bluuebunny/crossref_metadata_2025_split huggingface dataset:
Comparison of experimental data with the numerical simulation of planar entry flow: Role of the constitutive equation
Authors: Gotsis A. D. , Baird D. G. , Reddy J. N. 
Published: August 2005

AbstractThe goal of this research was to determine whether there is any interaction between the type of constitutive equation used and the degree of mesh refinement, as well as how the type of constitutive equation might affect the convergence and quality of the solution, for a planar 4:1 contraction in the finite eiement method. Five constitutive equations were used in this work: the Phan‐Thien–Tanner (PTT), Johnson–Segalman (JS), White–Metzner (WM), Leonov‐like and upper convected Maxwell (UCM) models. A penalty Galerkin finite element technique was used to solve the system of non‐linear differential equations. The constitutive equations were fitted to the steady shear viscosity and normal stress data for a polystyrene melt. In general it was found that the convergence limit based on the Deborah number De and the Weissenberg number We varied from model to model and from mesh to mesh. From a practical point of view it was observed that the wall shear stress in the downstream region should also be indicated at the point where convergence is lost, since this parameter reflects the throughput conditions. Because of the dependence of convergence on the combination of mesh size and constitutive equation, predictions of the computations were compared with birefringence data obtained for the same polystyrene melt flowing through a 4:1 planar contraction. Refinement in the mesh led to better agreement between the predictions using the PTT model and flow birefringence, but the oscillations became worse in the corner region as the mesh was further refined, eventually leading to the loss of convergence of the numerical algorithm. In comparing results using different models at the same wall shear stress conditions and on the same mesh, it was found that the PTT model gave less overshoot of the stresses at the re‐entrant corner. Away from the corner there were very small differences between the quality of the solutions obtained using different models. All the models predicted solutions with oscillations. However, the values of the solutions oscillated around the experimental birefringence data, even when the numerical algorithm would not converge. Whereas the stresses are predicted to oscillate, the streamlines and velocity field remained smooth. Predictions for the existence of vortices as well as for the entrance pressure loss (ΔPent) varied from model to model. The UCM and WM models predicted negative values for ΔPent.
A simple physical approach for deriving the characteristic equations of fluid dynamics
Authors: Wang B. N. , Hoffman J. D. 
Published: August 2005

AbstractA simple physical approach for deriving the characteristic equations of fluid dynamics is presented. The approach is based on the physical concept that information propagates through a flowfield along pathlines due to particle motion and along wavelines due to acoustic wave motion. The characteristic equations and compatibility equations are derived in vector forms which are valid in any co‐ordinate system.
A finite element solution to turbulent diffusion in a convective boundary layer
Authors: Pai Prasad , Tsang T. H. 
Published: August 2005

AbstractA second‐order closure turbulence model is used to simulate the plume behaviour of a passive contaminant dispersed in a convective boundary layer. A time‐splitting finite element scheme is used to solve the set of partial differential equations. It is shown that the second‐order closure model compares favourably with recent findings from laboratories, wind‐tunnel experiments and large‐eddy simulations. We also compare the second‐order closure model with the commonly used K‐diffusion model for the same meteorological conditions. Case studies also show the effects of model parameters and turbulence variables on the plume behaviour.
Radiation boundary conditions for finite element solutions of generalized wave equations
Authors: Johnsen Matthias , Paulsen Keith D. , Werner Francisco E. 
Published: August 2005

AbstractOn the basis of the dispersion relation of the generalized linear wave equation we derive a radiation boundary condition (RBC) that explicitly incorporates the physical parameters of the governing equation into the form of the boundary condition. Using finite element techniques we investigate the properties of the generalized RBC by examining forced and unforced solutions to the telegraph and Klein‐Gordon equations in one dimension. The results show that within the limits of the physical parameters of the problem the generalized RBC is an improvement over the Sommerfeld RBC when the governing equation contains additional terms that influence the propagation. These gains are achieved without introducing any computational overhead. A two‐dimensional example suggests that the 1D findings can generalize to higher dimensions.
A Chebyshev spectral collocation method using a staggered grid for the stability of cylindrical flows
Authors: Khorrami Mehdi R. 
Published: August 2005

AbstractA staggered spectral collocation method for the stability of cylindrical flows is developed. In this method the pressure is evaluated at different nodal points than the three velocity components. These modified nodal points do not include the two boundary nodes; therefore the need for the two artificial pressure boundary conditions employed by Khorrami et al. is eliminated. It is shown that the method produces very accurate results and has a better convergence rate than the spectral tau formulation. However, through extensive convergence tests it was found that elimination of the artificial pressure boundary conditions does not result in any significant change in the convergence behaviour of spectral collocation methods.
Unsteady flow calculation in a radial flow centrifugal pump with spiral casing
Authors: Morfiadakis Evangelos E. , Voutsinas Spyros G. , Papantonis Dimitris E. 
Published: August 2005

AbstractThe prediction of the two‐dimensional unsteady flow established in a radial flow centrifugal pump is considered. Assuming the fluid incompressible and inviscid, the velocity field is represented by means of source and vorticity surface distributions as well as a set of point vortices. Using this representation, a grid‐free (Lagrangian) numerical method is derived based on the coupling of the boundary element and vortex particle methods. In this context the source and vorticity surface distributions are determined through the non‐entry boundary condition together with the unsteady Kutta condition. In order to satisfy Kelvin's theorem, vorticity is shed at the trailing edges of the impeller blades. Then the vortex particle method is used to approximate the convection of the free vorticity distribution. Results are given for a pump configuration experimentally tested by Centre Technique des Industries Mécaniques (CETIM). Comparisons between predictions and experimental data show the capability of the proposed method to reproduce the main features of the flow considered.
Development of a parallel computational fluid dynamics algorithm on a hypercube computer
Authors: Braaten Mark E. 
Published: August 2005

AbstractOne of the main factors limiting the widespread use of computational fluid dynamics codes for engineering design is their very large requirements both in terms of computer memory and CPU time. Distributed memory parallel computers offer both the potential for a dramatic improvement in cost/performance over conventional supercomputers and the scalability to large numbers of processors that is required if performance beyond that of current supercomputers is to be achieved. As part of an evaluation to explore the potential of such machines for computational fluid mechanics applications, a concurrent algorithm for the solution of the Navier‐Stokes equations has been developed and demonstrated on a hypercube parallel computer. The algorithm is based on a domain decomposition of a well‐established serial pressure correction algorithm.The algorithm is demonstrated on both a 32‐node scalar and eight‐node vector Intel iPSC/2 for complicated two‐dimensional laminar and turbulent flow problems with different grid sizes and numbers of processors. Speed‐ups relative to a single processor of 12.9 with 16 processors and 20.2 with 32 processors are achieved on a scalar iPSC/2, demonstrating the parallel efficiency of the algorithm. Measured performance on a 32‐node scalar iPSC/2 exceeds one‐sixth that of a Cray X‐MP running the original serial algorithm. The performance of the algorithm on an eight‐node vector iPSC/2 exceeds that of the larger scalar hypercube and is about one‐fifth that of the Cray X‐MP. With cost/performance more than 10 times better than the Cray, these results dramatically show the cost effectiveness of vector hypercubes for this class of fluid mechanics algorithm.
A semi‐implicit collocation method: Application to thermal convection in 2D compressible fluids
Authors: Gauthier Serge 
Published: August 2005

AbstractA semi‐implicit pseudo‐spectral collocation method using a third‐order Runge‐Kutta numerical scheme for the full Navier‐Stokes equations is described. The Courant‐Friedrichs‐Lewy condition is overcome by the implicit handling of a diffusive term, as suggested by Harned and Kerner. All such terms are solved with an iterative scheme in the Fourier space. Simulation of thermal convection in 2D compressible fluids is made by expanding variables on a Fourier‐Chebyshev basis. We give some examples of sub‐ and supersonic steady solutions in the case where the heat flux at the upper boundary is governed by a black body.
The application of the method of characteristics for the simulation of nearly horizontal flow in two and three spatial dimensions
Authors: Matsoukis P. F. C. 
Published: August 2005

AbstractCertain free surface flows exhibit in nature negligible vertical accelerations and as a result the pressure within the fluid remains hydrostatic. The method of characteristics is developed as a solution technique for the integration of the partial differential equations describing this kind of flow. The equations are integrated over the depth to provide a two‐dimensional model which is then tested and validated by comparing its results with tide‐induced flows occurring in a number of cases where either analytical or observational data are available for comparison. On the basis of the results of the 2D model, a finite difference 3D model is developed which provides the values of the unknown velocities u, v and w along the three axes x, y and z. This combined 2D–3D model is verified by applying it in cases of wind‐induced flow inside closed or open basins for which the classical Ekman solution may be used as a testing means.
A stable algorithm for bed friction in three‐dimensional shallow sea modal models
Authors: Davies A. M. , Aldridge J. N. 
Published: August 2005

AbstractThe mathematical formulation of a three‐dimensional shallow sea model using a modal expansion in the veitical is briefly described.The importance of the time discretization of the vertical diffusion term and bottom friction term is discussed in some detail. Both stability theory and numerical calculations show the importance of time centring or evaluating the modal form of the viscosity term at the higher time step in order to develop a numerically efficient algorithm. Similar analysis and calculations show that in shallow water it is essential to time centre or evaluate bottom friction at the higher time step. In the case of linear bottom friction it is shown that this condition can be readily accomplished. However, using a quadratic friction formulation (a more physically realistic form), this cannot be readily achieved. A new algorithm is presented whereby a stable solution can be obtained even in shallow water using quadratic bottom friction.
An improved finite difference scheme for a Newtonian jet swell problem
Authors: Yu Tsai‐An , Liu Ta‐Jo 
Published: August 2005

AbstractThe finite difference scheme developed by Liu et al. for the Newtonian jet swell problem has been improved: an algebraic approach has been adopted for the numerical mapping; a new formulation for free surface iteration has been proposed; the discrete flow equations have been solved by a combination of the successive line underrelaxation method and the Picard method. With these modifications we are capable of achieving more accurate numerical solutions and a substantial saving in computing time.
Prediction of three‐dimensional general shape extrudates by an implicit iterative scheme
Authors: Legat Vincent , Marchal Jean‐Marie 
Published: August 2005

AbstractThis paper presents a numerical technique for solving three‐dimensional free surface problems in extrusion applications. The method is fully implicit in the sense that a Newton‐Raphson scheme is applied on all variables, and geometrically general. In particular, the die section shape may be complex and contains multiple corners: very few restrictions apply on the mesh generation because the method does not require the nodes to be located on straight lines (spines). A clear distinction is introduced between the directions associated with the kinematic condition and the remeshing rules. As a difference with respect to earlier publications, these concepts are handled separately. Only Stokes problems are solved in this paper and we have not introduced surface tension. Therefore corners in the die section propagate discontinuities in the extrudate shape, an a method for relocating corners without losing the quadratic convergence of the scheme is presented. Data structures used for the implementation are briefly discussed.We present results on the extrusion of various profiles, including a rectangular die (a benchmark problem) and various complex sections containing multiple corners.
Finite element modelling of natural‐convection‐controlled change of phase
Authors: Usmani A. S. , Lewis R. W. , Seetharamu K. N. 
Published: August 2005

AbstractThe problem of phase change in the presence of natural convection has been investigated. A model has been proposed based on the treatment of the release/absorption of latent heat as a heat source/sink in combination with the standard Galerkin finite element method with a primitive variable formulation on a fixed grid. To demonstrate the capabilities of the model, three cases of phase change of an aluminium alloy in the presence of natural convection arc considered, i.e. solidification, melting and combined solidification and melting. The solidification of water in a square cavity is modelled as another example, taking into account the density extremum, and the results are compared with a previously published work.
Second‐order boundary element method calculations of hydrodynamic interactions between particles in close proximity
Authors: Chan Chiu Y. , Beris Antony N. , Advani Suresh G. 
Published: August 2005

AbstractA second‐order boundary element technique was developed to simulate the 3D hydrodynamic interactions between multiple particles of arbitrary shape. This paper reports the results of an extensive validation procedure aimed at demonstrating the convergence characteristics of the technique, especially in cases where the particles are in close proximity. The quadratic elements are superior to the lower‐order elements in terms of accuracy, computer storage and CPU time required, thus resulting in a significant improvement in the overall computational efficiency. Superparametric discretization improves the accuracy over isoparametric discretization but lowers the convergence rate of the method. When the interparticle gap becomes very small (less than 1% of the particle radius), the numerical solution diverges owing to inaccurate determination of the element contributions in the gap region. An adaptive subdomain integration scheme was developed that dramatically improved the integration accuracy and provided convergent solutions for problems of very small gaps down to 0–01% of the particle diameter.
A finite difference method for 3D flows about bodies of complex geometry in rectangular co‐ordinate systems
Authors: Miyata Hideaki , Yamada Yoshihiro 
Published: August 2005

AbstractA finite difference simulation method is developed for 3D flow about a body of complex geometry. The Navier–Stokes equation is approximated by a high‐order‐accurate difference scheme in the framework of rectangular co‐ordinate systems. The configuration of the 3D body is represented by use of both surface porosity and volume porosity and the no‐slip body boundary conditions are approximately implemented on the boundary cells. The validity of the method is demonstrated by a numerical test of flow past a sphere at a Reynolds number of 1000. The complicated structure of separated vortices is well revealed by this test computation. The versatility of the method is shown by application to an ocean‐engineering problem of flow about a bay with an island.
Boundary element method for long‐time water wave propagation over rapidly varying bottom topography
Authors: Nachbin A. , Papanicolaou G. C. 
Published: August 2005

AbstractWe study numerically the linear water wave equations for shallow channels with rapidly varying bottom topography. We do not use the shallow water approximation because it is not valid when the bottom is rapidly varying. We use the boundary element method because it allows accurate tracking of the surface waves for long times. We present the results of a range of numerical validation experiments and a comparison between propagation over a periodic and a random rough bottom topography.
A problem of heat and mass transfer: Proof of the existence condition by a finite difference method
Authors: Gaultier M. , Lezaun M. , Vadillo F. 
Published: August 2005

AbstractWe solve by a finite difference method a system of simultaneous non‐linear partial differential equations which modelizes the transfer of heat and mass when a fluid evaporates from the hot wall and condenses on the cold wall of an upright rectangular cavity. The need to verify a certain condition associating the physical parameters of the fluid for the existence of steady state solutions is proved.
Numerical problems in simulating tidal flows with a frictional‐velocity‐dependent eddy viscosity and the influence of stratification
Authors: Davies Alan M. 
Published: August 2005

AbstractThe paper deals with the accurate determination of tidal current profiles in both homogeneous and stratified regions when a no‐slip condition is used at the seabed with a flow‐dependent eddy viscosity related to the depth‐mean current or the bed frictional velocity.Calculations show that it is essential to accurately resolve the high‐shear region which occurs at the bed and across the pycnocline/thermocline in the case of stratified flow. A computationally accurate and economic method of resolving these regions is demonstrated using the Galerkin method with a set of basis functions designed to accurately reproduce the high‐shear layers which occur in these regions.With a flow‐independent eddy viscosity a stability analysis can be readily performed and an unconditionally stable algorithm developed. However, with a flow‐dependent viscosity, in particular a viscosity computed from the frictional velocity, a non‐linear numerical instability can occur. A method of maintaining numerical stability in this case is also described.The importance of near‐bed resolution to the computed value of the frictional velocity is demonstrated and its influence on the total tidal velocity profile is illustrated by a number of idealized calculations using various eddy viscosity formulations.The influence of stratification on the computed tidal profiles is shown in the latter part of the paper.
Stratified flow under an ice keel—a numerical approach
Authors: Jameel M. I. , Rowe R. D. , Topham D. R. 
Published: August 2005

AbstractA numerical investigation of the flow of two immiscible stratified fluids under an isolated keel has been undertaken. The investigation utilized the two‐dimensional Euler equations for incompressible flow, and the solution of these equations has been obtained by using the well‐known finite volume marker and cell approach. Experimental drag‐force measurements are also presented for a family of two‐dimensional topographic models of fixed height with increasing surface slopes in a two‐layer density system. The range of flow speeds explored covers the Froude number range from subcritical to fully supercritical. The drag force measurements are augmented by detailed observations of the interface distortion. The results clearly show large drag increases arising from the internal wave systems generated in the stratified flow. Very good agreement has been found between the experimental and numerical results for both the interface shape between the two fluids and the drag force on a variety of keels.
Comparisons of TVD schemes for turbulent transonic projectile aerodynamics computations with a two‐equation model of turbulence
Authors: Lin Herng , Chieng Ching‐Chang 
Published: August 2005

AbstractThe development of a computer program to solve the axisymmetric full Navier‐‐Stokes equations with k‐ε two‐equation model of turbulence using various total variation diminishing (TVD) schemes is the primary interest of this study. The computations are performed for the turbulent, transonic, viscous flow over a projectile with/without supporting sting at zero angle of attack. The predicted results, as well as the convergence characteristics, by various TVD schemes are compared with each other. The results show that the TVD schemes of higher‐order accuracy do have influence on the regions of high gradients such as shock, base corner and base flow. However, the schemes of third‐order accuracy do not necessarily improve the agreement with measured data (which is not available on the base) than that of second‐order accuracy, but surely generate apparent different result of base flow. The supporting sting on the projectile base will complicate the base flow and the existence of the sting will slightly shift the shock location and slightly change the flow field after the shock. More iteration steps are needed to get the converged results in the computation for the projectile with sting.
Indented plate problem revisited
Authors: Cebeci Tuncer , Chen Hsun H. , Majeski Judith A. 
Published: August 2005

AbstractAn interactive boundary layer method, together with the en approach to the calculation of transition, has been used to investigate the flow over an indented surface for which previous calculations had led to numerical instabilities. The results show two possible reasons for these numerical difficulties. First, it is shown that the gradients of wall shear become very steep at larger Reynolds numbers, particularly in the vicinity of reattachment. Extremely fine numerical grids are required to resolve these gradients. Secondly, and perhaps of greater importance, transition is shown to occur within the region of recirculation for all Reynolds numbers except for the lowest ones. Thus, the calculated flows downstream of the transition locations are fictitious and may be expected to deviate from the corresponding real flows by increasing amounts as the Reynolds number becomes larger. Calculations involving laminar, transitional and turbulent flow have been performed and confirm this conjecture.