bluuebunny/crossref_metadata_2025_split huggingface dataset:
Prediction of incompressible flow separation with the approximate factorization technique
Authors: Michelassi V. , Benocci C. 
Published: August 2005

AbstractThis paper describes one application of the approximate factorization technique to the solution of incompressible steady viscous flow problems in two dimensions.The velocity‐pressure formulation of the Navier‐Stokes equations written in curvilinear non‐orthogonal co‐ordinates is adopted. The continuity equation is replaced with one equation for the pressure by means of the artificial compressibility concept to obtain a system parabolic in time. The resulting equations are discretized in space with centred finite differences, and the steady state solution obtained by a time‐marching ADI method requiring to solve 3 x 3 block tridiagonal linear systems.An optimized fourth‐order artificial dissipation is introduced to damp the numerical instabilities of the artificial compressibility equation and ensure convergence.The resulting solver is applied to the prediction of a wide variety of internal flows, including both streamlined boundaries and sharp corners, and fast convergence and good results obtained for all the configurations investigated.
Improved relaxation schemes for transonic potential calculations
Authors: Hafez M. , Lovell D. 
Published: August 2005

AbstractA block relaxation scheme, grouped in a red‐black ordering, is applied to transonic aerofoil calculations using body‐fitted co‐ordinates. The scheme is simple and easily vectorizable. Detailed comparisons with the approximate factorization method (AF2) are presented and it is shown that the new scheme is competitive in all cases considered. Transonic results, of engineering accuracy, on an 0‐type grid of 149 × 30 points, are usually obtained within 200 iterations (≃ 40s on a Cyber 175).
Entropy and vorticity corrections for transonic flows
Authors: Hafez M. , Lovell D. 
Published: August 2005

AbstractDifferent models for inviscid transonic flows are examined. The common assumptions that the flow is isentropic and irrotational are critically evaluated. Entropy and vorticity correction procedures for potential and stream function formulations are presented, together with the details of the treatment of shocks and wakes, and drag and lift calculations. The non‐uniqueness problem of the potential formulation is studied using different artificial viscosity forms. Numerical results are compared with Euler solutions.
A boundary‐type finite element model for water surface wave problems
Authors: Kashiyama Kazuo , Kawahara Mutsuto 
Published: August 2005

AbstractA new combinative method of boundary‐type finite elements and boundary solutions is presented to study wave diffraction‐refraction and harbour oscillation problems. The numerical model is based on the mild‐slope equation. The key feature of this method is that the discretized matrix equation can be formulated only by the calculation of a line integral, since the interpolation equation which satisfies the governing equation in each element is used. The numerical solutions are compared with existing analytical, experimental, observed and other numerical results. The present method is shown to be an effective and accurate method for water surface wave problems.
A numerical method for acoustic oscillations in tubes
Authors: Gary John M. 
Published: August 2005

AbstractA numerical method to obtain the neutral curve for the onset of acoustic oscillations in a helium‐filled tube is described. Such oscillations can cause a serious heat loss in the plumbing associated with liquid helium dewars. The problem is modelled by a second‐order, ordinary differential eigenvalue problem for the pressure perturbation. The numerical method to find the eigenvalues and track the resulting points along the neutral curve is tailored to this problem. The results show that a tube with a uniform temperature gradient along it is much more stable than one where the temperature suddenly jumps from the cold to the hot value in the middle of the tube.
Flux difference splitting for the Euler equations in one spatial co‐ordinate with area variation
Authors: Glaister P. 
Published: August 2005

AbstractAn approximate (linearized) Riemann solver is presented for the solution of the Euler equations of gas dynamics in one spatial co‐ordinate. This includes cylindrically and spherically symmetric geometries and also applies to narrow ducts with area variation. The method is Roe's flux difference splitting with a technique for dealing with source terms. The results of two problems, a spherically divergent infinite shock and a converging cylindrical shock, are presented. The numerical results compare favourably with those of Noh's recent survey and also with those of Ben‐Artzi and Falcovitz using a more complicated Riemann solver.
A finite element convergence study for shear‐thinning flow problems
Authors: Karagiannis A. , Mavridis H. , Hrymak A. N. , Vlachopoulos J. 
Published: August 2005

AbstractThe solution of the non‐linear set of equations arising from the application of the finite element method to non‐Newtonian fluid flow problems often requires large amounts of computer time. Four iteration schemes (Picard, Newton‐Raphson, Broyden and Dominant Eigenvalue method) are compared in three different flow geometries using a shear‐thinning fluid model. Points of comparison involve the computer time necessary to converge the equations, ease of implementation, radius of convergence and rate of convergence.
A boundary element formulation for natural convection problems
Authors: Kitagawa Koichi , Wrobel Luiz C. , Brebbia Carlos A. , Tanaka Masataka 
Published: August 2005

AbstractThis paper presents a boundary element formulation employing a penalty function technique for two‐dimensional steady thermal convection problems. By regarding the convective and buoyancy force terms in Navier‐Stokes equations as body forces, the standard elastostatics analysis can be extended to solve the Navier‐Stokes equations. In a similar manner, the standard potential analysis is extended to solve the energy transport equation. Finally, some numerical results are included, for typical natural convection problems, in order to demonstrate the efficiency of the present method.
Laminar natural convection in a partially divided rectangular cavity at high Rayleigh number
Authors: Winters Keith H. 
Published: August 2005

AbstractFinite element predictions of two‐dimensional laminar natural convection in a partially divided rectangular cavity at high Rayleigh number are presented. The walls are differentially heated, the horizontal surfaces are insulated and the cavity contains a partial vertical divider which is centrally located and whose height is varied. Detailed results are presented for an aluminium half‐divider in water for Rayleigh number up to 1011 and compared directly with recent experiments in a cavity of aspect ratio 1/2. The predicted flow and heat transfer are in good agreement with the measurements and confirm the existence of a high Rayleigh number regime with characteristic behaviour that differs significantly from that found at lower Rayleigh number. In addition, the effects of the divider height, the divider conductivity, the fluid Prandtl number and the cavity aspect ratio are studied. The results show that a direct simulation of the complex flow and heat transfer that occurs in partially divided cavities is possible for realistic physical conditions.
Turbulent flow in a tube containing an offset rod
Authors: Rapley C. W. 
Published: August 2005

AbstractA numerical finite volume prediction method for arbitrary‐shaped passages has been applied to the case of fully developed axial turbulent flow past a rod eccentrically placed in a circular tube. The numerical method was based on an orthogonal curvilinear mesh and employed an algebraic stress transport model to calculate the full three‐dimensional velocity field directly from the governing partial differential equations. This study is one of a series of applications of this prediction method to a range of different non‐circular passages that have been made in order to establish the capabilities and usefulness of this type of procedure. The present eccentric rod case was the subject of a comprehensive experimental investigation by Kacker1 which has enabled a detailed comparison to be made between the present predictions and the measurements. This comparison included local distributions of axial velocity, wall shear stress and secondary velocities; and although found to be satisfactory overall, some differences in detail revealed possible shortcomings in the measurement of secondary flow. This, together with other previously reported cases, indicates, that, although the present method cannot be expected to replace experiment in providing turbulent passage flow data, it has an important role to play in interpreting and supplementing experiments.
The numerical solution of Stokes flow in a domain with re‐entrant boundaries by the boundary element method
Authors: Mitra A. K. , Ingber M. S. 
Published: August 2005

AbstractNumerical solutions are presented for two‐dimensional low Reynolds number flow in a rotating tank with stationary barriers. The boundary element method is employed, assuming straight panels and quadratic source distribution. The feasibility of repositioning the nodes as a way to minimize the error is explored. A stretching parameter places smaller elements near the re‐entrant regions. Elementary error analysis shows uniform improvement in the solution with stretching. The changing eddy pattern for different numbers and sizes of the barriers is compared with experimental results.
Transient three‐dimensional flow in an enclosure with a hot spot on a vertical wall
Authors: Kuhn D. , Oosthuizen P. H. 
Published: August 2005

AbstractA numerical method for the solution of the vector potential/vorticity vector formulation of the transient, fully three‐dimensional Navier‐Stokes energy and continuity equations has been applied to simulate the development of natural convective flow within a ‘box’ after a sudden temperature change on a vertical portion of the wall. Only one cavity size has been considered, this having a vertical height of three times its width and a horizontal length of six times its width. A single heated rectangular hot spot or ‘element’ on an otherwise adiabatic wall is centred between the vertical end walls. The opposite vertical wall is held at the intial fluid temperature, and all other walls are assumed to be adiabatic. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy force. The numerical method is an underrelaxation Gauss‐Seidel method using finite differencing at each time step. Solutions have been obtained for a Prandtl number of 0.71, for Rayleigh numbers, based on the width, of between 0 and 100000 and for a number of heated element locations and sizes.
Numerical solutions of high‐Re recirculating flows in vorticity‐velocity form
Authors: Guj G. , Stella F. 
Published: August 2005

AbstractA numerical method for computing high‐Re laminar steady flows is presented. The incompressible Navier‐Stokes equations are expressed in terms of vorticity‐velocity variables, discretized in space by finite differences on a staggered grid and advanced in time by a scalar alternating direction implicit (ADI) procedure, which allows a fully vectorized computer code. The accuracy and efficiency of the present formulation are discussed in comparison with the standard ω‐ψ and u, v, P forms. Numerical results are presented for two test cases: the driven cavity at Re up to 5000 and the backward‐facing step at Re up to 800.
A Navier‐Stokes code for S‐shaped diffusers—a review
Authors: Loeffler Albert L. 
Published: August 2005

AbstractThree‐dimensional, compressible, internal flow solutions obtained using a thin‐layer Navier‐Stokes code are presented. The code, formulated by P.D. Thomas, is based on the Beam‐Warming implicit factorization scheme; the boundary conditions also are formulated implicitly. Turbulent flow is treated through the use of the Baldwin‐Lomax two‐layer, algebraic eddy viscosity model. Steady‐state solutions are obtained by solving numerically the time‐dependent equations from given initial conditions until the time‐dependent terms become negligible. The configuration considered is a rectangular cross‐section, S‐shaped centreline diffuser duct with an exit/inlet area ratio of 2.25. The Mach number at the duct entrance is 0.9, with a Reynolds number of 5.82 × 105. Convergence to the final results required about 2700 time steps or 11 hours of CPU time on our CRAY‐1M computer. The averaged residuals were reduced by about two orders of magnitude during the computations. Several regions of separated flow exist within the diffuser. The separated flow region on the upper wall, downstream of the second bend, is by far the largest and extends to the exit plane.
Boundary‐type finite element method for wave propagation analysis
Authors: Kawahara Mutsuto , Sakurai Hideyuki , Kashiyama Kazuo 
Published: August 2005

AbstractThe boundary‐type finite element method has been investigated and applied to the Helmholz and mild‐slope equations. Four types of interpolation function are examined based on trigonometric function series. Three‐node triangular, four‐node quadrilateral, six‐node triangular and eight‐node quadrilateral elements are tested; these are all non‐conforming elements. Three types of numerical example show that the three‐node triangular and four‐node quadrilateral elements are useful for practical analysis.
Laminar flow and heat transfer in a periodically converging‐diverging channel
Authors: Garg Vijay K. , Maji P. K. 
Published: August 2005

AbstractA finite difference solution for laminar viscous flow through a sinusoidally curved converging‐diverging channel is presented. The physical wavy domain is transformed into a rectangular computational domain in order to simplify the application of boundary conditions on the channel walls. The discretized conservation equations for mass, momentum and energy are derived on a control volume basis. The pseudo‐diffusive terms that arise from the co‐ordinate transformation are treated as source terms, and the resulting system of equations is solved by a semi‐implicit procedure based on line relaxation. Results are obtained for both the developing and the fully developed flow for a Prandtl number of 0.72, channel maximum width‐to‐pitch ratio of 1.0, Reynolds number ranging from 100 to 500 and wall amplitude‐to‐pitch ratio varying from 0.1 to 0.25. Results are presented here for constant fluid properties and for a prescribed wall enthalpy only.
Generalized potential flow theory and direct calculation of velocities applied to the numerical solution of the Navier‐Stokes and the Boussinesq equations
Authors: Zijl Wouter 
Published: August 2005

AbstractA formulation based on three scalar functions or potentials is applied to analyse the Navier‐Stokes and Boussinesq equations in three dimensions. In this formulation an explicit expression for the pressure exists, the so‐called generalized Bernoulli equation. Therefore the scalar functions formulation may be considered as a generalization of the well‐known potential flow and Bernoulli theory for irrotational fluid motion. The many advantages of this formulation applied to three‐dimensional Navier‐Stokes and Boussinesq flow will be discussed, and a numerical example is given as an illustration.
Magnetohydrodynamic flow past a porous rotating disk in a circular magnetic field
Authors: Kishore Kumar S. , Thacker William I. , Watson Layne T. 
Published: August 2005

AbstractThis paper studies the effects of a circular magnetic field on the flow of a conducting fluid about a porous rotating disk. Using modern quasi‐Newton and globally convergent homotopy methods, numerical solutions are obtained for a wide range of magnetic field strengths, suction and injection velocities and Alfven and disk speeds. Results are presented graphically in terms of three non‐dimensional parameters. There is excellent agreement with previous work and asymptotic formulae.
Acceleration of the pressure correction method for a rotating Navier‐Stokes problem
Authors: Lonsdale G. , Walsh J. E. 
Published: August 2005

AbstractThe behaviour of the pressure correction method is studied for the solution of the incompressible steady‐state Navier‐Stokes and continuity equations in a rotating cylindrical‐polar co‐ordinate system, the specific problem being that of laminar source‐sink flow between two corotating discs. Modifications to improve the linearization and the handling of the rotation terms are introduced, and we compare three extended pressure correction schemes and also the use of a multigrid algorithm in part of the calculation procedure as a linear solver.
Finite element, stream function‐vorticity solution of secondary flow in the channels of a rod bundle
Authors: Slagter W. 
Published: August 2005

AbstractA finite element method has been applied to predict the overall features of the fully developed turbulent flow in the non‐circular channels of a rod bundle. The finite element discretization is based on the conventional Galerkin method using an isoparametric quadrilateral element with mixed interpolation.The primary axial flow and turbulent kinetic energy distributions have been predicted for fully developed turbulent flow conditions right up to the wall. The secondary velocity is represented by the stream function‐vorticity formulation and the no‐slip boundary conditions are explicitly introduced in the nonlinear equations by a boundary vorticity formula. The Newton‐Raphson method is applied to the stream function‐vorticity equations and solved simultaneously by the frontal solution technique.A one‐equation eddy viscosity model of turbulence and an algebraic stress transport model have been used to predict primary axial velocity, secondary velocities and turbulent kinetic energy. The predictions obtained for a central subchannel of an equilateral‐triangular rod array with p/d= 1.3 are in reasonable agreement with experimental data.
Magnetohydrodynamic flow on a half‐plane
Authors: Sezgin Münevver 
Published: August 2005

AbstractWe investigate the magnetohydrodynamic flow (MHD) on the upper, half of a non‐conducting plane for the case when the flow is driven by the current produced by an electrode placed in the middle of the plane. The applied magnetic field is perpendicular to the plane, the flow is laminar, uniform, steady and incompressible. An analytical solution has been developed for the velocity field and the induced magnetic field by reducing the problem to the solution of a Fredholm's integral equation of the second kind, which has been solved numerically. Infinite integrals occurring in the kernel of the integral equation and in the velocity and magnetic field were approximated for large Hartmann numbers by using Bessel functions. As the Hartmann number M increases, boundary layers are formed near the non‐conducting boundaries and a parabolic boundary layer is developed in the interface region. Some graphs are given to show examples of this behaviour.
Non‐linear transient phenomena in a complex recirculating flow: A numerical investigation
Authors: Freitas Christopher J. , Street Robert L. 
Published: August 2005

AbstractA role of numerical methods in engineering research is illustrated in the present work, namely the use of computer algorithms as experimental facilities. A complex recirculating flow in a three‐dimensional cavity was simulated and an extensive data base was generated which complements data measured in concurrent physical experiments. The objective of this numerical investigation was to improve understanding of physical phenomena in recirculating flows. The dominant physical phenomena in this shear‐driven flow simulation are Taylor‐Görtler vortices. These structures are intimately coupled with the primary recirculating flow and the effects of end‐wall viscous damping.
Waves generated by an inclined‐plate wave generator
Authors: Wu Yung‐Chao 
Published: August 2005

AbstractThis paper describes the characteristics of small‐amplitude waves generated by a sinusoidally oscillating, inclined paddle‐type wavemaker operating in a constant‐depth channel. Two‐dimensional, linearized potential flow is assumed. A semi‐analytical method, the boundary collocation method, is used to establish the relationship between wave amplitude and paddle stroke. The numerical results are compared with the numerical results of the boundary integral equation method. It is found that the boundary collocation method is simpler and more flexible to implement and faster to compute. In addition, the numerical results are in reasonably good agreement with the laboratory experimental data. For the vertical wavemaker, which is a special case of the inclined wavemaker, an analytical series solution can be found. By using the boundary collocation method and the boundary integral equation method to solve the vertical wavemaker problem and comparing the results with the analytical series solution, it is found that the boundary collocation method yields a solution which is much more accurate than that from the boundary integral equation method. Finally, the relationships between wave amplitude and paddle stroke are established for different inclinations of the paddle‐type wavemaker, based on the boundary collocation method.
A frequency–time domain finite element model for tidal circulation based on the least‐squares harmonic analysis method
Authors: Westerink J. J. , Connor J. J. , Stolzenbach K. D. 
Published: August 2005

AbstractAn iterative type harmonic finite element model is developed for solving the full non‐linear form of the shallow water equations. The scheme iteratively updates time histories of the non‐linear terms which are then harmonically decomposed and used as forcing terms for the linear sets of equations which result from the harmonic separation of the shallow water equations.A least‐squares harmonic analysis procedure is used to decompose the non‐linear forcing terms. This procedure allows for the very efficient separation of extremely closely spaced harmonics, since it is highly selective with respect to the frequencies it considers. In addition tailoring the procedure and using very specific time steps and sampling periods significantly reduces the number of time samplings points required. In conjunction with the iterative nature of our scheme, the least‐squares procedure makes the scheme entirely general, allows for the direct assessment of all tidal constituents, including compound tides, and permits the clear cut and complete investigation of their mutual interaction through the non‐linearities. In addition this procedure readily computes very‐low‐frequency or residual type circulations.The FE formulation used shows a very low degree of spurious oscillations while remaining quite simple to implement. This control on nodal oscillations is especially important due to the energy transfer mechanisms involved in this type of iterative scheme.In an example application the effects of the various non‐linear overtide and compound tide type interactions are examined. It is demonstrated that not only are compound tides significant relative to the overtides, but they also influence the overtides.