bluuebunny/crossref_metadata_2025_split huggingface dataset:
Comparison of two numerical methods for the solution of non‐Newtonian flow in ducts
Authors: Liu Ta‐Jo , Lin Ho‐May , Hong Chin‐Nan 
Published: August 2005

AbstractTwo numerical methods, the Galerkin finite element method (FEM) and the boundary‐fitted co‐ordinate transformation method (BFCTM), have been applied to solve inelastic non‐Newtonian fluid flow in ducts of irregular cross‐section. Three representative fluid models, namely the power‐law, the Ellis and the Bingham models, have been analysed. The application of the FEM is straightforward, while for the BFCTM the accurate estimation of viscosity on the duct boundary and the proper mesh adjustment appear to be critical for generating convergent solutions. A detailed comparison of the two numerical methods in terms of volumetric flow rate, axial velocity, shear rate, viscosity and CPU time is given. Both methods can generate accurate solutions of velocity over a wide range of variables, but the FEM requires much less computing time to reach the same level of accuracy. Only the BFCTM can be used to approximate shear rate and viscosity with reasonable accuracy.
Prediction of oscillating thick cambered aerofoil aerodynamics by a locally analytic method
Authors: Chiang Hsiao‐Wei D. , Fleeter Sanford 
Published: August 2005

AbstractA complete first‐order model and locally analytic solution method are developed to analyse the effects of mean flow incidence and aerofoil camber and thickness on the incompressible aerodynamics of an oscillating aerofoil. This method incorporates analytic solutions, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual grid elements. The velocity potential is separated into steady and unsteady harmonic parts, with the unsteady potential further decomposed into circulatory and non‐circulatory components. These velocity potentials are individually described by Laplace equations. The steady velocity potential is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating aerofoil. A body‐fitted computational grid is then utilized. Solutions for both the steady and the coupled unsteady flow fields are obtained by a locally analytic numerical method in which locally analytic solutions in individual grid elements are determined. The complete flow field solution is obtained by assembling these locally analytic solutions. This model and solution method are shown to accurately predict the Theodorsen oscillating flat plate classical solution. Locally analytic solutions for a series of Joukowski aerofoils demonstrate the strong coupling between the aerofoil unsteady and steady flow fields, i.e. the strong dependence of the oscillating aerofoil aerodynamics on the steady flow effects of mean flow incidence angle and aerofoil camber and thickness.
A stable least‐squares finite element method for non‐linear hyperbolic problems
Authors: Jiang B. N. , Carey Graham F. 
Published: August 2005

AbstractA class of stable least‐square finite element methods for non‐linear hyperbolic problems is developed and some exploratory studies made. The methods are based on modifying the L2‐norm of the. residual and a related approximation to the H1‐norm of the residual. The effect of the additional terms in these residual functionals is to introduce a dissipative effect proportional to the solution gradient. This acts to stabilize the solution for non‐linear hyperbolic problems which generate shocks. Numerical results for a one‐dimensional nozzle and shock tube problem demonstrate the accuracy and stability of the method. Results are for an implicit scheme and calculations for linear, quadratic and cubic elements are given.
Axially symmetric cavitation flow at small cavitation numbers
Authors: Dagan A. 
Published: August 2005

AbstractA method for computing the drag coefficient of a body in an axially symmetric, steady‐state cavitation flow is presented. A ‘vortex ring’ distribution along the wetted body surface and along the cavity interface is assumed. Since the location of the cavitation interface is unknown a priori, an iterative procedure is used, where, for the first stage, an arbitrary cavitation interface is assumed. The flow field is then solved, and by an iterative process the location of the cavitation interface is corrected. Even though the flow field is governed by the linear Laplace equation, strong non‐linearity resulting from the kinematic boundary conditions appears along the cavitation interface. An improved numerical scheme for solving the dual Fredholm integral equations is obtained by formulating high‐order approximations to the singular integrals in order to reduce the matrix dimensions. Good agreement is found between the numerical results of the present work, experimental results and other solutions.
On the accuracy of least‐squares finite elements for a first‐order conservation equation
Authors: Wilders P. 
Published: August 2005

AbstractThe numerical solution of a single first‐order conservation equation by a least‐squares finite element method is considered. Isoparametric bilinear quadrilateral elements are used. The accuracy is studied numerically and it is shown that the discrete equations associated with nodal points on the boundaries should be modified in order to obtain an accurate numerical solution.
Two‐equation (k, ϵ) turbulence computations by the use of a finite element model
Authors: Utnes Torbjørn 
Published: August 2005

AbstractA finite element technique is presented and applied to some one‐ and two‐dimensional turbulent flow problems. The basic equations are the Reynolds averaged momentum equations in conjunction with a two‐equation (k, ϵ) turbulence model. The equations are written in time‐dependent form and stationary problems are solved by a time iteration procedure. The advection parts of the equations are treated by the use of a method of characteristics, while the continuity requirement is satisfied by a penalty function approach. The general numerical formulation is based on Galerkin's method. Computational results are presented for one‐dimensional steady‐state and oscillatory channel flow problems and for steady‐state flow over a two‐dimensional backward‐facing step.
Improving the accuracy of the least‐squares finite element approximation of the linearized steady Euler equations by an embedding method
Authors: Wilders P. 
Published: August 2005

AbstractThe standard least‐squares finite element method for the linearized Euler equations turns out to be inaccurate. This method is studied in detail for a system of composite type, obtained by transformation of the linearized Euler equations. The shortcomings of the method are clarified and an embedding method is constructed. It is shown numerically that this new method is O(h2)‐accurate.
Dynamics of non‐Newtonian fluid interfaces in a porous medium: Incompressible fluids
Authors: Pascal H. , Pascal F. 
Published: August 2005

AbstractThis paper concerns the applications of frontal advance theory to the dynamics of a moving flat interface in a porous medium, when both displacing and displaced fluids are of power law behaviour. The rheological effects of non‐Newtonian behaviour of these fluids on the interface position and its velocity are numerically illustrated and discussed with regard to the practical implications in oil displacement mechanisms. The results obtained should be useful in finding an optimal policy of injection in order to control the dynamics of the moving interface in field projects of enhanced oil recovery floods.
A comment on the paper ‘finite difference methods for the stokes and Navier‐Stokes equations’ by J. C. Strikwerda
Authors: Roache Patrick J. 
Published: August 2005

AbstractThis work comments on a recent paper by J. C. Strikwerda in SIAM Journal on Scientific and Statistical Computing, in an attempt to clear up the evident confusion regarding the use of a Poisson equation for pressure in incompressible Navier‐Stokes solutions.
Evaluation of FIDAP on some classical laminar and turbulent benchmarks
Authors: Sohn J. L. 
Published: August 2005

AbstractNumerical solutions of the Fluid Dynamics Analysis Package (FIDAP) for some laminar and turbulent flow problems, namely (1) two‐dimensional laminar flow inside a wall‐driven cavity, (2) two‐dimensional laminar flow over a backward‐facing step and (3) two‐dimensional turbulent flow over a backward‐facing step, are presented. The consistent integration penalty finite element method is used with Q2/P1 (nine‐node biquadratic velocity with linear discontinuous pressure) finite elements. Results of FIDAP on the above problems are compared with other numerical solutions and experimental data to evaluate its numerical accuracy. The influence of streamline upwinding is also investigated for all the test cases.
Heat exchanger analysis on a MicroVAX II/GPX
Authors: Haught Alan F. 
Published: August 2005

AbstractThe finite element code FIDAP was used to examine the fluid flow path within a flat plate tube/fin heat exchanger and the resulting heat transfer from the fins and tube walls. The mathematical formulation, mesh development and analysis procedure are presented, and the results obtained are compared with experimental observations of the fluid flow and measurements of the fluid heating. This problem illustrates the capabilities of finite element techniques for analysing complex three‐dimensional convection‐dominated heat transfer, and demonstrates the scope of problems which can be addressed on a Micro VAX II/GPX workstation.
Developing flows in narrow channels, containing heated obstacles
Authors: Torok Dennis , Gronseth Rosanne 
Published: August 2005

AbstractThe use of numerical techniques to augment experimentally collected temperature data of electrical components is illustrated. FIDAP, a finite element CFD code, is used to generate the numerical results. Comparisons of the numerical results with experimental data of HaCohen, experimentally derived correlations of Wirtz and Dykshoorn and numerical results of Heaton et al. are given. A discussion of modelling techniques, mesh refinement, numerical error and stability is presented with suggestions for improvement of flow models. The results generated by FIDAP, using 2D models, compare favourably (to within 10%) with the experimental data of HaCohen. The results indicate the possibility of augmenting experimental data collection with numerical results, at least in the regions of laminar and low turbulent flow.
Euler flow solutions for transonic shock wave–boundary layer interaction
Authors: Koren Barry 
Published: August 2005

AbstractSteady 2D Euler flow computations have been performed for a wind tunnel section, designed for research on transonic shock wave–boundary layer interaction. For the discretization of the steady Euler equations, an upwind finite volume technique has been applied. The solution method used is collective, symmetric point Gauss–Seidel relaxation, accelerated by non‐linear multigrid. Initial finest grid solutions have been obtained by nested iteration. Automatic grid adaptation has been applied for obtaining sharp shocks. An indication is given of the mathematical quality of four different boundary conditions for the outlet flow. Two transonic flow solutions with shock are presented: a choked and a non‐choked flow. Both flow solutions show good shock capturing. A comparison is made with experimental results.
Are fem solutions of incompressible flows really incompressible? (or how simple flows can cause headaches!)
Authors: Pelletier Dominique , Fortin Andre , Camarero Ricardo 
Published: August 2005

AbstractIt is generally accepted that mixed and penalty finite element methods can routinely solve the incompressible Navier–Stokes equations. This paper shows by means of simple examples that problems can arise even for the simpler Stokes equations. The causes of the problem fall in either of two categories: round‐off and ill conditioning, or a poor choice of pressure discretization. Nonsensical solutions can be obtained. Computation of the discrete divergence of the flow field is a simple and powerful tool to diagnose such conditions. In the first part of the paper several simple techniques for minimizing the effect of round‐off are reviewed. In the second part it is shown that, for coupled flow problems, care must be exercised in the choice of the pressure approximation. A unified treatment of various observations by different workers is presented. This should prove useful for general users of the finite element method.
Numerical simulation of axisymmetric turbulent flow in combustors and diffusers
Authors: Yung Chain‐Nan , Keith Theo. G. , De Witt Kennet H. J. 
Published: August 2005

AbstractNumerical studies of turbulent flow in an axisymmetric 45° expansion combustor and bifurcated diffuser are presented. The Navier‐Stokes equations incorporating a k–ϵ model were solved in a non‐orthogonal curvillinear co‐ordinate system. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass flux. Three finite differencing methods—hybrid, quadratic upwind and skew upwind—were used to represent the convection terms. Results were compared with existing experimental data. In general, good agreement between predicted and measured values was obtained.
Efficient quadrature for a boundary element method to compute three‐dimensional Stokes flow
Authors: Varnhorn Werner 
Published: August 2005

AbstractA collocation‐type boundary element method based on bilinear B‐splines is used for the numerical solution of the Stokes Dirichlet problem in bounded domains D ⊂ R3. The computation of the influence matrix requires the numerical evaluation of weakly singular integrals on the domain boundary if the usual double‐layer potential ansatz is chosen. Here mostly standard methods with disjoint grids for collocation and integration are used. We develop a special integration scheme based on triangular co‐ordinates near the singularity and show its efficiency compared with the method mentioned above.
A new look at Theodorsen's method in aerofoil theory
Authors: Bera Rajendra K. 
Published: August 2005

AbstractTheodorsen's method for calculating the incompressible potential flow past an aerofoil is viewed afresh. It is found that some simple modifications to the computational process make the computations relatively faster, easier and more accurate. The new modifications are applicable to the analysis of conventional aerofoils with up to moderate thickness and camber ratios. Several examples are presented to show the effectiveness of the modifications.
Numerical simulation of the hydrodynamic interaction between a sedimenting particle and a neutrally buoyant particle
Authors: Ingber Marc S. 
Published: August 2005

AbstractA new method for the simulation of the translational and rotational motions of a system containing a sedimenting particle interacting with a neutrally buoyant particle has been developed. The method is based on coupling the quasi‐static Stokes equations for the fluid with the rigid body equations of motion for the particles. The Stokes equations are solved at each time step with the boundary element method. The stresses are then integrated over the surface of each particle to determine the resultant forces and moments. These forces and moments are inserted into the rigid body equations of motion to determine the translational and rotational motions of the particles. Unlike many other simulation techniques, no restrictions are placed on the shape of the particles. Superparametric boundary elements are employed to achieve accurate geometric representations of the particles. The simulation method is able to predict the local fluid velocity, resolve the forces and moments exerted on the particles, and track the particle trajectories and orientations.
Three‐dimensional unsteady flow simulations: Alternative strategies for a volume‐averaged calculation
Authors: Perng Chin‐Yuan , Street Robert L. 
Published: August 2005

AbstractThis work builds on a SIMPLE‐type code to produce two numerical codes of greatly improved speed and accuracy for solution of the Navier–Stokes equations. Both implicit and explicit codes employ an improved QUICK (quadratic upstream interpolation for convective kinematics) scheme to finite difference convective terms for non‐uniform grids. The PRIME (update pressure implicit, momentum explicit) algorithm is used as the computational procedure for the implicit code. Use of both the ICCG (incomplete Cholesky decomposition, conjugate gradient) method and the MG (multigrid) technique to enhance solution execution speed is illustrated. While the implicit code is first‐order in time, the explicit is second‐order accurate. Two‐ and three‐dimensional forced convection and sidewall‐heated natural convection flows in a cavity are chosen as test cases. Predictions with the new schemes show substantial computational savings and very good agreement when compared to previous simulations and experimental data.
Multifronts and transputer networks for solving fluid mechanical finite element systems
Authors: Miles R. G. , Havard S. P. 
Published: August 2005

AbstractThis paper is concerned with the implementation of a multifrontal solver on a network of transputers. We briefly discuss the transputer, outline the frontal and multifrontal schemes and consider the implementation of these schemes on the network. Results are presented for two test problems in fluid mechanics showing that the solver displays close to linear speed‐up.
Some uses of Green's theorem in solving the Navier–Stokes equations
Authors: Dennis S. C. R. , Quartapelle L. 
Published: August 2005

AbstractThis paper gives a review of methods where Green's theorem may be employed in solving numerically the Navier–Stokes equations for incompressible fluid motion. They are based on the concept of using the theorem to transform local boundary conditions given on the boundary of a closed region in the solution domain into global, or integral, conditions taken over it. Two formulations of the Navier–Stokes equations are considered: that in terms of the streamfunction and vorticity for two‐dimensional motion and that in terms of the primitive variables of the velocity components and the pressure. In the first formulation overspecification of conditions for the streamfunction is utilized to obtain conditions of integral type for the vorticity and in the second formulation integral conditions for the pressure are found. Some illustrations of the principle of the method are given in one space dimension, including some derived from two‐dimensional flows using the series truncation method. In particular, an illustration is given of the calculation of surface vorticity for two‐dimensional flow normal to a flat plate. An account is also given of the implementation of these methods for general two‐dimensional flows in both of the mentioned formulations and a numerical illustration is given.
The development of advanced computational methods for turbomachinery blade design
Authors: Stow P. 
Published: August 2005

AbstractThe paper describes the basic components of a turbomachinery blade design system in use within Rolls‐Royce. A number of modelling aspects of the advanced computational methods in use and under development are reviewed together with areas for future research and development.A quasi‐3D blade design system which is used for both compressors and turbines is described covering through‐flow and blade‐to‐blade analysis. Various features of blade‐to‐blade analysis are discussed including the use of compatible design and analysis modes and coupled boundary layer analysis capable of handling attached and separated flow; examples are included to show capabilities. Advances being made in the development and application of Reynolds‐averaged Navier–Stokes models are covered showing capabilities with regard to loss and heat transfer prediction.A fully coupled quasi‐3D through‐flow and blade‐to‐blade analysis system is described and results presented to show basic capabilities.The need for 3D flow analysis is discussed and the elements of a 3D blade design system presented showing how this links to the traditional quasi‐3D system. Examples are given showing basic capabilities of the methods available and under development.Finally areas for future development are presented indicating the mathematical and numerical modelling problems to be addressed.
Navier–Stokes computation of transonic vortices over a round leading edge delta wing
Authors: Müller Bernhard , Rizzi Arthur 
Published: August 2005

AbstractA 3D Navier–Stokes solver has been developed to simulate laminar compressible flow over quadrilateral wings. The finite volume technique is employed for spatial discretization with a novel variant for the viscous fluxes. An explicit three‐stage Runge–Kutta scheme is used for time integration, taking local time steps according to the linear stability condition derived for application to the Navier–Stokes equations. The code is applied to compute primary and secondary separation vortices at transonic speeds over a 65° swept delta wing with round leading edges and cropped tips. The results are compared with experimental data and Euler solutions, and Reynolds number effects are investigated.
Analysis of incompressible massively separated viscous flows using unsteady Navier–Stokes equations
Authors: Ghia K. N. , Osswald G. A. , Ghia U. 
Published: August 2005

AbstractThe unsteady incompressible Navier–Stokes equations are formulated in terms of vorticity and stream‐function in generalized curvilinear orthogonal co‐ordinates to facilitate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the vorticity transport equation using the alternating direction implicit method, whereas the streamfunction equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a backstep in a doubly infinite channel, using clustered conformal co‐ordinates. One‐dimensional stretching functions, dependent on the Reynolds number and the asymptotic behaviour of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honour the multiple length scales of the separated flow model problem. The asymptotic behaviour of the finite differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second‐order‐accurate wiggle‐free solutions, i.e. with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem, prior to the onset of three‐dimensionality in the experiment.
Numerical solution of transonic flows on a streamfunction co‐ordinate system
Authors: Barron Ronald M. , Naeem R. K. 
Published: August 2005

AbstractA new method has been developed for the computation of steady two‐dimensional full‐potential transonic flow past symmetric aerofoils. This method utilizes von Mises variables (x, ψ), where ψ is taken as the streamfunction for the flow. The flow equations and appropriate boundary conditions are formulated in terms of the von Mises variables (x, ψ) for symmetric aerofoils at zero incidence. This yields a system of two equations for unknowns ρ(x, ψ) and y(x, ψ). Finite difference solutions have been computed using SLOR at subcritical and supercritical Mach numbers. The results are compared with available data and are in excellent agreement.