bluuebunny/crossref_metadata_2025_split huggingface dataset:
Finite element analysis in combustion phenomena
Authors: Chung T. J. , Kim Y. M. , Sohn J. L. 
Published: August 2005

AbstractThis paper is concerned with the exposition of finite element applications to combustion problems. The subject of computational fluid dynamics, including combustion calculations, has long been dominated by finite differences. Recently, however, the finite element method has emerged as a potential candidate for computational modelling in fluid mechanics. It is well known that reactive fluids with combustion present additional complications because of disparity in reaction rates commonly referred to as ‘stiff’. The present paper reviews basic questions arising from combustion problems in applications of finite element techniques to the solution of problems associated with chemical kinetics, diffusion, waves, convection, etc. Finally, an example of a hydrogen‐oxygen reaction is presented for practical applications. Extension to the finite element modelling of turbulence, sprays, boundary layers, shock waves, etc. in combustion must await significant developments of numerical strategies associated with a more complete understanding of physical phenomena and chemical kinetics.
Arbitrary Lagrangian–Eulerianc finite element method for unsteady, convective, incompressible viscous free surface fluid flow
Authors: Ramaswamy Balasubramaniam , Kawahara Mutsuto 
Published: August 2005

AbstractIn this paper, free surface flow problems involving large free surface motions are analysed using finite element techniques. In solving these problems an arbitrary Lagrangian‐Eulerian (ALE) kinematical description of the fluid domain is adopted, in which the nodal points can be displaced independently of the fluid motion. This formulation leads to an easy and accurate treatment of fluid‐fluid interfaces, and greater distortions in the fluid motions can be handled than would be allowed by a purely Lagrangian method.This paper describes the basic methodology, presents finite element approximations and discusses such matters as stability, accuracy and rezoning. The generality and the advantage of the present method are discussed, and its versatility is demonstrated through a few numerical experiments.
Finite element flux‐corrected transport (FEM–FCT) for the euler and Navier–Stokes equations
Authors: Löhner Rainald , Morgan Ken , Peraire Jaime , Vahdati Mehdi 
Published: August 2005

AbstractA high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux‐corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady‐state examples are solved to illustrate the performance of the algorithm.
A numerical model for non‐linear wave diffraction around large offshore structures
Authors: Li Baoyuan , Lu Yulin 
Published: August 2005

AbstractThe present paper describes a numerical model for predicting the non‐linear wave forces exerted on large coastal or offshore structures. The interaction is calculated from a known initial condition corresponding to still water in the immediate vicinity of the structure. A prescribed incident wave of large amplitude approaches the structure. The boundary constraints on the free surface are considered in the fully non‐linear versions. Not far away from the structure, an artificial open boundary is considered with a suitable description of the radiation boundary condition for an incident wave propagating inwards, and in addition the scattering wave being absorbed. The finite difference method and time stepping are adopted for numerical calculation in the present model. For illustration the wave forces on a surface‐piercing vertical cylinder subjected to two different incident wave trains were evaluated. Reasonably good agreement could be obtained between the numerical results and the analytical solution given by Isaacson.1.
A design method for two‐dimensional cascades of turbomachinery blades
Authors: Hart M. , Whitehead D. S. 
Published: August 2005

AbstractA design method for two‐dimensional cascades of turbomachinery blades is presented. A finite element potential flow program is extended to allow fluid to transpire through the blade surface, the displaced surface streamline defining a new blade geometry. The potential changes are related linearly to the transpired flow rates. New surface velocities may then be specified as a function of surface distance, in accordance with boundary layer considerations. Closure and smoothness of the new blade are successfully achieved, while large changes in the blade geometry are possible.
Analysis of convective diffusion problem with first‐order chemical reaction by boundary element method
Authors: Okamoto Naotaka 
Published: August 2005

AbstractA boundary element method is presented for a steady state convective diffusion problem with a first‐order chemical reaction. In the chemical reaction system the usual conservation law for calculation of the diagonal components of the matrix H cannot be satisfied. Thus in the boundary element formulation the emphasis is laid on how to compute these diagonal components. The main aim of this paper is to present the method of numerical quadrature to obtain the principal values, using the splitting technique to treat the singular integration.
Identification of non‐Darcy groundwater flow parameters
Authors: Goodwill I. M. , Kalliontzis C. 
Published: August 2005

AbstractNon‐Darcy groundwater flow parameters are identified for three different flow systems. In the first system, which is essentially one‐dimensional, the parameters are determined by means of an integral method. A rectangular parametric grid is used for the identification of the non‐Darcy friction coefficients in the second system, which is two‐dimensional. The parameters in the third system, which involves a hybrid simulation of three‐dimensional flow, are optimized by adopting a constrained non‐linear programming technique. This technique combines Cauchy's steepest‐descent method together with the modeller's subjective judgement of the results at the end of each iterative step. The paper is concluded with a brief description of the additional research which is thought to be necessary before the difficulties of optimizing the non‐Darcy flow parameters can be overcome.
Unsteady boundary layer and its separation over a heated circular cylinder
Authors: Kim Jae‐Soo , Chang Keun‐Shik 
Published: August 2005

AbstractA numerical method is developed to solve the coupled unsteady laminar momentum and thermal boundary layers over a circular cylinder impulsively started from rest. The present non‐iterative finite difference method, which requires relatively fewer grid points in the reversed flow region than any other method, can easily handle the separating boundary layer flows. The results indicate that the present method has accuracy comparable with the earlier methods, while consuming computer time approximately one order of magnitude less.The present numerical method allowed investigation of the effect of buoyancy parameter on the starting boundary layer. The time‐dependent behaviour of the boundary layer is studied in terms of the appearance of the singularity, the distribution of skin friction and wall heat flux, and the wall position of the inflection point of the velocity profile. The transient as well as buoyancy‐dependent patterns of the streamlines and isotherms are also studied.
The boundary integral equation method for the solution of wave‐obstacle interaction
Authors: Williams K. J. 
Published: August 2005

AbstractThe boundary integral equation method constitutes the basis of a number of computer programs used for the solution of wave‐obstacle interaction problems. For the case of obstacles in a constant depth fluid, the method assumes that the velocity potential at any point in the fluid may be represented by a distribution of Green's function sources over the immersed surface of the obstacle. Application of the obstacle kinematic boundary condition gives rise to an integral equation which may be solved, using numerical discretization, for the unknown source strength distribution function. Subsequent evaluation of the discretized velocity potential permits evaluation of the hydrodynamic interaction parameters.A series of numerical solutions have been carried out for a range of substantially rectangular obstacles, in a two‐dimensional domain, using varying levels of immersed profile discretization. The results, presented in the form of fixed and floating mode wave reflection and transmission, together with the motion response of the floating obstacle, demonstrate the significant sensitivity of the evaluated parameters to variations in the level of discretization.
Preconditioned conjugate gradients for solving the transient Boussinesq equations in three‐dimensional geometries
Authors: Dupont S. , Marchal J. M. 
Published: August 2005

AbstractIn this paper we present a new version of the ‘modified finite element method’ (MFEM) presented by Gresho, Chan, Lee and Upson.1 The main modification of the original algorithm is the introduction of a cost‐effective and memory‐saving iterative solver for the discretized Poisson equation for the pressure. The vectorization of the preconditioner has been especially considered. For low Prandtl number problems we also split the advection‐diffusion operator of the energy equation into explicit and implicit parts. In that sense the present approach is related to the recent implicitization of the diffusive terms introduced by Gresho and Chan2 and by Gresho.3 The algorithm is applied to the study of buoyancy‐driven flow oscillations occuring in a horizontal crucible of molten metal under the action of a horizontal temperature gradient.
Two‐dimensional analysis of pressure transients in pipelines
Authors: Nathan G. K. , Tan J. K. , Ng K. C. 
Published: August 2005

AbstractThe paper presents a two‐dimensional model for the investigation of pressure transients in pipelines. The governing equations have been established and a method of solving the equations using the centre implicit method is presented. The theoretically predicted values are compared with the experimentally determined pressure transients for horizontal pipelines with a valve at the end. The two‐dimensional model gives results which are accurate than those of the one‐dimensional model and are in good agreement with the experimental results.
A total linearization method for solving viscous free boundary flow problems by the finite element method
Authors: Kruyt N. P. , Cuvelier C. , Segal A. , van der Zanden J. 
Published: August 2005

AbstractIn this paper a total linearization method is derived for solving steady viscous free boundary flow problems (including capillary effects) by the finite element method. It is shown that the influence of the geometrical unknown in the totally linearized weak formulation can be expressed in terms of boundary integrals. This means that the implementation of the method is simple. Numerical experiments show that the iterative method gives accurate results and converges very fast.
On the smoothing properties of the SIMPLE pressure‐correction algorithm
Authors: Shaw G. J. , Sivaloganathan S. 
Published: August 2005

AbstractA local mode Fourier analysis is used to assess the suitability of the SIMPLE pressure‐correction algorithm to act as a smoother in a multigrid method. The necessary ellipticity of the Navier‐Stokes equations and their discrete representation are established. The theoretical analysis is compared with practical results.
A Petrov‐Galerkin method for the numerical solution of the Bradshaw‐Ferriss‐Atwell turbulence model
Authors: Stewart I. B. , Unsworth K. 
Published: August 2005

AbstractThe Bradshaw‐Ferriss‐Atwell model for 2D constant property turbulent boundary layers is shown to be ill‐posed with respect to numerical solution. It is shown that a simple modification to the model equations results in a well‐posed system which is hyperbolic in nature. For this modified system a numerical algorithm is constructed by discretizing in space using the Petrov‐Galerkin technique (of which the standard Galerkin method is a special case) and stepping in the timelike direction with the trapezoidal (Crank‐Nicolson) rule. The algorithm is applied to a selection of test problems. It is found that the solutions produced by the standard Galerkin method exhibit oscillations. It is further shown that these oscillations may be eliminated by employing the Petrov‐Galerkin method with the free parameters set to simple functions of the eigenvalues of the modified system.
Magnetohydrodynamic flow in electrodynamically coupled rectangular ducts
Authors: Sezgin Munevver 
Published: August 2005

AbstractIn Sezgin1,2 the problems considered are the magnetohydrodynamic (MHD) flows in an electrodynamically conducting infinite channel and in a rectangular duct respectively, in the presence of an applied magnetic field. In the present paper we extend the solution procedure of these papers to two rectangular channels connected by a barrier which is partially conductor and partially insulator. The problem has been reduced to the solution of a pair of dual series equations and then to the solution of a Fredholm's integral equation of the second kind. The infinite series obtained were transformed to finite integrals containing Bessel Junctions of the second kind to avoid the computations of slowly converging infinite series and infinite integrals with oscillating integrands. The results obtained compared well with those of Butsenieks and Shcherbinin3 which were obtained for the perfectly conducting barrier separating the flows.
Mixed convection about a non‐isothermal vertical surface in a porous medium
Authors: Seetharamu K. N. , Dutta Pradip 
Published: August 2005

AbstractThe problem of mixed convection about non‐isothermal vertical surfaces in a saturated porous medium is analysed using boundary layer approximations. The analysis is made assuming that the surface temperature varies as an arbitrary function of the distance from the origin. A perturbation technique has been applied to obtain the solutions. Using the differentials of the wall temperature, which are functions of distance along the surface, as perturbation elements, universal functions are derived for various values of the governing parameter Gr/Re. Both aiding and opposing flows are considered. The universal functions obtained can be used to estimate the heat transfer and fluid velocity inside the boundary layer for any type of wall temperature variation. As a demonstration of the method, heat transfer results have been presented for the case of the wall temperature varying as a power function of the distance from the origin. The results have been studied for various combinations of the parameters Gr/Re and the power index m, taking both aiding and opposing flows into consideration. On comparing these results with those obtained by a similarity analysis, the agreement is found to be good.
On the self‐induced motion of vortex sheets
Authors: Bera Rajendra K. 
Published: August 2005

AbstractAn accurate numerical scheme has been devised to study the self‐induced motion of an infinitely thin, free vortex sheet of finite span in an unbounded, inviscid, incompressible fluid. The new numerical scheme has been tested against two vortex sheet problems for which exact solutions have also been obtained. The agreement between the numerical and exact solutions is excellent. The scheme has been further tested against two more examples for which analytical solutions for small times were available. Here too the agreement is excellent.
A unified approach to direct and inverse boundary layer solutions
Authors: Kaufman K. C. , Hoffman G. H. 
Published: August 2005

AbstractA unified approach is presented for solving the two‐dimensional incompressible boundary layer equations. Solutions are obtained for direct and inverse options using the same equation formulation by a simple interchange of boundary conditions. A modified form of the mechul function scheme obtains inverse solutions with specification of transformed wall shear, skin friction coefficient or displacement thickness distributions. Direct solutions may be obtained without altering the block tridiagonal structure of the system by simply requiring no corrections on the streamwise pressure gradient parameter. Fourth‐order spline discretization approximates normal derivatives with two‐ and three‐point backward differences approximating streamwise derivatives, yielding a fully implicit solution method. The resulting spline/finite difference equations are solved by Newton‐Raphson iteration together with partial pivoting. The results of the study demonstrate the importance of proper linearization of all equations. The successful use of spline discretization is also tied to the use of strong two‐point boundary conditions at the wall for cases involving reversed flow. Numerical solutions are presented for several non‐similar flows and compared with published results.
A finite element model for the dissolution of corrosion pits in the presence of fluid flow
Authors: Harb John N. , Alkire Richard C. 
Published: August 2005

AbstractSimulation of the dissolution of an active corrosion pit in the presence of fluid flow was carried out with the use of finite element techniques. The model included multiple species in solution, reaction equilibria and transport by diffusion, convection and migration. The mathematical model was used to examine the effect of fluid flow on the pitting of nickel in neutral chloride solution. The pit dissolution rate was found to decrease with increasing flow owing to potential field effects. The capabilities demonstrated in this paper represent a significant advancement in the modelling of pitting corrosion phenomena.
Trefftz method for hydrodynamic pressure on rigid dams with non‐vertical upstream face
Authors: Wu Yung‐Chao , Yu Ding‐Jong 
Published: August 2005

AbstractBased on a two‐dimensional potential flow theory, earthquake‐induced hydrodynamic pressures on a rigid dam with a non‐vertical upstream face are examined by the Trefftz method. The effect of surface waves on the hydrodynamic pressure distribution is discussed in detail. Numerical values are given for different wave effect parameters and different geometries of the dam–water interface.
Velocity–pressure integrated versus penalty finite element methods for high‐Reynolds‐number flows
Authors: Kim S.‐W. , Decker Rand A. 
Published: August 2005

AbstractVelocity–pressure integrated and consistent penalty finite element computations of high‐Reynolds‐number laminar flows are presented. In both methods the pressure has been interpolated using linear shape functions for a triangular element which is contained inside the biquadratic flow element. It has been shown previously that the pressure interpolation method, when used in conjunction with the velocity‐pressure integrated method, yields accurate computational results for high‐Reynolds‐number flows. It is shown in this paper that use of the same pressure interpolation method in the consistent penalty finite element method yields computational results which are comparable to those of the velocity–pressure integrated method for both the velocity and the pressure fields. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine grid finite difference computational results. Advantages and disadvantages of the two finite element methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid‐driven cavity flow of Reynolds number 10 000, a laminar backward‐facing step flow and a laminar flow through a nest of cylinders.
A multigrid method for steady incompressible Navier–Stokes equations based on partial flux splitting
Authors: Dick E. 
Published: August 2005

AbstractFlux splitting is applied to the convective part of the steady Navier–Stokes equations for incompressible flow. Partial upwind differences are introduced in the split first‐order part, while central differences are used in the second‐order part. The discrete set of equations obtained is positive, so that it can be solved by collective variants of relaxation methods. The partial upwinding is optimized in the same way as for a scalar convection–diffusion equation, but involving several Peclet numbers. It is shown that with the optimum partial upwinding accurate results can be obtained. A full multigrid method in W‐cycle form, using red–black successive under‐relaxation, injection and bilinear interpolation, is described. The efficiency of this method is demonstrated.
Performance of iterative methods for Newtonian and generalized Newtonian flows
Authors: Carey G. F. , Wang K. C. , Joubert W. D. 
Published: August 2005

AbstractWe consider the use of accelerated gradient‐type iterative methods for solution of Newtonian and certain non‐Newtonian (power‐law and Bingham models) viscous flow problems. The formulations are based on penalty and mixed finite element methods, and such factors as the effect of the penalty parameter, asymmetry, continuation and preconditioning are examined.
Process splitting of the boundary conditions for the advection–dispersion equation
Authors: Aiyesimoju Kolawole O. , Sobey Rodney J. 
Published: August 2005

AbstractRational strategies are considered for the specification of the intermediate boundary condition at an inflow boundary where process splitting (fractional steps) is adopted in solving the advection–dispersion equation. Three lowest‐order methods are initially considered and evaluation is based on comparisons with an analytical solution. For flow and dispersion parameter ranges typical of rivers and estuaries, the given boundary condition for the complete advection–dispersion equation at the end of the complete time step provides a satisfactory estimate of the intermediate boundary value. This was further confirmed by the development and evaluation of two higher‐order methods. These required non‐centred discrete approximations for spatial derivatives, which offset any special advantages from the higher truncation error order.
Finite element solution of an enclosed turbulent diffusion flame
Authors: Benim A. C. 
Published: August 2005

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