, the solution is corrected by means of a fifth‐order spline interpolating polynomial along each row and column of the computational grid, explicitly. The validity and the efficiency of the present methods are demonstrated by means of three test problems.
Pressure and time treatment for Chebyshev spectral solution of a Stokes problem
Authors: Deville M. , Kleiser L. , Montigny‐Rannou F. 
Published: August 2005

AbstractTo investigate the influences of time scheme, pressure treatment and initial conditions in incompressible fluid dynamics, a Stokes problem is solved numerically on a slab geometry within the framework of spectral approximation in space. Four algorithms are examined: splitting schemes, influence matrix method, penalty formulation and pseudo‐spectral space‐time technique. It is shown that splitting schemes are less accurate than the other processes. Furthermore, the initial field should respect a compatibility condition to avoid singularities at the initial time. If it is not possible to build such a compatible field, the numerical procedure has to present good damping properties at the first steps of the time integration.
Buoyancy effects on turbulent swirling flows
Authors: Takhar H. S. , Halim M. A. 
Published: August 2005

AbstractA three‐parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time‐averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T′2. Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl.The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results.
On the effect of flow direction on mixed convection from a horizontal cylinder
Authors: Badr H. M. 
Published: August 2005

AbstractThe influence of free stream direction on mixed (natural and forced) convective heat transfer from a circular cylinder is investigated. The cylinder, which has an isothermal surface, is placed with its axis horizontal and normal to the oncoming flow. The free stream direction varies between the vertically upward (parallel flow) and the vertically downward (contraflow) directions. The investigation is based on the time integration of the unsteady, two‐dimensional equations of motion and energy until reaching steady conditions. The study is limited to Reynolds numbers up to Re = 40 and Grashoff numbers of Gr = Re2. The results are compared with the available experimental data and the agreement is satisfactory.
Development and application of an adaptive finite element method to reaction‐diffusion equations
Authors: Ramos J. I. 
Published: August 2005

AbstractAn adaptive finite element method is developed and applied to study the ozone decomposition laminar flame. The method uses a semidiscrete, linear Galerkin approximation in which the size of the elements is controlled by an integral which minimizes the changes in mesh spacing. The sizes and locations of the elements are controlled by the location and magnitude of the largest temperature gradient. The numerical results obtained with this adaptive finite element method are compared with those obtained using fixed‐node finite‐difference schemes and an adaptive finite‐difference method. It is shown that the adaptive finite element method developed here using 36 elements can yield as accurate flame speeds as fourth‐order accurate, fixed‐node, finite‐difference methods when 272 collocation points are employed in the calculations.
Numerical calculation of equivalent moment of inertia for a fluid in a cylindrical container with partitions
Authors: Partom Ilya S. 
Published: August 2005

AbstractA 3‐D numerical code was developed to solve the irrotational flow of an ideal fluid inside a moving cylindrical container with partitions. The problem is formulated in terms of two Poisson equations, the velocity equation and the pressure equation. These are expressed in terms of finite differences and solved by a procedure of line over relaxation. From the fluid pressure we computed the resultant moment on the container which was then expressed in terms of the equivalent moment of inertia. The code was checked against analytical results of Moiseyev and we found an agreement of 2–5 per cent even for a sparse mesh. We then demonstrated the capability of the code by computing the equivalent moment of inertia for various configurations with full and partial partitions.
Computation of high speed turbulent boundary‐layer flows using the k–ϵ turbulence model
Authors: Liakopoulos A. 
Published: August 2005

AbstractThe applicability of a finite element‐differential method to the computation of steady two‐dimensional low‐speed, transonic and supersonic turbulent boundary‐layer flows is investigated. The turbulence model chosen for the Reynolds shear stress and turbulent heat flux is the K‐ϵ two‐equation model. Calculations are extended up to the wall and the exact values of the dependent variables at the wall are used as boundary conditions. A number of transformations are carried out and the assumed solutions at a longitudinal station are represented by complete cubic spline functions. In essence, the method converts the governing partial differential equations into a system of ordinary differential equations by a weighted residuals method and invokes an ordinary differential equation solver for the numerical integration of the reduced initial‐value problem. The results of the computations reveal that the method is highly accurate and efficient. Furthermore, the accuracy and applicability of the k‐ϵ turbulence model are examined by comparing results of the computations with experimental data. The agreement is very good.
The addition of quasi‐three‐dimensional terms into a finite element method for transonic turbomachinery blade‐to‐blade flows
Authors: Cedar R. D. , Stow P. 
Published: August 2005

AbstractThis paper describes the extension of a purely two‐dimensional finite element method for the calculation of transonic turbomachinery blade‐to‐blade flows to include the quasi‐three‐dimensional terms. These terms account for the effect of variations in streamline radius, stream‐tube height and blade rotation.By approximating the stream surface as a piecewise linear function, then using a local developed cone transformation on an element basis, the finite element equations are shown to remain of the same form as the two‐dimensional equations.The numerical results presented demonstrate that the stream‐tube height, streamline radius and blade rotation terms must be included if the prediction of the Mach number distribution around a gas turbine blade is to be calculated correctly.
A finite element method for the solution of two‐dimensional transonic flows in cascades
Authors: Whitehead D. S. , Newton S. G. 
Published: August 2005

AbstractSteady two‐dimensional transonic flow is calculated in cascades of compressor and turbine blades using a mesh of triangular finite elements. A velocity potential is used, the equations being solved by the Newton‐Raphson technique. The resulting computer program is fast, and is shown to give good accuracy. Shock waves are well represented, provided they are not too strong.
A numerical procedure for the generation of orthogonal body‐fitted co‐ordinate systems with direct determination of grid points on the boundary
Authors: Papantonis Dimitris E. , Athanassiadis Nicholas A. 
Published: August 2005

AbstractThe procedure proposed is based on the solution by finite difference means of a set of Laplace's equations, by the application of a relaxation method.The curvilinear orthogonal grid so generated is fitted to a 2‐D physical domain with closed boundary and the contribution of the present work consists in the arbitrary choice of grid points on two adjacent boundaries, in order to achieve the desired density of grid points where the geometry of the boundaries varies rapidly.The method proposed is rapid and stable. Some characteristic examples are finally presented.
A review of some finite element methods to solve the stationary Navier‐Stokes equations
Authors: Segal A. 
Published: August 2005

AbstractIn this paper the integrated solution approach, the penalty function approach and the solenoidal approach for the finite element solution of the stationary Navier‐Stokes equations are compared. It is shown that both the penalty function approach and the solenoidal approach compare favourably to the integrated solution method. For fine meshes the solenoidal approach appears to be the cheapest method.
Application of the DuFort‐Frankel and Saul'ev methods with time splitting to the formulation of a three dimensional hydrodynamic sea model
Authors: Davies Alan M. 
Published: August 2005

AbstractA three dimensional hydrodynamic sea model of an arbitrary sea area is formulated using sigma co‐ordinates in the vertical. The solution of the equations using finite difference grids in the horizontal and the vertical is described.Discretization of the vertical viscosity term in the hydrodynamic equations using the DuFort‐Frankel and Saul'ev methods is developed. Some numerical instabilities occur with the DuFort‐Frankel method which can be overcome by splitting the hydrodynamic equations into equations describing the mean flow and equations describing the deviations from it. The computational advantages of solving these equations with different time steps are discussed.The accuracy and stability of the various methods is demonstrated for wind induced flow in a simple rectangular basin having dimensions representing the North Sea.
Application of the Dorodnitsyn finite element method to swirling boundary layer flow
Authors: Fletcher C. A. J. 
Published: August 2005

AbstractThe Dorodnitsyn finite element method for turbulent boundary layer flow with surface mass transfer is extended to include axisymmetric swirling internal boundary layer flow. Turbulence effects are represented by the two‐layer eddy viscosity model of Cebeci and Smith1 with extensions to allow for the effect of swirl. The method is applied to duct entry flow and a 10 degree included‐angle conical diffuser, and produces results in close agreement with experimental measurements with only 11 grid points across the boundary layer. The introduction of swirl (we/ue = 0.4) is found to have little effect on the axial skin friction in either a slightly favourable or adverse pressure gradient, but does cause an increase in the displacement area for an adverse pressure gradient. Surface mass transfer (blowing or suction) causes a substantial reduction (blowing) in axial skin friction and an increase in the displacement area. Both suction and the adverse pressure gradient have little influence on the circumferential velocity and shear stress components. Consequently in an adverse pressure gradient the flow direction adjacent to the wall is expected to approach the circumferential direction at some downstream location.
Conforming finite element computations applied to a spatially periodic, harmonic Navier‐Stokes problem
Authors: Borne Lionel , Chambon René , Auriault Jean‐Louis 
Published: August 2005

AbstractIn this paper computations in the two dimensional case of a harmonic Navier‐Stokes problem with periodic boundary conditions are presented. This study of an incompressible viscous fluid leads to a non‐symmetric linear problem (very low Reynolds number). Moreover unknown functions have complex values (monochromatic dynamic behaviour). Numerical treatment of the incompressibility condition is a generalization of the classical treatment of Stokes problem. A mixed formulation, where discrete pressure plays the role of Lagrange multipliers is used (Uzawa algorithm).Two conforming finite element methods are tested on different meshes. The second one uses a classical refinement in the shape function: the so‐called bulb function. All computational tests show that the use of a bulb function on each element gives better results than refinement in the mesh without introducing too many degrees of freedom. Finally numerical results are compared to experimental data.
Isothermal flow past a blowing sphere
Authors: Cliffe K. A. , Lever D. A. 
Published: August 2005

AbstractSteady, axisymmetric, isothermal, incompressible flow past a sphere with uniform blowing out of the surface is investigated for Reynolds numbers in the range 1 to 100 and surface velocities up to 10 times the free stream value. A stream‐function‐velocity formulation of the flow equations in spherical polar co‐ordinates is used and the equations are solved by a Galerkin finite‐element method. Reductions in the drag coefficients arising from blowing are computed and the effects on the viscous and pressure contributions to the drag considered. Changes in the surface pressure, surface vorticity and flow patterns for two values of the Reynolds number (1 and 40) are examined in greater detail. Particular attention is paid to the perturbation to the flow field far from the sphere.
A transient solution method for the finite element incompressible Navier‐Stokes equations
Authors: Yoshida Yutaka , Nomura Takashi 
Published: August 2005

AbstractA numerical procedure for solving the time‐dependent, incompressible Navier‐Stokes equations is presented. The present method is based on a set of finite element equations of the primitive variable formulation, and a direct time integration method which has unique features in its formulation as well as in its evaluation of the contribution of external functions. Particular processes regarding the continuity conditions and the boundary conditions lead to a set of non‐linear recurrence equations which represent evolution of the velocities and the pressures under the incompressibility constraint. An iteration process as to the non‐linear convective terms is performed until the convergence is achieved in every integration step. Excessively artificial techniques are not introduced into the present solution procedure. Numerical examples with vortex shedding behind a rectangular cylinder are presented to illustrate the features of the proposed method. The calculated results are compared with experimental data and visualized flow fields in literature.
An efficient matrix solver for finite‐element analysis of non‐Newtonian fluid flow problems
Authors: Liu Ta‐Jo 
Published: August 2005

AbstractWhen the Galerkin finite‐element method with a nine‐node isoparametric Lagrangian element is applied to solve non‐Newtonian fluid flow problems, a considerable amount of computing time is required to solve the discretized non‐linear system of equations by Newton's method. A method proposed by Broyden has been modified to compute the Jacobian matrix associated with Newton's method. This modified Broyden's method can be combined with the frontal method to efficiently solve the linearized finite‐element equations during the iteration. Numerical results of a sample problem concerning the determination of the pressure‐drop/flow‐rate relationship for power‐law fluids in rectangular ducts show that the application of this new method can reduce computing time substantially.
A numerical study of the applicability of the Boussinesq approximation for a fluid‐saturated porous medium
Authors: Gartling D. K. , Hickox C. E. 
Published: August 2005

AbstractThe regions of applicability of the Boussinesq approximation are investigated for natural convection in a fluid‐saturated porous medium. A perturbation method is used to assess the relative importance of individual terms in the differential equations which describe the natural convection process. Specific limits to the validity of the Boussinesq approximation are identified for water and air. For water, it is shown that the restrictions imposed by the classical Boussinesq approximation can be relaxed by allowing for the variation of thermophysical properties with temperature while still retaining the incompressible form of the continuity relation. Results of the analysis are verified through numerical calculations performed for steady natural convection in a planar, water‐saturated porous region.
A study of penalty elements for incompressible laminar flows
Authors: Dhatt Gouri , Hubert Guy 
Published: August 2005

AbstractA finite element model is developed based on the penalty formulation to study incompressible laminar flows. The study includes a number of new quadrilateral and triangular elements for 2‐dimensional flows and a number of new hexahedral and tetrahedral elements for 3‐dimensional flows. All elements employ continuous velocity approximations and discontinuous pressure approximations respecting the LBB condition of numerical instability. An incremental Newton–Raphson method coupled with the Broyden method is used to solve the non‐linear equations. Several numerical examples (colliding flow, cavity flow, etc.) are presented to assess the efficiency of elements.
Improved averaging method for turbulent flow simulation. Part II: Calculations and verification
Authors: Dakhoul Youssef M. , Bedford Keith W. 
Published: August 2005

AbstractThis is the second of two articles intended to develop, apply and verify a new method for averaging the momentum and mass transport equations for turbulence. Part I presented the theoretical development of a new space‐time filter (STF) averaging procedure. The new method, as well as all existing averaging procedures, are applied to the one‐dimensional transient equations of momentum and scalar transport in a Burgers' flow field. Dense‐grid ‘exact’ results from the unaveraged equations are presented to depict the dynamic behaviour of the flow field and serve as a basis for verifying the coarse‐grid STF predictions. In this paper, a finite difference procedure is used to numerically solve the new STF averaged equations, as well as the other forms of the averaged equations derived in Part I. All averaged equations are solved on the same coarse grid. The velocity and scalar fields, predicted from each equation form, are intercompared according to a verification procedure based on the statistical and spectral properties of the results. It is found that the new STF procedure improves coarse‐grid dynamic predictions over the existing methods of averaging.
Transition bifurcation branches in non‐linear water waves
Authors: Toro E. F. 
Published: August 2005

AbstractWe are concerned with the numerical computation of progressive free surface gravity waves on a horizontal bed. They are regarded as families of bifurcation branches (λ,A)Q of constant discharge Q.Numerically we determine two transition values Q1 and Q2 with corresponding transition bifurcation branches that classify waves into three disjoint branch sets B1, B2 and B3. Their members are families of waves (λ,A)Q satisfying the conditions 0<Q2 ⩽Q, Q <Q2 ⩽Q and Q <Q2 <B/27, respectively.The bifurcation patterns are analysed in some detail from the computed bifurcation diagram, which shows that in B1 bifurcation is to the left and the amplitude A increases as the wavelength λ decreases; in B2 bifurcation is to the right and turning points are observed nearly at breaking point. In B3 bifurcation is to the right and A increases monotonically with λ.
Measurement of velocity and kinetic energy of turbulence in swirling flows and their numerical prediction
Authors: Sampath S. , Ganesan V. 
Published: August 2005

AbstractSwirling flows are often employed in gas turbine combustion systems and high intensity industrial furnaces. A detailed analysis of the turbulence in the flow is necessary to achieve optimum combustion conditions. In this paper a method has been described to measure the turbulence levels in three directions using a hot wire anemometer. So far there is no established method available for measurement of turbulence in swirling and recirculating flows.The present method, it is hoped, will bridge the gap. The merit of the present method is the use of a single‐wire probe rather than the X‐probe. The method has been used for the measurement of turbulence levels in swirling recirculating flows generated by vane swirlers. From the measured turbulence levels, the kinetic energy of turbulence has been calculated and the results are compared with a well‐established numerical prediction method.Mean velocity measurements have also been made using a 3‐hole Pitot probe. The agreement between the measured and predicted values is quite satisfactory.