bluuebunny/crossref_metadata_2025_split huggingface dataset:
Finite difference and finite element methods for mhd channel flows
Authors: Ramos J. I. , Winowich N. S. 
Published: November 2005

AbstractA Galerkin finite element method and two finite difference techniques of the control volume variety have been used to study magnetohydrodynamic channel flows as a function of the Reynolds number, interaction parameter, electrode length and wall conductivity. The finite element and finite difference formulations use unequally spaced grids to accurately resolve the flow field near the channel wall and electrode edges where steep flow gradients are expected. It is shown that the axial velocity profiles are distorted into M‐shapes by the applied electromagnetic field and that the distortion increases as the Reynolds number, interaction parameter and electrode length are increased. It is also shown that the finite element method predicts larger electromagnetic pinch effects at the electrode entrance and exit and larger pressure rises along the electrodes than the primitive‐variable and streamfunction–vorticity finite difference formulations. However, the primitive‐variable formulation predicts steeper axial velocity gradients at the channel walls and lower axial velocities at the channel centreline than the streamfunction–vorticity finite difference and the finite element methods. The differences between the results of the finite difference and finite element methods are attributed to the different grids used in the calculations and to the methods used to evaluate the pressure field. In particular, the computation of the velocity field from the streamfunction–vorticity formulation introduces computational noise, which is somewhat smoothed out when the pressure field is calculated by integrating the Navier–Stokes equations. It is also shown that the wall electric potential increases as the wall conductivity increases and that, at sufficiently high interaction parameters, recirculation zones may be created at the channel centreline, whereas the flow near the wall may show jet‐like characteristics.
A test problem for outflow boundary conditions—flow over a backward‐facing step
Authors: Gartling David K. 
Published: November 2005

AbstractA numerical solution for steady incompressible flow over a two‐dimensional backward‐facing step is developed using a Galerkin‐based finite element method. The Reynolds number for the simulations is 800. Computations are performed on an extended channel length to minimize the effect of the outflow boundary on the upstream recirculation zones. A thorough mesh refinement study is performed to validate the results. Extensive profile data at several channel locations are provided to allow future testing and evaluation of outflow boundary conditions.
A Chebyshev matrix method for the spatial modes of the Orr–Sommerfeld equation
Authors: Danabasoglu Gökhan , Biringen Sedat 
Published: November 2005

AbstractThe Chebyshev matrix collocation method is applied to obtain the spatial modes of the Orr‐Sommerfeld equation for Poiseuille flow and the Blasius boundary layer. The problem is linearized by the companion matrix technique. For semi‐infinite domains a mapping transformation is used. The method can be easily adapted to problems with boundary conditions requiring different transformations.
Laminar mixed convection in the entrance region of horizontal rectangular ducts
Authors: Nonino C. , Giudice S. Del 
Published: November 2005

AbstractA generally applicable finite element procedure for the prediction of laminar mixed convection in horizontal straight ducts of arbitrary cross‐section is presented. The procedure, based on the parabolized simplification of the complete Navier‐Stokes equations and on the Boussinesq approximation of the buoyancy terms, is validated through comparisons of computed results with the available literature data for mixed convection in the entrance region of a rectangular duct of aspect ratio a=2. Uniform heating at different sides is considered as the thermal boundary condition, although the proposed formulation allows specification of most thermal boundary conditions of practical interest.
Characteristic‐based flux limiters of an essentially third‐order flux‐splitting method for hyperbolic conservation laws
Authors: Lin Herng , Chieng Ching‐Chang 
Published: November 2005

AbstractA flux limiter based on characteristic variables is extended by a control volume flux formulation to approximate the convection term at the cell interface for an essentially third‐order‐accurate scheme. The basic algorithm uses implicit MUSCL‐type flux splitting and the approximate factorization method. It is applied to three test problems: (i) a one‐dimensional shock tube problem; (ii) a two‐dimensional problem of an oblique shock step with Mach numbers 3 and 10 and a shock angle of 59°;(iii) a two‐dimensional problem of transonic inviscid flow past an NACA0012 aerofoil with Mach number 0·8 at zero angle of attack. The computational results by the new flux limiter function are compared with the results of direct applications of the SMART algorithm, Leonard's SHARP algorithm, the third‐order Van Leer flux‐splitting method with a smooth limiter, Harten's second‐order unwind‐biased TVD scheme, Chakravarthy's third‐order MUSCL‐type TVD scheme and the exact solution. The comparison shows that the present method gives the most accurate and least oscillatory results with a rapid rate of convergence.
Three‐dimensional laminar flow and heat transfer in the entrance region of trapezoidal ducts
Authors: Farhanieh Bijan , Sunden Bengt 
Published: November 2005

AbstractThe laminar convective flow and heat transfer in a duct with a trapezoidal cross‐sectional area are studied numerically. The governing equations are solved numerically by a finite volume formulation in complex three‐dimensional geometries using co‐located variables and Cartesian velocity components. Details of the numerical method are presented. The accuracy of the method was also established by comparing the calculated results with the analytical and numerical results available in the open literature. The Nusselt numbers are obtained for the boundary condition of a uniform wall temperature whereas the friction factors are calculated for no‐slip conditions at the walls. The asymptotic values of the Nusselt numbers, friction factors. incremental pressure drops, axial velocity and momentum rate and kinetic energy correction factors approach the available fully developed values. Various geometrical dimensions of the cross‐section are considered.
Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM
Authors: Ganesh Ram K. 
Published: November 2005

AbstractThe total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post‐processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross‐section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far‐field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.
Calculating hydrodynamics problems for a liquid film flowing radially on a flat horizontal surface
Authors: Siwoń Bogdan , Ennaoui Mustapha 
Published: November 2005

AbstractA mathematical hydrodynamic model of a thin liquid film flowing radially on a flat horizontal surface has been elaborated. The model consisted of continuity and momentum equations which were resolved by means of the integral method. In fact, several versions of the model were examined; they differed mainly in film velocity distribution. The predictions of the different versions were then compared with liquid film thicknesses obtained from experimental investigation. The best version was applied in further calculations.
A spectral collocation method for compressible, non‐similar boundary layers
Authors: Pruett C. David , Streett Craig L. 
Published: November 2005

AbstractAn efficient and highly accurate algorithm based on a spectral collocation method is developed for numerical solution of the compressible, two‐dimensional and axisymmetric boundary layer equations. The numerical method incorporates a fifth‐order, fully implicit marching scheme in the streamwise (timelike) dimension and a spectral collocation method based on Chebyshev polynomial expansions in the wall‐normal (spacelike) dimension. The discrete governing equations are cast in residual form and the residuals are minimized at each marching step by a preconditioned Richardson iteration scheme which fully couples energy, momentum and continuity equations. Preconditioning on the basis of the finite difference analogues of the governing equations results in a computationally efficient iteration with acceptable convergence properties. A practical application of the algorithm arises in the area of compressible linear stability theory, in the investigation of the effects of transverse curvature on the stability of flows over axisymmetric bodies. The spectral collocation algorithm is used to derive the non‐similar mean velocity and temperature profiles in the boundary layer of a ‘fuselage’ (cylinder) in a high‐speed (Mach 5) flow parallel to its axis. The stability of the flow is shown to be sensitive to the gradual streamwise evolution of the mean flow and it is concluded that the effects of transverse curvature on stability should not be ignored routinely.
Supercomputer simulation of liquid drop formation on a solid surface
Authors: Greenspan Donald 
Published: November 2005

AbstractUsing a molecular‐dynamics‐type approach, we show how to simulate the formation of a liquid drop on a solid surface. Application is made to the case in which the liquid is water and the solid is graphite. The dynamical equations are large systems of nonlinear, ordinary differential equations which must be solved numerically. CRAY X‐MP/24 simulations and related contact angle calculations are described and discussed.
Numerical analysis of time‐dependent Boussinesq models
Authors: van der Houwen P. J. , Mooiman J. , Wubs F. W. 
Published: November 2005

AbstractIn this paper we analyse numerical models for time‐dependent Boussinesq equations. These equations arise when so‐called Boussinesq terms are introduced into the shallow water equations. We use the Boussinesq terms proposed by Katapodes and Dingemans. These terms generalize the constant depth terms given by Broer. The shallow water equations are discretized by using fourth‐order finite difference formulae for the space derivatives and a fourth‐order explicit time integrator. The effect on the stability and accuracy of various discrete Boussinesq terms is investigated. Numerical experiments are presented in the case of a fourth‐order Runge‐Kutta time integrator.
The integrated singular basis function method for the stick‐slip and the die‐swell problems
Authors: Georgiou Georgios , Olson Lorraine , Schultz William 
Published: November 2005

AbstractWe further develop a new singular finite element method, the integrated singular basis function method (ISBFM), for the solution of Newtonian flow problems with stress singularities. The ISBFM is based on the direct subtraction of the leading local solution terms from the governing equations and boundary conditions of the original problem, followed by a double integration by parts applied to those integrals with singular contributions. The method is applied to the stick‐slip and the die‐swell problems and improves the accuracy of the numerical results in both cases. In the case of the die‐swell problem it considerably accelerates the convergence of the free surface profile with mesh refinement. The advantages and disadvantages of the ISBFM when compared to other singular methods are also discussed.
Application of a moving grid method to a class of 1D brine transport problems in porous media
Authors: Zegeling P. A. , Verwer J. G. , Van Eijkeren J. C. H. 
Published: November 2005

AbstractThe background of this paper is the study of transport of pollutants by groundwater flow when released from a repository in a rock salt formation. Flow in regions surrounding such formations may be strongly influenced by variations in salt concentrations, a factor requiring special attention in the development of realistic mathematical models for predicting transport of pollutants. Indispensable for this development are advanced numerical methods. The aim of this paper is to illustrate the application of such a method to a class of non‐linear brine transport problems in one space dimension. Our method is based on the method of lines for solving time‐dependent partial differential equations. The method is of the finite difference type, implicit and thus applicable to wide classes of (one‐space‐dimensional) partial differential equation systems. The main feature of the method, however, is that it can automatically move the spatial grid for evolving time and thus is able to refine the grid in regions with large, special transitions. The grid refinement has provea to be a very valuable facility in the numerical modelling of brine transport problems involving low and high salt concentrations. From the user's point of view an additional advantage of the moving grid method is that it can be implemented in advanced, user‐oriented method‐of‐lines software packages based on implicit stiff ODE solvers. In the brine transport application discussed here we have used the package SPRINT.
A finite volume Navier‐Stokes algorithm for adaptive grids
Authors: Kallinderis Yannis 
Published: November 2005

AbstractA compact, finite volume, time‐marching scheme for the two‐dimensional Navier‐Stokes equations of viscous fluid flow is presented. The scheme is designed for unstructured (locally refined) quadrilateral meshes. An earlier inviscid equation (Euler) scheme is employed for the convective terms and the emphasis is on treatment of the viscous terms. An essential feature of the algorithm is that all necessary operations are restricted to within each cell, which is very important when dealing with unstructured grids. Numerical issues which have to be addressed when developing a Navier‐Stokes scheme are investigated. These issues are not limited to the particular Navier‐Stokes scheme developed in the present work but are general problems. Specifically, the extent of the numerical molecule, which is related to the compactness of the scheme and to its suitability for unstructured grids, is examined. An approach which considers suppression of odd‐even mode decoupling of the solution when designing a scheme is presented. In addition, accuracy issues related to grid stretching as well as boundary layer solution contamination due to artificial dissipation are addressed. Although the above issues are investigated with respect to the specific scheme presented, the conclusions are valid for an entire class of finite volume algorithms. The Navier‐Stokes solver is validated through test cases which involve comparisons with analytical, numerical and experimental results. The solver is coupled to an adaptive algorithm for high‐Reynolds‐number aerofoil flow computations.
Numerical modelling of cavities on axisymmetric bodies at zero and non‐zero angle of attack
Authors: Ingber Marc S. , Hailey Chris E. 
Published: November 2005

AbstractThe flow about submerged, fully cavitating axisymmetric bodies at both zero and non‐zero angle of attack is considered in this paper. A cavity closure model that relates the point of detachment, the angle that the separating streamline makes with the body and the cavity length is described. The direct boundary element method is used to solve the potential flow problem and to determine the cavity shape. A momentum integral boundary layer solver is included in the formulation so that shear stresses can be incorporated into the drag calculations. The numerical predictions based on the proposed closure model are compared with water tunnel measurements and photographs.
Invariant discretization of the incompressible Navier‐Stokes equations in boundary fitted co‐ordinates
Authors: Segal A. , Wesseling P. , Van Kan J. , Oosterlee C. W. , Kassels K. 
Published: November 2005

AbstractThe discretization of the incompressible Navier‐Stokes equation on boundary‐fitted curvilinear grids is considered. The discretization is based on a staggered grid arrangement and the Navier‐;Stokes equations in tensor formulation including Christoffel symbols. It is shown that discretization accuracy is much enhanced by choosing the velocity variables in a special way. The time‐dependent equations are solved by a pressure‐correction method in combination with a GMRES method. Special attention is paid to the discretization of several types of boundary conditions. It is shown that fairly non‐smooth grids may be used using our approach.
Large‐eddy simulation of turbulent flow and heat transfer in plane and rib‐roughened channels
Authors: Ciofalo M. , Collins M. W. 
Published: November 2005

AbstractLarge‐eddy simulation results are presented and discussed for turbulent flow and heat transfer in a plane channel with and without transverse square ribs on one of the walls. They were obtained with the finite‐difference code Harwell‐FLOW3D, Release 2, by using the PISOC pressure‐velocity coupling algorithm, central differencing in space, and Crank‐Nicolson time stepping. A simple Smagorinsky model, with van Driest damping near the walls, was implemented to model subgrid scale effects. Periodic boundary conditions were imposed in the streamwise and spanwise directions. The Reynolds number based on hydraulic diameter (twice the channel height) ranged from 10 000 to 40 000. Results are compared with experimental data, k‐ϵ predictions, and previous large‐eddy simulations.
Flow field modelling near a well with a conductive fracture
Authors: Li Y. C. , Huang N. C. 
Published: November 2005

AbstractIn the technology of oil recovery the oil production rate can be increased by generation of a vertical sand‐filld conductive fracture on the wall of the well. Oil diffuses through the conductive fracture to the well. In this paper the seepage flow and isothermal deformation fields in both the formation and fracture and the oil production rate at the well are studied by modelling the formation as an infinite poroelastic medium saturated with a one‐phase compressible fluid. The fracture is treated as a one‐dimensional poroelastic medium. Darcy flows are considered in both the formation and fracture. The plane strain condition is imposed. Our solution is obtained numerically by a finite element method based on a variational principle. The accuracy of the analysis is studied by comparison of the numerical solutions of some problems with their analytical solutions. Since we are dealing with the transient flow problem of an infinite region, an extrapolation technique is employed to find the finite element solution. The production rate of a well with the conductive fracture is compared with that of a well without the conductive fracture.
A finite element method for a three‐dimensional second‐order closure model of turbulent diffusion in a convective boundary layer
Authors: Pai Prasad , Tsang Tate T. H. 
Published: November 2005

AbstractA three‐dimensional second‐order closure dispersion model is used to simulate the plume behaviour of a passive contaminant in a convective boundary layer. A time‐splitting finite element method together with a non‐linear filtering scheme is used to solve the three‐dimensional second‐order closure transport equations. The model results show good agreement with laboratory data for a ground level source.
Numerical simulation of laminar and turbulent flows around rectangular cylinders
Authors: Okajima Atsushi , Ueno Hisanori , Sakai Haruhisa 
Published: November 2005

AbstractBy a finite volume method, laminar flows around bluff bodies with a rectangular cross‐section of various width‐to‐height ratios from 0·2 to 10 and with a cross‐section of a round leading edge and a square trailing edge have been computed on body‐fitted curvilinear co‐ordinates at Reynolds numbers of (1, 4, 7) × 103. Turbulent flows have also been computed by a standard k‐ϵ turbulence model. Computed results are compared with experimental data at a Reynolds number of 103 and clearly show the effects of the shape of the bluff body on the aerodynamic characteristics. We can successfully simulate some interesting phenomena whereby the flow pattern changes critically when the side ratio B/H is about 2·1 and 6; that is, a fully separated flow, an alternately reattached one and a stationarily reattached one. The results also reveal interactions between the wake and separation bubbles. There are, however, significant discrepancies between the results from the k‐ϵ turbulence model and experiments.
Stepwise increase in the Strouhal number for flows around flat plates
Authors: Ozono Shigehira , Ohya Yuji , Nakamura Yasuharu , Nakayama Ryuzo 
Published: November 2005

AbstractThe unsteady viscous flow around flat plates with square leading and trailing edges is investigated by using a finite difference computation of the incompressible two‐dimensional Navier‐Stokes equations. The chord‐to‐thickness ratio of a plate ranges from d/h=3 to 9, with a Reynolds number based on the plate's thickness equal to 103. The numerical analysis confirms the finding obtained in our previous experiment that vortex shedding from flat plates with square leading and trailing edges is caused by the impinging shear layer instability. The Strouhal number based on the plate's chord increases stepwise with increasing d/h in accordance with the experiment. The numerical analysis also gives some crucial information on the complicated vortical flow occurring near the trailing edge. Finally, the mechanism of the impinging shear layer instability is discussed in the light of the experimental and numerical findings.
Turbulence modelling for deep ocean radionuclide disposal
Authors: Onishi Yasuo , Trent Donald S. 
Published: November 2005

AbstractIn this study the adequacy of the k‐ϵ turbulence model and the feasibility of the three‐dimensional hydrodynamic‐transport models TEMPEST and FLESCOT for deep ocean radionuclide disposal assessment were evaluated qualitatively. TEMPEST and FLESCOT were applied to a hypothetical, two‐dimensional, deep ocean case with and without stratifications. TEMPEST with the k‐ϵ model was applied to obtain quasi‐steady state eddy viscosity distributions. With calculated eddy viscosity distributions as part of the input, FLESCOT then calculated distributions of velocity, water temperature, sediment and the dissolved and sediment‐sorbed radionuclide, assuming that the radionuclide was disposed on the ocean bottom.Results revealed that the computed eddy viscosity increased almost linearly with vertical distance near the ocean bottom, then rapidly decreased towards a molecular viscosity value when the vertical gradient of the velocity distribution became very small. The results also demonstrate the importance of the density gradient to suppress the turbulent kinetic energy production, resulting in reduced eddy viscosity, producing the maximum computed eddy viscosity of 0·2 Pa s, which compares well with the reported value of 0·07 Pa s in the deep ocean. Thus the k‐ϵ turbulence model appears to be qualitatively applicable to the deep ocean environment.