bluuebunny/crossref_metadata_2025_split huggingface dataset:
Transient simulation of 2–3D stratified and intermittent two‐phase flows. Part II: Applications
Authors: Moe Randi 
Published: August 2005

AbstractIn this paper a new type of transient multidimensional two‐fluid model has been applied to simulate intermittent or slug flow problems. Three different approaches to modelling interfacial friction, including an interfacial tracking scheme, have been investigated. The numerial method is based on an implicit finite difference scheme, solved directly in two steps applying a separate equation for the pressure. 2D predictions of Taylor bubble propagation in horizontal and inclined channels have been compared with experimental data and analytical solutions. The 2D model has also been applied to investigate a number of special phenomena in slug flow, including slug initiation, bubble turning in downflow and the bubble centring process at large liquid flow rates.
p‐version least squares finite element formulation for two‐dimensional, incompressible fluid flow
Authors: Winterscheidt Daniel , Surana Karan S. 
Published: August 2005

AbstractA p‐version least squares finite element formulation for non‐linear problems is applied to the problem of steady, two‐dimensional, incompressible fluid flow. The Navier‐Stokes equations are cast as a set of first‐order equations involving viscous stresses as auxiliary variables. Both the primary and auxiliary variables are interpolated using equal‐order C0 continuity, p‐version hierarchical approximation functions. The least squares functional (or error functional) is constructed using the system of coupled first‐order non‐linear partial differential equations without linearization, approximations or assumptions. The minimization of this least squares error functional results in finding a solution vector {δ} for which the partial derivative of the error functional (integrated sum of squares of the errors resulting from individual equations for the entire discretization) with respect to the nodal degrees of freedom {δ} becomes zero. This is accomplished by using Newton's method with a line search. Numerical examples are presented to demonstrate the convergence characteristics and accuracy of the method.
Natural convection flow in a square cavity revisited: Laminar and turbulent models with wall functions
Authors: Barakos G. , Mitsoulis E. , Assimacopoulos D. 
Published: August 2005

AbstractNumerical simulations have been undertaken for the benchmark problem of natural convection flow in a square cavity. The control volume method is used to solve the conservation equations for laminar and turbulent flows for a series of Rayleigh numbers (Ra) reaching values up to 1010. The k‐ϵ model has been used for turbulence modelling with and without logarithmic wall functions. Uniform and non‐uniform (stretched) grids have been employed with increasing density to guarantee accurate solutions, especially near the walls for high Ra‐values. ADI and SIP solvers are implemented to accelerate convergence. Excellent agreement is obtained with previous numerical solutions, while some discrepancies with others for high Ra‐values may be due to a possibly different implementation of the wall functions. Comparisons with experimental data for heat transfer (Nusselt number) clearly demonstrates the limitations of the standard k‐ϵ model with logarithmic wall functions, which gives significant overpredictions.
Generalized integral transform solution for boundary layer flow over a sphere
Authors: Lage P. L. C. , Rangel R. H. 
Published: August 2005

AbstractThe generalized integral transform technique is applied to the boundary layer equations for flow over a sphere in their primitive variables. Even though a diffusion‐based eigenvalue problem is used, the velocity profile, shear stress and separation point have been calculated with high accuracy. Low‐order approximations are shown to be accurate near the surface and the predictions of the separation point is very good. Comparison with finite difference results shows the better convergence behaviour of the integral transform method.
Comparison of variants of the bi‐conjugate gradient method for compressible Navier‐Stokes solver with second‐moment closure
Authors: Chuang C. C. , Chieng C. C. 
Published: August 2005

AbstractVariants of the bi‐conjugate gradient (Bi‐CG) method are used to resolve the problem of slow convergence in CFD when it is applied to complex flow field simulation using higher‐order turbulence models. In this study the Navier‐Stokes and Reynolds stress transport equations are discretized with an implicit, total variation diminishing (TVD), finite volume formulation. The preconditioning technique of incomplete lower‐upper (ILU) factorization is incorporated into the conjugate gradient square (CGS), bi‐conjugate gradient stable (Bi‐CGSTAB) and transpose‐free quasi‐minimal residual (TFQMR) algorithms to accelerate convergence of the overall itertive methods. Computations have been carried out for separated flow fields over transonic bumps, supersonic bases and supersonic compression corners. By comparisons of the convergence rate with each other and with the conventional approximate factorization (AF) method it is shown that the Bi‐CGSTAB method gives the most efficient convergence rate among these methods and can speed up the CPU time by a factor of 2·4–6·5 as compared with the AF method. Moreover, the AF method may yield somewhat different results from variants of the Bi‐CG method owing to the factorization error which introduces a higher level of convergence criterion.
A numerical study of pulsatile laminar flows in a pipe with a ring‐type constriction
Authors: Shi Z. D. , Lee T. S. , Winoto S. H. 
Published: August 2005

AbstractNumerical simulations have been carried out to study pulsatile laminar flows in a pipe with an axisymmetric ringtype constriction. Three types of pulsatile flows were investigated, namely a physiological flow, a pure sinusoidal flow and a non‐zero mean velocity sinusoidal flow. The laminar flow governing equations were solved by the SIMPLE algorithm on a non‐staggered grid and a modified Crank‐Nicolson approximation was used to discretrize the momentum equations with respect to time. The maximum flow Reynolds numer (Re) is 100. The Womersley number (Nw) ranges from 0 to 50, with the corresponding Strouhal number (St) ranging from 0 to 3·98. The constriction opening ratio (d/D) and thickness ratio (h/D) are fixed at 0·5 and 0·1 respectively. Within the time period investigated, all these pulsatile flows include both forward and backward flows. The unsteady recirculation region and the recirculation points change in size and location with time. For Nw ≤ 1 and St≤ 1·56 x 10−3 the three pulsatile flows have the same simple relation between the instantaneous flow rate and pressure loss (Δp) across the constriction and the pressure gradient in the axial direction (dp/dz) in the fully developed flow region. The phase angles between the flow rate and pressure loss and the pressure gradient are equal to zero. With increasing Nw and St, the phase angle between the flow rate and the dp/dz becomes larger and has its maximum value of 90° at Nw = 50 and St = 3·98. The three pulsatile flows also show different relations between the flow rate and the pressure gradient. The pure sinusoidal flow has the largest maximum pressure gradient and the non‐zero mean velocity sinusoidal flow has the smallest. For larger Nw and St the fully developed velocity profiles in the fully developed flow region have a smaller velocity gradient along the radial direction in the central region. The maximum recirculation length increases for Nw ranging from 0 to 4·2, while this length becomes very small at Nw = 50 and St = 3·98. The deceleration tends to enlarge the recirculation region and this effect appears for Nw ≥ 3 and St ≥ 1·43×10−2. Linear relations exist between the flow rate and the instantaneous maximum values of velocity, vorticity and shear stress.
Time‐dependent liquid metal flows with free convection and a deformable free surface
Authors: McClelland Matthew A. 
Published: August 2005

AbstractThe finite element method is employed to investigate time‐dependent liquid metal flows with free convection, free surfaces and Marangoni effects. The liquid circulates in a two‐dimensional shallow trough with differentially heated vertical walls. The spatial formulation incorporates mixed Lagrangian approximations to the velocity, pressure, temperature and free surface position. The time integration is performed with the backward Euler and trapezoid rule methods with step size control. The Galerkin method is used to reduce the problem to a set of non‐linear equations which are solved with the Newton–Raphson method. Calculations are performed for conditions relevant to the electron beam vaporization of refractory metals. The Prandtl number is 0·015 and Grashof number are in the transition range between laminar and turbulent flow. The results reveal the effects of flow intensity, surface tension gradients, mesh refinement and time integration strategy.
Applied mathematics and turbulence modelling
Authors: Mohammadi B. , Pironneau O. 
Published: August 2005

AbstractTurbulence modelling is done traditionally in fluid mechanics departments. However, mathematical tools such as frame invariance, multiple scale expansions and the like are of great help.We shall demonstrate these facts by applying mathematical and numerical tools to the K–ε model. We shall investigate wall laws. Reynolds hypothesis, positivity of k and ε and flows with multiple scales.We shall also take this opportunity to review some mathematical results relevant to turbulence modelling.
A general algorithm for compressible and incompressible flow—Part I. the split, characteristic‐based scheme
Authors: Zienkiewicz O. C. , Codina R. 
Published: August 2005

AbstractThe paper outlines the formulation of a novel algorithm which can be used for the solution of both compressible and incompressible Navier‐Stokes or Euler equations. Full incompressibility can be dealt with if the algorithm is used in its semi‐explicit form and its structure permits arbitrary interpolation functions to be used avoiding the Babuška‐Brezzi restriction. In a fully explicit version it introduces a rational form of balancing dissipation avoiding the use of arbitrary parameters and forms for this.
Triphasic finite element model for swelling porous media
Authors: Snijders H. , Huyghe J. M. , Janssen J. D. 
Published: August 2005

AbstractThe equations describing the mechanical behaviour of intervertebral disc tissue and other swelling porous media are three coupled partial differential equations in which geometric and physical non‐linearities occur. The boundary conditions are deformation‐dependent. To solve the equations for an arbitrary geometry and arbitrary boundary conditions, we use the finite element (FE) method. The differential equations are rewritten in an integral form by means of the weighted residual method. The domain of the integral is defined via a set of shape functions (i.e. finite elements). By applying the Gauss theorem and rewriting with respect to the reference state (total Lagrange), non‐linear equations are obtained. These are solved by means of the Newton‐Raphson technique. In order to get a finite set of equations, the weighted residual equations are discretized. The shape functions are chose as weighting functions (Galerkin method). This discretization results in a non‐symmetric stiffness matrix. A general description is given for the elements implemented into the commercial FE package DIANA (DIANA Analysis B.V., Delft, Netherlands). The numerical results of unconfined compression of a schematic intervertebral disc with varying proteoglycan concentration are given.
Reproducing kernel particle methods
Authors: Liu Wing Kam , Jun Sukky , Zhang Yi Fei 
Published: August 2005

AbstractA new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time‐frequency and space‐wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics (SPH) methods, moving least squares methods (MLSM), diffuse element methods (DEM) and element‐free Galerkin methods (EFGM). The proposed method maintains the advantages of the free Lagrange or SPH methods; however, because of the addition of a correction function, it gives much more accurate results. Therefore it is called the reproducing kernel particle method (RKPM). In computer implementation RKPM is shown to be more efficient than DEM and EFGM. Moreover, if the window function is C∞, the solution and its derivatives are also C∞ in the entire domain. Theoretical analysis and numerical experiments on the 1D diffusion equation reveal the stability conditions and the effect of the dilation parameter on the unusually high convergence rates of the proposed method. Two‐dimensional examples of advection‐diffusion equations and compressible Euler equations are also presented together with 2D multiple‐scale decompositions.
Simulation of 2D external viscous flows by means of a domain decomposition method using an influence matrix technique
Authors: Shen Wen‐Zhong , Loc Ta Phuoc 
Published: August 2005

AbstractTwo‐dimensional external viscous flows are numerically approximated by means of a domain decomposition method which combines a vortex method and a finite difference method. The vortex method is used in the flow region which is dominated by convective effects, whereas the finite difference method is used in the flow region where viscous diffusion effects are dominant. An influence matrix technique combined with the uniformity condition of the pressure is used to enforce the tangential velocity boundary condition. Comparisons between numerical and experimental data show that the method is well adapted for simulating two‐dimensional flows.
A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations
Authors: Li Ming , Tang Tao , Fornberg Bengt 
Published: August 2005

AbstractWe note in this study that the Navier‐Stokes equations, when expressed in streamfunction‐vorticity form, can be approximated to fourth‐order accuracy with stencils extending only over a 3 x 3 square of points. The key advantage of the new compact fourth‐order scheme is that it allows direct iteration for low‐to‐medium Reynolds numbers. Numerical solutions are obtained for the model problem of the driven cavity and compared with solutions available in the literature. For Re ⩽ 7500 point‐SOR iteration is used and the convergence is fast.
Finite element computations of two‐dimensional arterial flow in the presence of a transverse magnetic field
Authors: Sharma G. C. , Kapoor Jaya 
Published: August 2005

AbstractA finite element solution of the Navier‐Stokes equations for steady flow under the magnetic effect through a double‐branched two‐dimensional section of a three‐dimensional model of the canine aorta is discussed. The numerical scheme involves transforming the physical co‐ordinates to a curvilinear boundary‐fitted co‐ordinate system. The shear stress at the wall is calculated for a Reynolds number of 1000 with the branch‐to‐main aortic flow rate ratio as a parameter. The results are compared with earlier works involving experimental data and found to be in reasonable qualitative agreement. The steady flow, shear stress and branch flow under the effect of a magnetic field have been discussed in detail.
Finite element solution of the equations governing the flow of electrolyte in charged microporous membranes
Authors: James A. E. , Stillman J. D. , Williams D. J. A. 
Published: August 2005

AbstractElectrical double‐layer effects are unimportant in flows through porous media except when the Debye length k−1 is comparable in magnitude with the pore radius a. Under these conditions the equations governing the flow of electrolyte are those of Stokes, Nernst‐Planck and Poisson. These equations are non‐linear and require numerical solution. The finite element method provides a useful basis for solution and various algorithms are investigated. The numerical stability and errors of each scheme are analysed together with the development of an appropriate finite element mesh. The electro‐osmotic flow of a typical electrolyte (barium chloride) through a uniformly charged cylindrical membrane pore is investigated and the ion fluxes are post‐computed from the numerical solutions. The ion flux is shown to be strongly dependent on both zeta potential and pore radius, ka, indicating the effects of overlapping electrical double layers.
The development of a structured mesh grid adaption technique for resolving shock discontinuities in upwind Navier‐Stokes codes
Authors: Patel M. K. , Pericleous K. A. , Baldwin S. 
Published: August 2005

AbstractA technique is described for the adaptation of a structured control volume mesh during the iterative solution process of the Navier‐Stokes equations. The scalar equidistribution method is adopted, in conjunction with a Laplace‐like grid solver to make a curvilinear body‐fitted grid sensitive to local flow gradients. Hence, whilst the total number of grid nodes remains constant during a computation, their relative position is continuously adjusted to promote clustering of cells in regions where gradients are high. The focus of this work is in compressible aerodynamics, where such clustering would be desirable in regions containing shocks but also in boundary layers. The technique is three‐dimensional and operates in a series of user‐defined grid subdomains or patches. These patches act as reference frames within which grid activity takes place. Bi‐cubic splines are extensively used to define the aerodynamic surfaces forming the calculation boundaries and to ensure that grid movement does not compromise surface integrity. The technique is applied to aerofoils, wing surfaces, transonic ducts and nozzles and a supersonic wedge cascade. Significant sharpening of both normal and oblique shock discontinuities is demonstrated over static grid simulations and with fewer overall grid nodes. The technique is successful in both inviscid and viscous (turbulent) simulations.
Advection of axisymmetric interfaces by the volume‐of‐fluid method
Authors: Mashayek F. , Ashgriz N. 
Published: August 2005

AbstractA criterion is proposed for the advection of axisymmetric interfaces. The location of an interface is followed by a volume‐tracking technique wherein a volume fraction parameter is assigned to each of the cells in a Eulerian grid system. The interface is discretized into a set of line segments fitted at the boundary of every pair of neighbouring computational cells. The orientation of a line segment is obtained by inspecting the volume fractions of two neighbouring cells. The volume fractions are then advected using the velocity components at the boundary of the two cells. The following advection criterion is proposed: for advection in the axial direction the axial velocity u is assumed constant in the vicinity of each cell face; for advection in the radial direction the radial velocity v times the radial distance r is assumed constant in the vicinity of each cell face, i.e. rβv = const., where β = 0 for Cartesian and β = 1 for axisymmetric systems. The above criterion is used to develop an algorithm for the advection of axisymmetric interfaces which is referred to as the ‘axisymmetric flux line segment model for advection and interface reconstruction’ or A‐FLAIR.
A hybrid finite‐element–volume‐of‐fluid method for simulating free surface flows and interfaces
Authors: Mashayek F. , Ashgriz N. 
Published: August 2005

AbstractA numerical technique is developed for the simulation of free surface flows and interfaces. This technique combines the strength on the finite element method (FEM) in calculating the field variables for a deforming boundary and the versatility of the volume‐of‐fluid (VOF) technique in advection of the fluid interfaces. The advantage of the VOF technique is that it allows the simulation of interfaces with large deformations, including surface merging and breaking. However, its disadantage is that is solving the flow equations, it cannot resolve interfaces smaller than the cell size, since information on the subgrid scale is lost. Therefore the accuracy of the interface reconstruction and the treatment of the boundary conditions (i.e. viscous stresses and surface tension forces) become grid‐size‐dependent. On the other hand, the FEM with deforming interface mesh allows accurate implementation of the boundary conditions, but it cannot handle large surface deformations occurring in breaking and merging of liquid regions. Combining the two methods into a hybrid FEM‐VOF method eliminates the major shortcomings of both. The outcome is a technique which can handle large surface deformations with accurate treatment of the boundary conditions. For illustration, two computational examples are presented, namely the instability and break‐up of a capillary jet and the coalescence collision of two liquid drops.
Transmission‐line modelling of nonlinear reactive components and mutual inductances
Authors: Wong Chi‐Chung 
Published: August 2005

AbstractTransmission‐line models (TLMs) for nonlinear reactive components and mutual inductances are derived. The model for nonlinear reactive components is shown to be an improvement on the previous one. TLM results with the mutual inductance model are compared with the exact solution, and good agreement is found.
Time domain absorbing boundary condition in Layered media
Authors: Lin C. C. , Mei K. K. 
Published: August 2005

AbstractAn absorbing boundary condition for simple layered media is presented. The method enables the modelling of open space radiation and scattering problems when the source (or scatterer) and a plane interface between two media are both located within the finite‐difference or finite‐element region. The projection operator method is used to take into account the presence of reflected waves at the media interface. The derivation of the projection operator is presented for one, two and three dimensions. Examples of electromagnetic radiation and scattering in two dimensions are presented to illustrate the numerical implementation and validity of the new absorbing boundary condition.
A hybrid modelling technique for underwater acoustic scattering
Authors: Orme E. A. , Johns P. B. , Arnold J. M. 
Published: August 2005

AbstractA numerical method using impulse analysis of a transmission‐line matrix is used to model the scattering of underwater acoustic waves. The method is demonstrated by observation of plane and curved wavefronts travelling through the medium, and by plane wavefronts being scattered by a reflecting boundary.
Radar cross‐section reduction studies of partially open cavity structures
Authors: Chou Ri‐Chee , Lee Shung‐Wu 
Published: August 2005

AbstractShooting and bouncing rays (SBR) is a numerical method based on geometric optics developed to compute the electromagnetic scattering from jet inlets and partially open cavity structures. This method is used to study the effects of shaping on the radar cross‐section (RCS) of cavities. Two cylindrical cavity structures are analysed: one with a uniform circular cross‐section, and the other with a non‐uniform cross‐section varying from a triangular shape to a circular shape. By bending the longitudinal axis of a cylindrical cavity, a significant reduction in RCS at near axial incidence can be achieved.