bluuebunny/crossref_metadata_2025_split huggingface dataset:
A finite element analysis of laminar unsteady flow of viscoelastic fluids through channels with non‐uniform cross‐sections
Authors: Ponnalagarsamy R. , Kawahara M. 
Published: August 2005

AbstractThe effects of non‐Newtonian behaviour of a fluid and unsteadiness on flow in a channel with non‐uniform cross‐section have been investigated. The rheological behaviour of the fluid is assumed to be described by the constitutive equation of a viscoelastic fluid obeying the Oldroyd‐B model. The finite element method is used to analyse the flow. The novel features of the present method are the adoption of the velocity correction technique for the momentum equations and of the two‐step explicit scheme for the extra stress equations. This approach makes the computational scheme simple in algorithmic structure, which therefore implies that the present technique is capable of handling large‐scale problems. The scheme is completed by the introduction of balancing tensor diffusivity (wherever necessary) in the momentum equations. It is important to mention that the proper boundary condition for pressure (at the outlet) has been developed to solve the pressure Poisson equation, and then the results for velocity, pressure and extra stress fields have been computed for different values of the Weissenberg number, viscosity due to elasticity, etc. Finally, it is pertinent to point out that the present numerical scheme, along with the proper boundary condition for pressure developed here, demonstrates its versatility and suitability for analysing the unsteady flow of viscoelastic fluid through a channel with non‐uniform cross‐section.
Least‐squares finite element methods for compressible Euler equations
Authors: Jiang Bo‐Nan , Carey G. F. 
Published: August 2005

AbstractA method based on backward finite differencing in time and a least‐squares finite element scheme for first‐order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L2‐norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high‐order elements, computed solutions based on the L2‐method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1‐norm of the residual is proposed and leads to a successful scheme with high‐degree elements. Finally, a conservative least‐squares finite element method is also developed. Numerical results for two‐dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.
A least‐squares procedure for the solution of transport problems
Authors: Bensabat J. , Zeitoun D. G. 
Published: August 2005

AbstractIn this paper a least‐squares formulation associated with a conjugate gradient algorithm is proposed for the solution of transport problems. In this procedure the advection–diffusion equation is first discretized in time using an implicit scheme. At each time step the resulting partial differential equation is replaced by an optimal control problem. This minimization problem involves the minimization of a functional defined via a state equation. This functional is chosen in order to force the numerical solution of the advection–diffusion equation to be equal to the hyperbolic advective part of this equation. The effectiveness of the method is shown through a one‐dimensional example involving advective and diffusive transport. No oscillation and high accuracy have been obtained for the entire range of Peclet numbers with a Courant number well in excess of unity.
Application of a vortex lattice numerical model in the calculation of inviscid incompressible flow around delta wings
Authors: Bandyopadhyay G. 
Published: August 2005

AbstractThe flow over a flat plate delta wing at incidence and in sideslip is studied using vortex lattice models based on streamwise penelling. For the attached flow problem the effect of sideslip is simulated by modifying the standard vortex lattice model for zero sideslip by aligning the trailing vortices aft of the wing along the resultant flow direction. For the separated flow problem a non‐linear vortex lattice model is developed for both zero and non‐zero sideslip angles in which the shape and position of the leading edge separation vortices are calculated by an iterative procedure starting from an assumed initial shape. The theoretical values are compared with available theoretical and experimental results.
A scheme for automatic generation of boundary‐fitted depth‐ and depth‐gradient‐ dependent grids in arbitrary two‐dimensional regions
Authors: Nielsen Per , Skovgaard Ove 
Published: August 2005

AbstractIn this paper we present a scheme for the numerical generation of boundary‐fitted grids that adapt to both water depth and depth gradient. The scheme can be used in arbitrary two‐dimensional regions and is based on the application of the well‐known control function approach to generate adaptive grids. The method includes the evaluation of water depths at the grid points from a known distribution of depth points and their associated depths plus a procedure for the numerical evaluation of depth gradients. It is demonstrated that the smoothness of the grid can be enhanced by introducing a suitable filtering technique.
A moving finite element method for the population balance equation
Authors: Tsang T. H. , Rao A. 
Published: August 2005

AbstractA moving finite element algorithm has been compared against the upwind‐differencing and Smolarkiewicz methods for the population balance equation of multicomponent particle growth processes. Analytical solutions and an error function have been used to test the numerical methods. The moving finite elements technique is much more accurate than other methods for a wide range of parameters. Since this method uses moving grids, it is able to model very narrow particle size distributions. It is also shown that the method can be extended to solve condensational growth problems which include particle curvature and non‐continuum mass transfer effects.
Boundary element calculation of shallow water waves
Authors: Kaneko N. , Utagawa N. , Kawahara M. 
Published: August 2005

AbstractA boundary element method is proposed for studying periodic shallow water problems. The numerical model is based on the shallow water equation. The key feature of this method is that the boundary integral equations are derived using the weighted residual method and the fundamental solutions for shallow water wave problems are obtained by solving the simultaneous singular equations. The accuracy of this method is studied for the wave reflection problem in a rectangular tank. As a result of this test, it has been shown that the number of element divisions and the distribution of nodes are significant to the accuracy. For numerical examples of external problems, the wave diffraction problems due to single cylindrical, double cylindrical and plate obstructions are analysed and compared with the exact and other numerical solutions. Relatively accurate solutions are obtained.
Global pressure relaxation for laminar two‐dimensional internal flow
Authors: Rosenbaum D. , Rubin S. G. 
Published: August 2005

AbstractThis study extends the reduced Navier–Stokes (RNS) global pressure relaxation procedure developed by Rubin and co‐workers for external flow to internal flow applications. The streamwise pressure gradient is split into a backward‐differenced or initial value component, as in boundary layer marching, and a forward‐differenced or boundary value component that represents the elliptic downstream effects. The streamwise convection terms are upwind‐differenced and all other streamwise derivatives are backward‐differenced. We thus obtain a standard boundary layer marching technique imbedded in a conventional line relaxation technique. For compressible flow the pressure iteration determines the interior flow interation as well as the inlet mass flux that is consistent with the outflow pressure boundary condition. Results have been computed for incompressible flow in both rectangular and curved channels, and for subsonic compressible flow in the simulation of an aerofoil in a wind tunnel. Converged solutions were obtained over a range of Reynolds numbers generating small to moderately large separation bubbles.
Thermocapillary flow and natural convection in a melt column with an unknown melt/solid interface
Authors: Lan C. W. , Kou Sindo 
Published: August 2005

AbstractA vertical melt column set up between an upper heating rod and a lower sample rod, i.e. the so‐called halfzone system, is a convenient experimental tool for studying convection in the melt in floating‐zone crystal growth. In order to help understand the convection observed in the melt column, a computer model has been developed to describe steady state, axisymmetrical thermocapillary flow and natural convection in the melt. The governing equations and boundary conditions are expressed in general non‐orthogonal curvilinear co‐ordinates in order to accurately treat the unknown melt/solid interface as well as all other physical boundaries in the system. The effects of key dimensionless variables on the following items are discussed: (1)convection and temperature distribution in the melt; (2) the shape of the melt/solid interface; (3) the height of the melt column. These dimensionless variables are the Grashof, Marangoni and Prandtl numbers.
A computational method for the hydrodynamics of fractured‐porous media
Authors: Grandi G. M. , Ferreri J. C. 
Published: August 2005

AbstractA numerical method based on the boundary‐fitted finite difference method (BFDM) is presented in this paper. The boundaries are external (the boundary of the physical domain) and internal (which corresponds to the fracture network). The difference between this approach and the usual one lies in the inclusion of discrete fractures in the volume that represents the porous medium. The numerical model has been used in the prediction of the flow pattern in several internationally recognized verification cases and applied to the solution of hypothetical problems of interest to us in the field of nuclear waste repository modelling. The results obtained show that the numerical approach considered gives accurate and reliable predictions of the hydrodynamics of fractured‐porous media, thus justifying its use for the above‐mentioned studies.
Numerical solutions for impulsively started and decelerated viscous flow past a circular cylinder
Authors: Wang Xuegeng , Dalton Charles 
Published: August 2005

AbstractA finite difference study of the unsteady two‐dimensional flow past a circular cylinder has been conducted using vorticity and streamfunction as the dependent variables. The two cases considered were impulsively started and decelerated flows. The impulsively started problem was considered to validate the method and has yielded results which agree quite closely with existing results from both calculations and experiments. The decelerated flow analysis produced results which can be explained in terms of induced velocity effects from existing wake vortices for both suddenly stopped and uniformly decelerated flows.
Higher‐order difference approximations of the Navier‐Stokes equations
Authors: Luchini Paolo 
Published: August 2005

AbstractA discretization scheme is presented which, unlike the standard higher‐order finite difference and spline methods, does not give rise to unphysical solution modes and boundary conditions. Practical application of this scheme is achieved via the DCMG algorithm recently developed by the same author, which turns out to be able to find a converged solution of the ψ‐ζ Navier‐Stokes equations in about the same time for highorder as for low‐order discretization schemes. Examples are presented for the driven cavity problem to explore the accuracy of the new method. Finally, a local analysis is performed of the corner singularities which exist in driven cavity flow, and their effect on the overall accuracy of the solutions obtained by polynomial interpolation methods is investigated.
Three‐dimensional hydrodynamics on finite elements. Part II: Non‐linear time‐stepping model
Authors: Lynch Daniel R. , Werner Francisco E. 
Published: August 2005

AbstractThe development and application of a non‐linear 3D hydrodynamic model are described. The model is based on the wave equation rearrangement of the primitive 3D shallow water equations with a general eddy viscosity formulation for the vertical shear. A Galerkin procedure is used to discretize these on simple sixnode elements: linear triangles in the horizontal with linear variations in the vertical. Resolution of surface, bottom and interfacial boundary layers is facilitated and total flexibility is preserved for specifying spatial and temporal variations in the vertical viscosity and density fields. A semi‐implicit time‐stepping algorithm allows the solutions for elevation and velocity to be uncoupled during each time step. The elevation solution is essentially a 2D wave equation calculation with a stationary sparse matrix representing the gravity waves. With nodal quadrature the subsequent velocity calculation is achieved by factoring only a tridiagonal diffusion matrix representing the vertical viscous terms. As a result the overall calculation scales computationally as only a 2D problem but provides the full 3D solution. Application to field‐scale problems is illustrated for the English Channel/Southern Bight system and the Lake Maracaibo system.
Dynamical eigenfunction decomposition of turbulent channel flow
Authors: Ball K. S. , Sirovich L. , Keefe L. R. 
Published: August 2005

AbstractThe results of an analysis of low‐Reynolds‐number turbulent channel flow based on the Karhunen‐Loéve(K‐L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier‐Stokes equations at a Reynolds number Re,= 80 (based on the wall shear velocity and channel half‐width). The K‐L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K‐L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90% of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, posses viscous boundary layers at the walls and are much richer in harmonics than the original basis functions. Chaotic temporal behaviour is observed in all modes and increases for higher‐order eigenfunctions. The structure and dynamical behaviour of the eigenmodes are discussed as well as their use in the representation of the turbulent flow.
Examination of wall damping for the k‐ε turbulence model using direct simulations of turbulent channel flow
Authors: Miner E. Wade , Swean Thomas F. , Handler Robert A. , Leighton Richard I. 
Published: August 2005

AbstractHandler, Hendricks and Leighton have recently reported results for the direct numerical simulation (DNS) of a turbulent channel flow at moderate Reynolds number. These data are used to evaluate the terms in the exact and modelled transport equations for the turbulence kinetic energy k and the isotropic dissipation function ε. Both modelled transport equations show significant imbalances in the high‐shear region near the channel walls. The model for the eddy viscosity is found to yield distributions for the production terms which do not agree well with the distributions calculated from the DNS data. The source of the imbalance is attributed to the wall‐damping function required in eddy viscosity models for turbulent flows near walls. Several models for the damping function are examined, and it is found that the models do not vary across the channel as does the damping when evaluated from the DNS data. The Lam‐Bremhorst model and the standard van Driest model are found to give reasonable agreement with the DNS data. Modification of the van Driest model to include an effective origin yields very good agreement between the modelled production and the production calculated from the DNS data, and the imbalance in the modelled transport equations is significantly reduced.
Computations for a jet impinging obliquely on a flat surface
Authors: Chuang Shu‐Hao , Wei Ching‐Yuan 
Published: August 2005

AbstractA SIMPLE‐C algorithm and Jones‐Launder k‐ε two‐equation turbulence model are used to simulate a two‐dimensional jet impinging obliquely on a flat surface. Both the continuity and momentum equations for the unsteady state are cast into suitable finite difference equations. The pressure, velocity, turbulent kinetic energy and turbulent energy dissipation rate distributions are solved and show good agreement with various experimental data. The calculations show that the flow field structure of the jet impinging obliquely on a flat surface is strongly affected by the oblique impingement angle. The maximum pressure zone of the obliquely impinging jet flow field moves towards the left as the oblique impingement angle is decreased.
Simulation of two‐ and three‐dimensional internal subsonic flows using a finite element method
Authors: Buffat Marc 
Published: August 2005

AbstractIn this paper a finite element method is presented to predict internal subsonic flows. Using a low‐Mach‐number approximation, the pressure is decomposed into a mean thermodynamic contribution and a dynamic fluctuation to deal with the complex role of the pressure in internal aerodynamics. A semi‐implicit time integration and a finite element method with a moving mesh are described to take into account complex geometries and moving boundaries. An Uzawa algorithm accelerated by a preconditioned residual method is introduced to solve the coupled non‐symmetric linear system for the velocity components and the pressure. An efficient conjugate gradient method combined with an incomplete LU preconditioning is used to solve the non‐symmetric linear systems arising from the discretization. The implementation of the numerical scheme on parallel supercomputers is also discussed. Efficient algorithms for the finite element assembly phase and for the solution of linear systems are described which take advantage of the parallel architecture of the new generation of supercomputers. With this technique a global speed‐up of 10 is achieved on a supercomputer with eight processors. To illustrate the capabilities of the numerical method, 2D and 3D simulations of flows in the combustion chamber of a reciprocating engine and around the combustor dome of a gas turbine engine are presented.
Heat transfer during melting in rectangular enclosures—a finite element analysis
Authors: Sarkar A. , Sastri V. M. K. 
Published: August 2005

AbstractThis paper is devoted to the finite element analysis of heat transfer during melting in rectangular enclosures. The effects of aspect ratio and subcooling on the motion of the interface and the Nusselt number have been investigated. The different schemes employed in the present work throw useful light on the choice of the appropriate method for dealing with such phase change problems.
Domain decomposition methods in computational fluid dynamics
Authors: Gropp William D. , Keyes David E. 
Published: August 2005

AbstractThe divide‐and‐conquer paradigm of iterative domain decomposition or substructuring has become a practical tool in computational fluid dynamics applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi‐uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. We illustrate these features on the classic model problem of flow over a backstep using Newton's method as the non‐linear iteration. Multiple discretizations (second‐order in the operator and first‐order in the preconditioner) and locally uniform mesh refinement pay dividends separately and can be combined synergistically. We include sample performance results from an Intel iPSC/860 hypercube implementation.
A numerical method for the determination of slip characteristics between the layers of a two‐layer slurry flow
Authors: Nassehi V. , Khan A. R. 
Published: August 2005

AbstractThe observed phenomenon of slip between the layers of a flowing slurry is modelled mathematically by a finite‐element‐based numerical technique. This technique enables us to quantify variables such as the slip velocity and shear stress distribution at the interlayer boundary and the pressure drop within the flow domain.
A fire field model implemented in a parallel computing environment
Authors: Ierotheou C. S. , Galea E. R. 
Published: August 2005

AbstractThis paper describes the implementation of a fire field model in the parallel computing environment offered by multiple transputers. The fire model is built into the general purpose SIMPLE‐based CFD code HARWELL‐FLOW3D. The technique of domain decomposition has been applied tb convert the conventional serial version of FLOW3D into a code capable of efficiently utilizing an arbitrary number of transputers. Fire simulations consisting of up to 24 000 computational cells are performed on parallel systems with up to 15‐processors. The run time for this simulation has been reduced from over 4 days on a single processor to just over 8 h on the 15‐processor system. An interactive graphics system has also been developed which runs in parallel with the main computations.
A slope modification method for shallow water equations
Authors: Rao V. Subba , Latha G. 
Published: August 2005

AbstractA slope modification method is proposed for non‐oscillatory schemes based on the Lax‐Friedrich solver. The modified scheme is proved to be total‐variation‐diminishing (TVD) and second‐order accurate. Application of the scheme to the shallow water equations produces sharp profiles for shocks and achieves high accuracy in the smooth regions of the solution.
Orthogonal arrays: An introduction and their application in optimizing underrelaxation factors in ‘simple’‐based algorithm
Authors: Gopinath R. , Ganesan V. 
Published: August 2005

AbstractThe primary aim of this paper is to demonstrate how the ‘design‐of‐experiments’ techniques which are successful in physical experiments could also be adapted to a numerical simulation code.As an example this technique is applied to a general finite difference code used for predicting three‐dimensional turbulent recirculating flows. Here the equations for velocities and continuity are solved using the algorithm called SIMPLE, which stands for semi‐implicit method for pressure‐linked equations. Physical modelling of turbulence is taken care of by means of kinetic energy and turbulence dissipation rate equations.The objective is to optimize the underrelaxation factors of primary and secondary flow variables so that the number of iterations required for convergence is minimum. This is done by the orthogonal array technique (a particular type of design‐of‐experiment technique).The geometry considered for this purpose is that of a simple gas turbine can combustor and the study is restricted to the isothermal non‐reacting condition.Tests are carried out on three different grid configurations. In each case the underrelaxation factor for velocities contributed most to speed up the rate of convergence. Also, for each grid configuration the underrelaxation factor settings for minimum iterations for convergence was found to be same. Hence it is proposed that when doing grid independence tests for any similar flow situation, all the underrelaxation factors could be optimized on coarse grids.