bluuebunny/crossref_metadata_2025_split huggingface dataset:
Multigrid solution of the Navier–Stokes equations on highly stretched grids
Authors: Sockol Peter M. 
Published: November 2005

AbstractRelaxation‐based multigrid solvers for the steady incompressible Navier–Stokes equations are examined to determine their computational speed and robustness. Four relaxation methods were used as smoothers in a common tailored multigrid procedure. The resulting solvers were applied to three two‐dimensional flow problems, over a range of Reynolds numbers, on both uniform and highly stretched grids. In all cases the L2 norm of the velocity changes is reduced to 10−6 in a few 10's of fine‐grid sweeps. The results of the study are used to draw conciusions on the strengths and weaknesses of the individual relaxation methods as well as those of the overall multigrid procedure when used as a solver on highly stretched grids.
On the instability of a full non‐parallel flow—Kovasznay flow
Authors: Chen H. B. 
Published: November 2005

AbstractThe local instability of a full non‐parallel flow is investigated. The basic flow is a horizontal uniform flow about a vertical array of periodic bound eddies. This flow was found by Kovasznay as an exact solution to the Navier–Stokes equations. The problem is formulated as an initial value problem with two sets of complete orthogonal functions. A new approach to the problem with semi‐infinite domain is given computationally with a new modified rational Chebyshev function. The linear stability analysis of the Kovasznay flow is performed with respect to the odd–rational Chebyshev mode and the even–rational Chebyshev mode for the evolution of disturbances. While symmetrical vortex sheets appeared through the process of big eddies breaking into small eddies in the odd–rational Chebyshev mode, the von Kármán vortex street phenomena is found in the even–rational Chebyshev mode. The mode corresponding to antisymmetric velocity perturbation is found to be far more unstable than symmetric disturbance. An organized structure is developed after the onset of instability. Several general characteristics of non‐parallel flow stability are discussed.
Numerical modelling and computation of fluid pressure transients with air entrainment in pumping installations
Authors: Lee T. S. 
Published: November 2005

AbstractIn pumping installations such as sewage pumping stations, where gas content and air entrainment exist, the computation of fluid pressure transients in pipelines becomes grossly inaccurate when a constant wave speed is assumed. An accurate numerical model with gas release and absorption has been developed in this paper and used to compute the fluid pressure transients in the pumping mains of selected pumping installations. Free and dissolved gases in the transported fluid and cavitation at vapour pressure are also modelled. When compared with the gas‐free case, computations show that entrained, entrapped or released gases amplify the positive pressure peak, increase surge damping and produce asymmetric pressure surges. While the upsurge with air entrainment in the pipelines was considerably amplified, the downsurge was only marginally reduced. The computed results show good agreement with the data available.
Simulation of impacts of fluid free surfaces with solid boundaries
Authors: Johnson David B. , Raad Peter E. , Chen Shea 
Published: November 2005

AbstractDeficiencies associated with the simulation of impacts of fluid free surfaces with solid boundaries by use of marker‐and‐cell methods are identified and addressed. New procedures are introduced that affect the movement of markers in cells adjacent to a solid boundary, the flags of the cells that comprise a solid boundary and the pressure boundary condition for a cell in which impact occurs. Combined with fundamental changes in the sequence of steps in the computational cycle, these new procedures allow the intentional treatment of impact. As a result, improved estimates are obtained of the pressure associated with the cells adjacent to a boundary along which impact occurs. Consequently, more appropriate adjustments are made of the tentative internal velocities associated with such cells. In addition, a special procedure is presented for the adjustment of the tentative internal velocity between two surface cells. Finally, a new cell type termed a corner cell is defined and a procedure for its treatment is presented. Numerical examples are included to illustrate the previous deficiencies associated with the simulation of impact as well as the effectiveness of the new methods presented in this paper. Validation of the new methods is achieved by comparison with experimental results for spillage over a containment dike.
Dynamic vorticity condition: Theoretical analysis and numerical implementation
Authors: Wu Jie‐Zhi , Wu Xiao‐Hui , Ma Hui‐Yang , Wu Jain‐Ming 
Published: November 2005

AbstractThe dynamic boundary conditions for vorticity, derived from the incompressible Navier‐Stokes equations, are examined from both theoretical and computational points of view. It is found that these conditions can be either local (Neumann type) or global (Dirichlet type), both containing coupling with the boundary pressure, which is the main difficulty in applying vorticity‐based methods. An integral formulation is presented to analyse the structure of vorticity and pressure solutions, especially the strength of the coupling. We find that for high‐Reynolds‐number flows the coupling is weak and, if necessary, can be effectively bypassed by simple iteration. In fact, even a fully decoupled approximation is well applicable for most Reynolds numbers of practical interest. The fractional step method turns out to be especially appropriate for implementing the decoupled approximation. Both integral and finite difference methods are tested for some simple cases with known exact solutions. In the integral approach smoothed heat kernels are used to increase the accuracy of numerical quadrature. For the more complicated problem of impulsively started flow over a circular cylinder at Re = 9500 the finite difference method is used. The results are compared against numerical solutions and fine experiments with good agreement. These numerical experiments confirm our thoeretical analysis and show the advantages of the dynamic condition in computing high‐Reynolds‐number flows.
Pressure‐based method for combustion instability analysis
Authors: Kim Y. M. , Chen Z. J. , Chen C. P. , Ziebarth J. P. 
Published: November 2005

AbstractAn improved pressure‐based method has been applied to predict the two‐dimensional instability analysis of liquid‐fuelled rocket engines. This method is non‐iterative for transient flow calculations and applicable to all‐speed flows. Validation cases include the shock‐tube problem, the blast flow field and unsteady spraycombusting flows. Computations for the combustion instability analysis were carried out for various combustion parameters such as spray initial conditions and combustor geometries. Unsteady behaviours of the stable and unstable spray flame fields and effects of acoustic oscillations on the fuel droplet vaporization and combustion process are studied in detail. The present numerical model successfully demonstrates the capability of predicting combustion instability as well as fast transient compressible flows at all speeds.
Efficient higher‐order backward characteristics schemes for transient advection
Authors: Yu T. S. , Li C. W. 
Published: November 2005

AbstractThe use of the highest‐order ((N – 1)th‐order) Lagrangian interpolation Polynomial for the approximation of the exact solution in the backward characteristics scheme with N nodes is inefficient owing to the excessive number of terms in the polynomial. New schemes based on a combination of lower‐order polynomials to approximate the exact solution are developed, with the relative weighting of the polynomials determined by Fourier mode analysis. With the addition of a flux limiter and a modified discriminator, the resulting schemes are oscillation‐free, highly accurate, efficient and more cost‐effective as compared with those schemes using the highest‐order Lagrangian polynomial.
Decay of confined, two‐dimensional, spatially periodic arrays of vortices: A numerical investigation
Authors: Valentine Daniel T. 
Published: November 2005

AbstractThe disarrangement of a perturbed lattice of vortices was studied numerically. The basic state is an exponentially decaying, exact solution of the Navier‐Stokes equations. Square arrays of vortices with even numbers of vortex cells along each side were perturbed and their evolution was investigated. Whether the energy in the perturbation grows somewhat before it decays or decays monotonically depends on the initial strength of the vortices of the basic state, the extent of lateral confinement and the structure of the perturbation. The critical condition for temporally local instability, i.e. the critical amplitude of the basic state that must be exceeded to allow energy transfer from the basic state to the perturbation, is discussed. In the strongly confined case of a square lattice of four vortices the appearance of enchancement of global rotation is the result of energy transfer from the basic state to a temporally local unstable mode. Energy is transferred from the basic state to larger‐scaled structures (inverse cascade) only if the scales of the larger structures are inherently contained in the initial structure of the perturbation. The initial structure of the double array of vortices is not maintained except for a very special form of perturbation. The facts that large scales decay more slowly than small scales and that, when non‐linearities are sufficiently strong, energy is transferred from one scale to another explain the differences in the disarrangement process for different initial strengths of the vortices of the basic state. The stronger vortices, i.e. the vortices perturbed in a manner that increases their strength, tend to dominate the weaker vortices. The pairing and subsequent merging (or capture) of vortices of like sense into larger‐scale vortices are described in terms of peaks in the evolution of the square root of the palinstrophy divided by the enstrophy.
Accurate computation of convective transport in transient two‐phase flow
Authors: Andrews M. J. 
Published: November 2005

AbstractThe Van Leer method for the computation of convective fluxes is extended to two‐phase flow. By preventing spurious undershoots and overshoots, the scheme preserves physical realism while maintaining high‐order accuracy. This is particulary important for two‐phase flows, since phase exchange terms are typically a function of volume fraction products and numerical diffusion can incorrectly mix the two phases. The scheme described here is constructed to guarantee that the sum of the volume fractions is always unity and that the volume fractions are always greater than or equal to zero. Various test problems are computed to demonstrate the accuracy of the method and to show how the scheme might be incorporated in existing computational methods. In addition to multiphase flow applications, setting equal phase velocities results in a volume marker scheme that is well suited to single‐phase interface tracking problems.
Computation of backward‐facing step flows by a second‐order Reynolds stress closure model
Authors: Hwang Robert R. , Peng Y. F. 
Published: November 2005

AbstractThis paper scrutinizes the predictive ability of the differential stress equation model in complex shear flows. Two backward‐facing step flows with different expansion ratios are solved by the LRR turbulence model with an anisotropic dissipation model and the near‐wall regions of the separated side resolved by a near‐wall model. The computer code developed for solving the transport equations is based on the finite‐volume‐finite‐difference method. In the numerical solution of the time‐averaged momenum equations the Reynolds stresses are treated partially as a diffusion term and partially as a source term to avoid numerical instability. Computational results are compared with experimental data. It is found that the near‐wall region of the separated side resolved by the near‐wall model, the LRR model with a simple modification of an anisotropic dissipation model can predict backward step flows well.
Numerical study of a piston‐driven unsteady flow in a pipe with sudden expansion
Authors: Ströll H. , Durst F. , Perić M. , Scheuerer G. 
Published: November 2005

AbstractThis paper presents results of the numerical study of a piston‐driven unsteady flow in a pipe with sudden expansion. The piston closes the larger‐diameter pipe and moves between two limiting positions with strong acceleration or deceleration at the beginning and end of each stroke and constant velocity in between. The piston velocity in the exhaust stroke is about four times higher than in the intake stroke. Periodic piston movement in this fashion creates a complex unsteady flow between the piston head and the plane of sudden expansion. The numerical method is implicit and of finite volume type, using a moving grid and a collocated arrangement of variables. Second‐order spatial discretization, fine grids and a multigrid solution method were used to ensure high accuracy and good efficiency. Spatial and temporal discretization errors were of the order of 1% and 0.1% respectively. The features of the flow are discussed and the velocity profiles are compared with experimental data, showing good qualitative and quantitative agreement.
On Taylor weak statement finite element methods for computational fluid dynamics
Authors: Chaffin D. J. , Baker A. J. 
Published: November 2005

AbstractA Taylor series augmentation of a weak statement (a ‘Taylor weak statement’ or ‘Taylor‐Galerkin’ method) is used to systematically reduce the dispersion error in a finite element approximation of the one‐dimensional transient advection equation. A frequency analysis is applied to determine the phase velocity of semi‐implicit linear, quadratic and cubic basis one‐dimensional finite element methods and of several comparative finite difference/finite volume algorithms. The finite element methods analysed include both Galerkin and Taylor weak statements. The frequency analysis is used to obtain an improved linear basis Taylor weak statement finite element algorithm. Solutions are reported for verification problems in one and two dimensions and are compared with finite volume solutions. The improved finite element algorithms have sufficient phase accuracy to achieve highly accurate linear transient solutions with little or no artificial diffusion.
Numerical analysis of finite amplitude motion of waves and a moored floating body under severe storm conditions
Authors: Takikawa Kiyoshi , Yamada Fumihiko , Sato Keiji , Furuta Hideki 
Published: November 2005

AbstractThe motion of a moored floating body under the action of wave forces, which is influenced by fluid forces, shape of the floating body and mooring forces, should be analysed as a complex coupled motion system. Especially under severe storm conditions or resonant motion of the floating body it is necessary to consider finite amplitude motions of the waves, the floating body and the mooring lines as well as non‐linear interactions of these finite amplitude motions.The problem of a floating body has been studied on the basis of linear wave theory by many researchers. However, the finite amplitude motion under a correlated motion system has rarely been taken into account.This paper presents a numerical method for calculating the finite amplitude motion when a floating body is moored by non‐linear mooring lines such as chains and cables under severe storm conditions.
A higher‐order boundary element method for three‐dimensional potential problems
Authors: Yuelong Zang , Yumin Cheng , Wu Zhang 
Published: November 2005

AbstractA method of eliminating the singularities involved in boundary element methods for three‐dimensional potential problems is presented and the non‐singular expressions of integrals on an element on which the singular point is situated are given for linear and quadratic interpolation functions. Numerical examples are compared with analytical solutions to show that the higher‐order interpolations have better precision.
Numerical analysis of fluid flow and mass transfer in a channel with a porous bottom wall
Authors: Yucel Nuri , Turkoglu Hasmet 
Published: November 2005

AbstractThe flow of a solution between parallel plates is considered. The bottom plate is porous, while the top one is an impermeable solid. A computer program based on the control volume approach was developed to analyse the flow and concentration fields. The effects of the slip at the porous wall on the velocity and particle concentration distributions were investigated. It was observed that as the slip increases, the concentration on the porous wall decreases and the maximum velocity moves towards the porous wall. The concentration on the porous wall increases in the flow direction. This increase in the particle concentration along the porous wall may cause a reduction of the porosity and hence a variation in the suction rate along the porous wall. In order to take this effect into account, a linearly varying transverse velocity along the porous wall was considered. The results were compared with the data available in the literature.
Transient solutions for three‐dimensional lid‐driven cavity flows by a least‐squares finite element method
Authors: Tang Li Q. , Cheng Tiwu , Tsang Tate T. H. 
Published: November 2005

AbstractA time‐accurate least‐squares finite element method is used to simulate three‐dimensional flows in a cubic cavity with a uniform moving top. The time‐ accurate solutions are obtained by the Crank‐Nicolson method for time integration and Newton linearization for the convective terms with extensive linearization steps. A matrix‐free algorithm of the Jacobi conjugate gradient method is used to solve the symmetric, positive definite linear system of equations. To show that the least‐squares finite element method with the Jacobi conjugate gradient technique has promising potential to provide implicit, fully coupled and time‐accurate solutions to large‐scale three‐dimensional fluid flows, we present results for three‐dimensional lid‐driven flows in a cubic cavity for Reynolds numbers up to 3200.
The use of a reformulation of the hydrostatic approximation Navier‐Stokes equations for geophysical fluid problems
Authors: Zuur E. A. H. 
Published: November 2005

AbstractIn order to simulate geophysical general circulation processes, to simplify the governing equations of motion, often the vertical momentum equation of the Navier‐Stokes equations is replaced by the hydrostatic approximation equation. The resulting equations are reformulated and a variational formulation of the linearized problem is derived. Iteration schemes are presented to solve this problem. A finite element method is discussed, as well as a finite difference method which is based on a grid that is often used in geophysical general circulation models. The schemes are extended to the non‐linear case. Numerical examples are presented to demonstrate the performance of the derived iteration schemes.
Functional demonstration of surface carbonic anhydrase IV activity on rat astrocytes
Authors: Svichar Nataliya , Esquenazi Susana , Waheed Abdul , Sly William S. , Chesler Mitchell 
Published: November 2005

AbstractBuffering of the brain extracellular fluid is catalyzed by carbonic anhydrase (CA) activity. Whereas the extracellular isoform CA XIV has been localized exclusively to neurons in the brain, and to glial cells in the retina, there has been uncertainty regarding the form or forms of CA on the surface of brain astrocytes. We addressed this issue using physiological methods on cultured and acutely dissociated rat astrocytes. Prior work showed that the intracellular lactate‐induced acidification (LIA) of astrocytes is diminished by benzolamide, a poorly permeant, nonspecific CA inhibitor. We demonstrate that pretreatment of astrocytes with phosphatidylinositol‐specific phospholipase C (PI‐PLC) results in a similar inhibition of the mean LIA (by 66 ± 3%), suggesting that the glycosylphosphatidylinositol‐anchored CA IV was responsible. Pretreatment of astrocytes with CA IV inhibitory antisera also markedly reduced the mean LIA in both cultured cortical (by 46 ± 4%) and acutely dissociated hippocampal astrocytes (by 54 ± 8%). Pre‐immune sera had no effect. The inhibition produced by PIPLC or CA IV antisera was not significantly less than that by benzolamide, suggesting that the majority of detectable surface CA activity was attributable to CA IV. Thus, our data collectively document the presence of CAIV on the surface of brain astrocytes, and suggest that this is the predominant CA isoform on these cells. © 2005 Wiley‐Liss, Inc.
Tandem‐pore domain potassium channels are functionally expressed in retinal (Müller) glial cells
Authors: Skatchkov S.N. , Eaton M.J. , Shuba Y.M. , Kucheryavykh Y.V. , Derst C. , Veh R.W. , Wurm A. , Iandiev I. , Pannicke T. , Bringmann A. , Reichenbach A. 
Published: November 2005

AbstractTandem‐pore domain (2P‐domain) K+‐channels regulate neuronal excitability, but their function in glia, particularly, in retinal glial cells, is unclear. We have previously demonstrated the immunocytochemical localization of the 2P‐domain K+ channels TASK‐1 and TASK‐2 in retinal Müller glial cells of amphibians. The purpose of the present study was to determine whether these channels were functional, by employing whole‐cell recording from frog and mammalian (guinea pig, rat and mouse) Müller cells and confocal microscopy to monitor swelling in rat Müller cells. TASK‐like immunolabel was localized in these cells. The currents mediated by 2P‐domain channels were studied in isolation after blocking Kir, KA, KD, and BK channels. The remaining cell conductance was mostly outward and was depressed by acid pH, bupivacaine, methanandamide, quinine, and clofilium, and activated by alkaline pH in a manner consistent with that described for TASK channels. Arachidonic acid (an activator of TREK channels) had no effect on this conductance. Blockade of the conductance with bupivacaine depolarized the Müller cell membrane potential by about 50%. In slices of the rat retina, adenosine inhibited osmotic glial cell swelling via activation of A1 receptors and subsequent opening of 2P‐domain K+ channels. The swelling was strongly increased by clofilium and quinine (inhibitors of 2P‐domain K+ channels). These data suggest that 2P‐domain K+ channels are involved in homeostasis of glial cell volume, in activity‐dependent spatial K+ buffering and may play a role in maintenance of a hyperpolarized membrane potential especially in conditions where Kir channels are blocked or downregulated. © 2005 Wiley‐Liss, Inc.