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  • 1
    Electronic Resource
    Electronic Resource
    Implicit schemes for unsteady Euler equations on triangular meshes (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 647-668 
    Details
    ISSN: 0271-2091
    Keywords: Euler equations ; Finite element method ; Implicit scheme ; Unsteady flow ; Transonic flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An implicit finite element method is presented for the solution of steady and unsteady inviscid compressible flows on triangular meshes under transonic conditions. The method involves a first-order time-stepping scheme with a finite element discretization that reduces to central differencing on a rectangular mesh. On a solid wall the slip condition is prescribed and the pressure is obtained from an approximation of the normal momentum equation. With this solver no artificial viscosity is added to ensure the success of the calculation. Numerical examples are given for steady and unsteady cases.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650180703
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  • 2
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    Finite element implementation of boundary conditions for the pressure Poisson equation of incompressible flow (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 1009-1019 
    Details
    ISSN: 0271-2091
    Keywords: Pressure Poisson equation ; Incompressible flow ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper we address the problem of the implementation of boundary conditions for the derived pressure Poisson equation of incompressible flow. It is shown that the direct Galerkin finite element formulation of the pressure Poisson equation automatically satisfies the inhomogeneous Neumann boundary conditions, thus avoiding the difficulty in specifying boundary conditions for pressure. This ensures that only physically meaningful pressure boundary conditions consistent with the Navier-Stokes equations are imposed. Since second derivatives appear in this formulation, the conforming finite element method requires C1 continuity. However, for many problems of practical interest (i.e. high Reynolds numbers) the second derivatives need not be included, thus allowing the use of more conventional C0 elements. Numerical results using this approach for a wall-driven contained flow within a square cavity verify the validity of the approach. Although the results were obtained for a two-dimensional problem using the p-version of the finite element method, the approach presented here is general and remains valid for the conventional h-version as well as three-dimensional problems.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650181102
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  • 3
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    Application of streamwise diffusion to time-dependent free convection of liquid metals (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 1061-1071 
    Details
    ISSN: 0271-2091
    Keywords: Streamwise diffusion ; Taylor-Galerkin method ; Finite element method ; Free convection ; Liquid metals ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical analysis is given for the application of streamwise diffusion to high-intensity flows with marginal spatial resolution. Terms are added to the momentum equation which are similar to those used in the Petrov-Galerkin, Taylor-Galerkin and balancing tensor diffusivity methods. Values for the streamwise viscosity are obtained from mesh refinement studies. An illustration is given for the time-dependent free convection of a liquid metal in a cavity with differentially heated sided walls. The spatial problem is solved with the Galerkin finite element method and the time integration is performed with the backward Euler method. Solution quality and computation time are compared for results with and without added streamwise diffusion. For the cases presented, streamwise diffusion eliminates spurious oscillations and saves computation time without compromising the solution.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650181104
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  • 4
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    On the implementation of symmetric and antisymmetric periodic boundary conditions for incompressible flow (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 1153-1165 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Incompressible flow ; Finite element method ; Finite volume method ; Periodic boundary condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper we consider symmetric and antisymmetric periodic boundary conditions for flows governed by the incompressible Navier-Stokes equations. Classical periodic boundary conditions are studied as well as symmetric and antisymmetric periodic boundary conditions in which there is a pressure difference between inlet and outlet. The implementation of this type of boundary conditions in a finite element code using the penalty function formulation is treated and also the implementation in a finite volume code based on pressure correction. The methods are demonstrated by computation of a flow through a staggered tube bundle.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650181203
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  • 5
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    Development of the direct stress solution technique for three-dimensional hydrodynamic models using finite elements (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 295-319 
    Details
    ISSN: 0271-2091
    Keywords: Three-dimensional circulation model ; Direct stress solution ; Internal mode solution ; Velocity profile ; Boundary layers ; Tidal flow ; Wind-driven flow ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Velocity varies rapidly near sheared boundaries. Therefore in many practical fluid problems it can be inefficient to solve discrete equations with velocity as the dependent variable. Conversely, shear stress varies slowly near sheared boundaries, suggesting that it may be well suited for use as the dependent variable in discrete equations.This paper describes a formulation of the internal mode equations for a three-dimensional hydrodynamic model using shear stress as the dependent variable. The resulting direct stress solution (DSS), coupled with a spatial discretization using linear finite elements, yields a system matrix that can be set up and solved with the efficiency of a banded matrix with bandwidth 8. If the eddy viscosity distribution is assumed to be piecewise linear over the depth (with an arbitrary number of time-varying segments), the recovery of velocity from stress can be easily accomplished in closed form, thereby avoiding any difficulty resulting from the logarithmic singularity in the velocity profile that occurs at a boundary.Results from tidal and wind-driven test cases with realistic boundary layers are used to demonstrate the accuracy and computational advantages of a DSS formulation versus a standard velocity-based formulation.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650190403
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  • 6
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    Gradient method of optimal control applied to the operation of a dam water gate (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 463-477 
    Details
    ISSN: 0271-2091
    Keywords: Water gate of dam ; Gradient method ; Optimal control ; Finite element method ; Hydraulic model ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An extension of the authors' previous methods is presented for the optimal control of flood propagation via a dam gate, based on a combination of the finite element and gradient methods. It is assumed in previous papers that the control duration is the same as the duration of the flood. However, the duration of the control does not necessarily coincide with that of the flood flow. To overcome this difficulty, the gradient method is applied to solve the free terminal time-fixed terminal condition problem. It is shown that the water elevation can be controlled exactly the same as with the previously presented method. It is also shown that the computation can be terminated at a far shorter time than the terminal time of the flood.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650190602
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  • 7
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    Diffraction contrast near heterostructure boundaries - its nature and its application (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Microscopy Research and Technique 24 (1993), S. 288-298 
    Details
    ISSN: 1059-910X
    Keywords: α/δ-Boundary ; Strain analysis ; Finite element method ; 90°-wedges ; Life and Medical Sciences ; Cell & Developmental Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Natural Sciences in General
    Notes: Two phenomena of diffraction contrast arising at or near III-V compound hetero-structure boundaries are described and quantitatively analyzed. In the first observation α/δ-fringe contrast at boundaries inclined to the electron beam is discussed. Theoretical fringe profiles are generated according to the theory by Gevers et al. in 1964, which are then compared with experimental profiles. Applications to the characterization of AlGaAs/GaAs and InGaAsP/InP interfaces regarding composition, abruptness, and lattice tilt are presented. In the second study a new and very sensitive characterization technique for the direct determination of the strain in strainedlayer structures is described. The method uses electron microscope images of 90°-wedges, which exhibit a shift in the thickness contours due to strain relaxation at the edge, and compares these to images which are obtained theoretically by implementing finite element strain calculations in wedges in the dynamical theory of diffraction contrast. The considerable potential of this method is demonstrated on the strain analysis of strained GaInAs/GaAs structures. © 1993 Wiley-Liss, Inc.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/jemt.1070240403
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  • 8
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    Surface waves propagation in shallow water: A finite element model (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 447-459 
    Details
    ISSN: 0271-2091
    Keywords: Shallow water ; Boussinesq equations ; Finite element method ; Solitary wave ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A two-dimensional (in-plane) numerical model for surface waves propagation based on the non-linear dispersive wave approach described by Boussinesq-type equations, which provide an attractive theory for predicting the depth-averaged velocity field resulting from that wave-type propagation in shallow water, is presented. The numerical solution of the corresponding partial differential equations by finite-difference methods has been the subject of several scientific works. In the present work we propose a new approach to the problem: the spatial discretization of the system composed by the Boussinesq equations is made by a finite element method, making use of the weighted residual technique for the solution approach within each element. The model is validated by comparing numerical results with theoretical solutions and with results obtained experimentally.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650160602
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  • 9
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    Incompressible low-speed-ratio flow in non-uniform distensible tubesThis research project is supported by the Dutch Foundation for Scientific Research NWO. (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 597-612 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Finite element method ; Distensible tubes ; Wave propagation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The fluid flow in distensible tubes is analysed by a finite element method based on an uncoupled solution of the equations of wall motion and fluid flow. Special attention is paid to the choice of proper boundary conditions. Computations were made for sinusoidal flow in a distensible uniform tube with the Womersley parameter α = 5, and a ratio between tube radius and wavelenth from 0·0001 to 0·5. The agreement between the numerical results and Womersley's analytic solution depends on the speed ratio between fluid and wave velocity, and is fair for speed ratios up to 0·05. The analysis of the flow field in a distensible tube with a local inhomogeneity revealed a marked influence of wave phenomena and wall motion on the velocity profiles.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650160704
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  • 10
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    Preconditioned finite element algorithms for 3D Stokes flows (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 667-685 
    Details
    ISSN: 0271-2091
    Keywords: 3D Stokes flow ; Finite element method ; Uzawa algorithm ; Preconditioned conjugale gradient method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Preconditioned conjugate gradient algorithms for solving 3D Stokes problems by stable piecewise discontinuous pressure finite elements are presented. The emphasis is on the preconditioning schemes and their numerical implementation for use with Hermitian based discontinuous pressure elements. For the piecewise constant discontinuous pressure elements, a variant implementation of the preconditioner proposed by Cahouet and Chabard for the continuous pressure elements is employed. For the piecewise linear discontinuous pressure elements, a new preconditioner is presented. Numerical examples are presented for the cubic lid-driven cavity problem with two representative elements, i.e. the Q2-PO and the Q2-P1 brick elements. Numerical results show that the preconditioning schemes are very effective in reducing the number of pressure iterations at very reasonable costs. It is also shown that they are insensitive to the mesh Reynolds number except for nearly steady flows (Rem → 0) and are almost independent of mesh sizes. It is demonstrated that the schemes perform reasonably well on non-uniform meshes.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650170803
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  • 11
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    Solution of free-boundary problems using finite-element/Newton methods and locally refined grids: Application to analysis of solidification microstructure (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 827-843 
    Details
    ISSN: 0271-2091
    Keywords: Local mesh refinement ; Free boundary ; Finite element method ; Co-ordinate mapping ; Solidification ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650160906
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  • 12
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    Segregated finite element algorithms for the numerical solution of large-scale incompressible flow problems (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 323-348 
    Details
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Finite element method ; Segregated solution algorithms ; Iterative solvers ; Implicit preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents results of an ongoing research program directed towards developing fast and efficient finite element solution algorithms for the simulation of large-scale flow problems. Two main steps were taken towards achieving this goal. The first step was to employ segregated solution schemes as opposed to the fully coupled solution approach traditionally used in many finite element solution algorithms. The second step was to replace the direct Gaussian elimination linear equation solvers used in the first step with iterative solvers of the conjugate gradient and conjugate residual type. The three segregated solution algorithms developed in step one are first presented and their integrity and relative performance demonstrated by way of a few examples. Next, the four types of iterative solvers (i.e. two options for solving the symmetric pressure type equations and two options for solving the non-symmetric advection-diffusion type equations resulting from the segregated algorithms) together with the two preconditioning strategies employed in our study are presented. Finally, using examples of practical relevance the paper documents the large gains which result in computational efficiency, over fully coupled solution algorithms, as each of the above two main steps are introduced. It is shown that these gains become increasingly more dramatic as the complexity and size of the problem is increased.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170405
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  • 13
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    Finite element analysis of lift build-up due to aerofoil indicial motion (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 401-416 
    Details
    ISSN: 0271-2091
    Keywords: Finite element method ; Aerofoil indicial motion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper the problem of impulsively started aerofoil or suden change of incidence of an aerofoil in incompressible potential flow is investigated. The essence of solution lies in the representation of a timely and spatially varying wake in a largely irrotational potential flow field. This is achieved by representing the wake through velocity potential difference, which seems to be the only way of imposing a velocity difference condition in the finite element context with velocity potentials as the basic unknowns. Superposition is employed to meet various boundary conditions, which is justified by the linearity of the problem. The finite element solutions are compared with those from singularity method.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170505
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  • 14
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    Compressible gas flow between closely spaced plates (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 299-325 
    Details
    ISSN: 0271-2091
    Keywords: Compressible gas bearing ; Choked flow ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A theoretical analysis is presented to solve numerically the steady state Navier-Stokes equations, continuity equation and energy equation for a compressible ideal gas flow between two closely spaced, in general nonparallel, infinitely wide plates (siider bearing). The analysis includes the gas inertia effect and covers both non-choked and choked flows. The results of the present analysis compare very well with both analytical and experimental results of compressible flow in a slider bearing comprised of two parallel and stationary plates. It was found that for choked flow the gas inertia effect is important, while the consideration of the energy equation does not affect the accuracy of the calculated flow substantially. Finally, the stiffness of a slider bearing is presented for different geometrical characteristics of the bearing.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140305
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  • 15
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    Numerical method for unsteady viscous hydrodynamical problem with free boundaries (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 681-705 
    Details
    ISSN: 0271-2091
    Keywords: Unsteady Navier-Stokes equations ; Finite element method ; Viscous flow ; Free boundary flow ; Multiphase flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element method for the transient incompressible Navier-Stokes equations with the ability to handle multiple free boundaries is presented. Problems of liquid-liquid type are treated by solving two coupled Navier-Stokes problems for two separate phases. The possibility to solve problems of liquid-gas, liquid-liquid-gas or liquid-liquid-liquid type is demonstrated too. Surface tension effects are included at deformable interfaces.The method is of Lagrangian type with mesh redefinition. A predictor-corrector scheme is used to compute the position of the deformable interface with automatic control of its accuracy and smoothness. The method is provided with an automatic choice of the time integration step and an optional spline filtration of the truncation error at the free surface. In order to show the accuracy of the method, tests and comparisons are presented. Numerical examples include motion of bubbles and multiple drops.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650140604
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  • 16
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    Boundary-conforming mapping applied to computations of highly deformed solidification interfaces (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 981-1003 
    Details
    ISSN: 0271-2091
    Keywords: Co-ordinate mapping ; Finite element method ; Free-boundary ; Solidification ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new boundary-conforming mapping is developed for the calculation of highly deformed cellular solidification interfaces in a model of directional solidification of a binary alloy. The mapping is derived through a variational fomulation that is designed so that the grid penetrates the grooves between cells along the interface without causing a loss of ellipticity of the mapping equations. A finite element/Newton method is presented for simultaneous solution of the free boundary problem described by the solutal model of directional solidification and the mapping equations. Results are compared to previous calculations and demonstrate the importance of accurate representation of the interface shape for understanding the solution structure.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650140807
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  • 17
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    Periodic solution of turbulent oscillating channel flows (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 443-457 
    Details
    ISSN: 0271-2091
    Keywords: Turbulent oscillating flows ; Finite element method ; The method of averaging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The time-dependent turbulent Navier-Stokes equations are solved numerically by a finite element method with an algebraic eddy viscosity model (Baldwin-Lomax formulation) for oscillating turbulent channel flows. The method of averaging is used to analyse the resulting periodic motion of the fluid. Numerical results are obtained for various Strouhal numbers and relative amplitudes. A comparison is made between the numerical and published experimental results. It appears that for low relative amplitudes in a certain range of frequencies the agreement is satisfactory.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650140405
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  • 18
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    Implementation of the Lagrange-Galerkin method for the incompressible Navier-Stokes equations (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 23-36 
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    ISSN: 0271-2091
    Keywords: Incompressible Navier-Stokes equations ; Finite element method ; Lagrange-Galerkin method ; Geometric search algorithm ; Vortex shedding ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is concerned with the implementation of Lagrange-Galerkin finite element methods for the Navier-Stokes equations. A scheme is developed to efficiently handle unstructed meshes with local refinement, using a quad-tree-based algorithm for the geometric search. Several difficulties that arise in the construction of the right-hand side are discussed in detail and some useful tricks are proposed.The resulting method is tested on the lid-driven square cavity and the vortex shedding behind a rectangular cylinder and is found to give satisfactory agreement with previous works. A detailed analysis of the effect of time discretization is included.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650150103
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  • 19
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    Flow field modelling near a well with a conductive fracture (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 545-569 
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    ISSN: 0271-2091
    Keywords: Oil recovery ; Porous medium ; Conductive fracture ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In 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.
    Additional Material: 21 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650150504
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  • 20
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    Computation of incompressible viscous flows by the third-order upwind finite element method (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 1013-1024 
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    ISSN: 0271-2091
    Keywords: Third-order upwind scheme ; Finite element method ; Petrov-Galerkin formulation ; Mixed formulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A third-order upwind finite element scheme is presented for numerical solutions of incompressible viscous flow problems. In order to achieve the third-order upwind approximation for only the convection term in the Navier-Stokes equations, a simplified Petrov-Galerkin formulation in which a modified weighting function is expressed by the sum of a standard weighting function and its second and third spatial derivatives is employed. The mixed method is also employed in the formulation so that a discretization with high-order accuracy in space is carried out by the use of linear elements. Because a truncation error caused by the third-order upwind approximation is smaller than that of a first-order upwind scheme, it is expected that the third-order upwind scheme will greatly improve the numerical solutions of the Navier-Stokes equations. Numerical results in one and two dimensions are presented to illustrate the effectiveness of the proposed scheme.
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    URL: http://dx.doi.org/10.1002/fld.1650150907
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    An orthogonal mapping technique for the computation of a viscous free-surface flow (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 1243-1258 
    Details
    ISSN: 0271-2091
    Keywords: Free surface ; Viscous flow ; Finite element method ; Orthogonal mappings ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper we describe finite element computations of the free-surface flow of a viscous fluid down an undulating inclined plane. The technique developed here employs an orthogonal mapping that is computed along with the velocity and pressure. This is allied to a technique to compute symbolically the Jacobian and other derivatives required for numerical continuation methods. The solutions obtained are compared with laboratory experiments and finite element computations reported by Pritchard and co-workers. The finite element computational method used by these authors employs spines to represent the free surface. An excellent agreement is shown to exist between the new computations and the laboratory experiments, and with the numerical solutions of Pritchard and co-workers.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650151102
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    Numerical analysis of convection-diffusion with chemical reaction by combined finite and boundary element methods (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 465-479 
    Details
    ISSN: 0271-2091
    Keywords: Convective diffusion ; Chemical reaction ; Finite element method ; Boundary element method ; Combined method ; Coupling method ; COD ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical method is presented to analyse a steady convection-diffusion problem with a first-order chemical reaction defined on an infinite region. The present method is based on the combined finite element and boundary element methods. For one- and two-dimensional examples in an infinite region the numerical results by the present method are in excellent agreement with the exact solutions. As a practical application, the simulation of the concentration distribution of the chemical oxygen demand at Kojima Bay is carried out.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650130405
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    A 3D finite element method for the simulation of thermoconvective flows and its performances on a vector-parallel computer (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 929-946 
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    ISSN: 0271-2091
    Keywords: Three-dimensional flows ; Thermoconvective flow ; Finite element method ; Preconditioned conjugate gradient methods ; Rayleigh-Bénard convection ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A three-dimensional finite element method for the simulation of thermoconvective flows is presented. Vector-parallel performances of some preconditioned conjugate gradient methods are compared for solving both large linear systems and the Stokes problem. As significant examples, numerical experiments on the steady two- and three-dimensional Rayleigh-Bénard convection at high Prandtl number are reported.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650121003
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    Variational formulation of three-dimensional viscous free-surface flows: Natural imposition of surface tension boundary conditions (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 691-698 
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    ISSN: 0271-2091
    Keywords: Curvature ; Finite element method ; Free surface flow ; Navier-Stokes equations ; Spectral element method ; Surface tension ; Three-dimensional ; Variational form ; Viscous incompressible flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present a new surface-intrinsic linear form for the treatment of normal and tangential surface tension boundary conditions in C0-geometry variational discretizations of viscous incompressible free-surface flows in three space dimensions. The new approach is illustrated by a finite (spectral) element unsteady Navier-Stokes analysis of the stability of a falling liquid film.
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    URL: http://dx.doi.org/10.1002/fld.1650130603
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    Lagrangian finite element method for free surface Navier-Stokes flow using fractional step methods (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 805-840 
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    ISSN: 0271-2091
    Keywords: Finite element method ; Lagrangian description ; Fractional step method ; Navier-Stokes equation ; Linear interpolation ; Free surface ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a finite element analysis based on the Lagrangian description for unsteady incompressible viscous fluid flow with a free surface. The behaviour of the fluid is expressed by the unsteady Navier-Stokes equation. For numerical integration in time the fractional step method is used. This method is useful because one can use the same linear interpolation functions for both velocity and pressure. In this paper, four variations of the fractional step method are presented and the numerical results are compared. To confirm the effectiveness of these methods, solitary wave propagation is analysed.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650130702
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    Grey-body surface radiation coupled with conduction and convection for general geometries (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 1029-1053 
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    ISSN: 0271-2091
    Keywords: Grey-body radiation ; Finite element method ; Incompressible fluid flow ; Macrosurfaces ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a numerical technique for the simulation of the effects of grey-diffuse surface radiation on the temperature field of fluid flows using FIDAP, a general purpose incompressible, viscous fluid code. The radiating surface relationships assume a non-participating medium, constant surface temperature and heat fluxes at the discretized elemental level.The technique involves the decoupling of energy and radiation exchange equations. A concept of macrosurfaces, each containing a number of radiating boundary surfaces, is introduced. These boundary macroelements then carry the information from the radiating boundary into the fluid regime. A number of simulations illustrating the algorithm are presented.
    Additional Material: 19 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650130806
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    A decomposed Crouzeix-Raviart element for the finite element solution of the Navier-Stokes equation (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 1073-1083 
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    ISSN: 0271-2091
    Keywords: Crouzeix-Raviart ; Analytical integration ; Brezzi-Babuška condition ; Navier-Stokes ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A methodology for the decomposition of the Crouzeix-Raviart finite element into six linear subelements is described. The resulting element is shown to satisfy the Brezzi-Babuška compatibility condition. The error bounds are also established. A comparison in accuracy between this and the standard Crouzeix-Raviart element is presented for driven cavity flows. Other results include the execution time for the DCR element and the Crouzeix-Raviart element along with both analytical and numerical integration. It is shown that the decomposed element results in shorter execution times with only marginal changes in accuracy.
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    Finite element method for shallow water equation including open boundary condition (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 939-953 
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    ISSN: 0271-2091
    Keywords: Finite element method ; Shallow water equation ; Open boundary condition ; Parameter identification ; Tokyo Bay ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A method to deal with an open boundary condition in the analysis of water surface waves, the tide, etc. by means of the finite element method is proposed in this paper. The present method has two important features relating to the treatment of the open boundary condition. The first feature is to consider the non-reflective virtual boundary condition which has been developed in the numerical wave analysis method. The incident wave conditions without spurious reflected waves can be imposed at the open boundary. The second feature is to identify the amplitude of the components of incident waves in terms of observed water elevations in the field of standing waves. This can be done as a parameter identification based on an optimization problem by applying the conjugate gradient method. The applicability of this method to wave propagation problems is verified by several numerical computations.
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    Numerical solution of plane and axially symmetric jet flow problems based on the variational inequality formulation (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 213-222 
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    ISSN: 0271-2091
    Keywords: Jet flow ; Variational inequality ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The numerical analysis of plane and axially symmetric jet flows of an incompressible inviscid fluid is treated. A new formulation of the variational inequality type is developed from the variational principle associated with jet problems. A successive approximation method is formulated by the combined use of variational inequality and the finite element method. Numerical examples based on the iterative method are presented. The results obtained agree well with those by other methods.
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    URL: http://dx.doi.org/10.1002/fld.1650100207
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    Self-adaptive hierarchic finite element solution of the one-dimensional unsaturated flow equation (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 227-246 
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    ISSN: 0271-2091
    Keywords: Adaptive ; Finite element method ; p-version ; Unsaturated flow ; Hierarchic ; Non-linear ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The advantages associated with the use of self-adaptive methods for the solution of problems which require the prediction of a frontal position in time are well known. In this paper a self-adaptive finite element solution for the non-linear unsaturated flow equation is developed using hierarchic p-version enrichment of the interpolating space. Additional computational advantages are demonstrated for an iteration scheme in which iterations after enrichment are performed only over a subdomain. Numerical solutions are presented for a one-dimensional infiltration scenario.
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    Boundary node correction and superconvergence in the FEM (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 713-721 
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    ISSN: 0271-2091
    Keywords: Boundary node correction ; Pressure smoothing ; Finite element method ; Superconvergence ; Posterior error analysis ; Multiple mesh extrapolation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Convergence improvement and superconvergence behaviour, obtained by the simple boundary node correction (BNC) procedure for certain stress-like variables of smoothed FEM solutions, are reported in this paper. The effectiveness of BNC is shown through three examples of steady flow problems, and a posterior error analysis based on the multiple-mesh extrapolation technique has been used for estimating the convergence rates.
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    Two-dimensional sloshing analysis by Lagrangian finite element method (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 453-477 
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    ISSN: 0271-2091
    Keywords: Finite element method ; Lagrangian description ; Velocity correction method ; Sloshing analysis ; Waves in a container ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two dimensional sloshing analysis has been carried out by the Lagrangian finite element method. For the integration in time, the velocity correction method with the same interpolation functions for velocity and pressure is successfully used. The Lagrangian treatment to pursue the free surface position is presented. The comparison with the experiments shows extremely good agreement. It is shown that the large amplitude sloshing waves in a container can be analyzed by the present method.
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    Finite element analysis of creeping flows using marker particles (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 397-404 
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    ISSN: 0271-2091
    Keywords: Numerical analysis ; Finite element method ; Transient flow ; Free surface flow ; Creeping flow ; Power-law fluid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The penalty function formulation of the finite element method is described for the analysis of transient incompressible creeping flows. Marker particles are utilized to represent moving free surfaces and to visualize the flow patterns. For determining the movement of markers from element to element, the area coordinate system of the linear triangular element is introduced.With the method presented, a punch indentation problem and an injection problem for an L-shaped cavity are solved for Newtonian and power-law fluids.
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    Transient flow past a circular cylinder: A benchmark solution (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 985-1000 
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    ISSN: 0271-2091
    Keywords: Outflow boundary conditions ; Vortex shedding ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The simulation of the von Karman vortex street behind a circular cylinder has long been used as a benchmark problem to test the performance of numerical algorithms for solving the Navier-Stokes equations. It is particularly suited for comparing different numerical outflow boundary conditions since the computational domain must necessarily be terminated in the vortex street itself. This paper presents detailed numerical results of the flow past a cylinder at a Reynolds number of 100 on a very fine mesh which has been purposely designed to extend past the typically used dimensions. Hopefully, these results can form a basis of a benchmark solution for the comparison of the effects of different outflow boundary conditions.
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    URL: http://dx.doi.org/10.1002/fld.1650110706
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    Finite element technique to solve the elastic strain for Leonov fluid flow (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1059-1072 
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    ISSN: 0271-2091
    Keywords: Viscoelastic flow ; Leonov model ; Convective integration ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The finite element method is used to find the elastic strain (and thus the stress) for given velocity fields of the Leonov model fluid. With a simple linearization technique and the Galerkin formulation, the quasi-linear coupled first-order hyperbolic differential equations together with a non-linear equality constraint are solved over the entire domain based on a weighted residual scheme. The proposed numerical scheme has yielded efficient and accurate convective integrations for both the planar channel and the diverging radial flows for the Leonov model fluid. Only the strain in the inflow plane is required to be prescribed as the boundary conditions. In application, it can be conveniently incorporated in an existing finite element algorithm to simulate the Leonov viscoelastic fluid flow with more complex geometry in which the velocity field is not known a priori and an iterative procedure is needed.
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    Numerical analysis of the developing fluid flow in a circular duct rotating steadily about a parallel axis (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 151-165 
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    ISSN: 0271-2091
    Keywords: Numerical analysis ; Fluid flow ; Rotating circular duct ; Finite cell method ; Finite element method ; Swirl ; Inlet boundary conditions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical analysis of the flow pattern in the inlet region of a circular pipe rotating steadily about an axis parallel to its own is presented. Both finite cell and finite element methods are used to analyse the problem and they give qualitatively similar results which show that a swirling fluid motion is induced in the pipe inlet region. The analyses show that the direction of swirl is opposite to that of the pipe rotation when viewed along the flow axis and that its magnitude depends on the speed of pipe rotation and throughflow Reynolds number. Neither numerical analysis predicts the marked upturn in friction factor (or pressure drop) which has been observed experimentally. However, a dependence on the pipe inlet boundary conditions is demonstrated.
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    A pressure-smoothing scheme for incompressible flow problems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 557-567 
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    ISSN: 0271-2091
    Keywords: Pressure-smoothing scheme ; Least square ; Finite element method ; Incompressible flow ; Newtonian and Maxwell fluids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A pressure-smoothing scheme for Stokes and Navier-Stokes flows of Newtonian fluids and for Stokes flow of Maxwell fluids is described. The stress deviator obtained from the calculated velocity field is substituted into the governing equilibrium equation. The resulting equation is then solved to obtain a new, smoothed pressure by a least square finite element method.
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    Multifronts and transputer networks for solving fluid mechanical finite element systems (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 731-740 
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    ISSN: 0271-2091
    Keywords: Multifrontal solver ; Transputer networks ; Fluid mechanics ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is concerned with the implementation of a multifrontal solver on a network of transputers. We briefly discuss the transputer, outline the frontal and multifrontal schemes and consider the implementation of these schemes on the network. Results are presented for two test problems in fluid mechanics showing that the solver displays close to linear speed-up.
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    A finite element method for analysis of fluid flow, heat transfer and free interfaces in Czochralski crystal growth (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 453-492 
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    ISSN: 0271-2091
    Keywords: Czochralski crystal growth ; Finite element method ; Free boundary problem ; Incompressible fluid flow ; Heat transfer ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element algorithm is presented for simultaneous calculation of the steady state, axisymmetric flows and the crystal, melt/crystal and melt/ambient interface shapes in the Czochralski technique for crystal growth from the melt. The analysis is based on mixed Lagrangian finite element approximations to the velocity, temperature and pressure fields and isoparametric approximations to the interface shape. Galerkin's method is used to reduce the problem to a non-linear algebraic set, which is solved by Newton's method. Sample solutions are reported for the thermophysical properties appropriate for silicon, a low-Prandtl-number semiconductor, and for GGG, a high-Prandtl-number oxide material. The algorithm is capable of computing solutions for both materials at realistic values of the Grashof number, and the calculations are convergent with mesh refinement. Flow transitions and interface shapes are calculated as a function of increasing flow intensity and compared for the two material systems. The flow pattern near the melt/gas/crystal tri-junction has the asymptotic form predicted by an inertialess analysis assuming the meniscus and solidification interfaces are fixed.
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    A finite element analysis of the steady laminar entrance flow in a 90° curved tube (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 275-287 
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    ISSN: 0271-2091
    Keywords: Curved pipe flow ; Entrance flow ; Finite element method ; Penalty function method ; Experimental validation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A standard Galerkin finite element penalty function method is used to approximate the solution of the three-dimensional Navier-Stokes equations for steady incompressible Newtonian entrance flow in a 90° curved tube (curvature ratio δ = 1/6) for a triple of Dean numbers (κ = 41, 122 and 204). The computational results for the intermediate Dean number (κ = 122) are compared with the results of laser-Doppler velocity measurements in an equivalent experimental model. For both the axial and secondary velocity components, fair agreement between the computational and experimental results is found.
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    A finite element analysis of a free surface drainage problem of two immiscible fluids (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 569-582 
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    ISSN: 0271-2091
    Keywords: Flow analysis ; Free surface problem ; Finite element method ; Blast furnace ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A sharp interface problem arising in the flow of two immiscible fluids, slag and molten metal in a blast furnace, is formulated using a two-dimensional model and solved numerically. This problem is a transient two-phase free or moving boundary problem, the slag surface and the slag-metal interface being the free boundaries. At each time step the hydraulic potential of each fluid satisfies the Laplace equation which is solved by the finite element method. The ordinary differential equations determining the motion of the free boundaries are treated using an implicit time-stepping scheme. The systems of linear equations obtained by discretization of the Laplace equations and the equations of motion of the free boundaries are incorporated into a large system of linear equations. At each time step the hydraulic potential in the interior domain and its derivatives on the free boundaries are obtained simultaneously by solving this linear system of equations. In addition, this solution directly gives the shape of the free boundaries at the next time step. The implicit scheme mentioned above enables us to get the solution without handling normal derivatives, which results in a good numerical solution of the present problem. A numerical example that simulates the flow in a blast furnace is given.
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    Forces on oscillating bodies in viscous fluid (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 519-536 
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    ISSN: 0271-2091
    Keywords: Fluid forces ; Viscous incompressible flow ; Fluid-structure interaction ; Finite element method ; Steady streaming ; Added mass ; Added damping ; Added force ; Oscillation flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper describes a method for determining the fluid forces on oscillating bodies in viscous fluid when the corresponding flow problem has been solved using the finite element method. These forces are characterized by the concept of added mass, added damping and added force. Numerical results are obtained for several example body shapes. Comparison is made with exact analytical results and other finite element results for the limiting cases of Stoke's flow and inviscid flow, and good agreement is obtained. The results for finite values of the body amplitude parameter β show the appearance of added force from the steady streaming component of the flow for asymmetric bodies. Results are also obtained for the associated flow where the fluid remote from a fixed body is oscillating.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080503
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  • 43
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    Developing flows in narrow channels, containing heated obstacles (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 1543-1561 
    Details
    ISSN: 0271-2091
    Keywords: Developing flow ; CFD ; FIDAP ; Finite element method ; Electronic packaging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The use of numerical techniques to augment experimentally collected temperature data of electrical components is illustrated. FIDAP, a finite element CFD code, is used to generate the numerical results. Comparisons of the numerical results with experimental data of HaCohen, experimentally derived correlations of Wirtz and Dykshoorn and numerical results of Heaton et al. are given. A discussion of modelling techniques, mesh refinement, numerical error and stability is presented with suggestions for improvement of flow models. The results generated by FIDAP, using 2D models, compare favourably (to within 10%) with the experimental data of HaCohen. The results indicate the possibility of augmenting experimental data collection with numerical results, at least in the regions of laminar and low turbulent flow.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650081206
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  • 44
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    Laminar natural convection in a partially divided rectangular cavity at high Rayleigh number (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 247-281 
    Details
    ISSN: 0271-2091
    Keywords: Natural convection ; Finite element method ; High Rayleigh number ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Finite element predictions of two-dimensional laminar natural convection in a partially divided rectangular cavity at high Rayleigh number are presented. The walls are differentially heated, the horizontal surfaces are insulated and the cavity contains a partial vertical divider which is centrally located and whose height is varied. Detailed results are presented for an aluminium half-divider in water for Rayleigh number up to 1011 and compared directly with recent experiments in a cavity of aspect ratio 1/2. The predicted flow and heat transfer are in good agreement with the measurements and confirm the existence of a high Rayleigh number regime with characteristic behaviour that differs significantly from that found at lower Rayleigh number. In addition, the effects of the divider height, the divider conductivity, the fluid Prandtl number and the cavity aspect ratio are studied. The results show that a direct simulation of the complex flow and heat transfer that occurs in partially divided cavities is possible for realistic physical conditions.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080302
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  • 45
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    A total linearization method for solving viscous free boundary flow problems by the finite element method (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 351-363 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Finite element method ; Viscous flow ; Free boundary flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper a total linearization method is derived for solving steady viscous free boundary flow problems (including capillary effects) by the finite element method. It is shown that the influence of the geometrical unknown in the totally linearized weak formulation can be expressed in terms of boundary integrals. This means that the implementation of the method is simple. Numerical experiments show that the iterative method gives accurate results and converges very fast.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080308
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  • 46
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    A Petrov-Galerkin method for the numerical solution of the Bradshaw-Ferriss-Atwell turbulence model (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 493-517 
    Details
    ISSN: 0271-2091
    Keywords: Turbulent boundary layer flow ; Hyperbolic systems ; Finite element method ; Petrov-Galerkin method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Bradshaw-Ferriss-Atwell model for 2D constant property turbulent boundary layers is shown to be ill-posed with respect to numerical solution. It is shown that a simple modification to the model equations results in a well-posed system which is hyperbolic in nature. For this modified system a numerical algorithm is constructed by discretizing in space using the Petrov-Galerkin technique (of which the standard Galerkin method is a special case) and stepping in the timelike direction with the trapezoidal (Crank-Nicolson) rule. The algorithm is applied to a selection of test problems. It is found that the solutions produced by the standard Galerkin method exhibit oscillations. It is further shown that these oscillations may be eliminated by employing the Petrov-Galerkin method with the free parameters set to simple functions of the eigenvalues of the modified system.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080502
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  • 47
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    Two-equation (k, ∊) turbulence computations by the use of a finite element model (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 965-975 
    Details
    ISSN: 0271-2091
    Keywords: Finite element method ; Turbulent flow ; Method of characteristics ; Penalty function approach ; Galerkin method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element technique is presented and applied to some one- and two-dimensional turbulent flow problems. The basic equations are the Reynolds averaged momentum equations in conjunction with a two-equation (k, ∊) turbulence model. The equations are written in time-dependent form and stationary problems are solved by a time iteration procedure. The advection parts of the equations are treated by the use of a method of characteristics, while the continuity requirement is satisfied by a penalty function approach. The general numerical formulation is based on Galerkin's method. Computational results are presented for one-dimensional steady-state and oscillatory channel flow problems and for steady-state flow over a two-dimensional backward-facing step.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080808
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  • 48
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    Evaluation of FIDAP on some classical laminar and turbulent benchmarks (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 1469-1490 
    Details
    ISSN: 0271-2091
    Keywords: Finite element method ; Incompressible fluids ; Laminar and turbulent flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical solutions of the Fluid Dynamics Analysis Package (FIDAP) for some laminar and turbulent flow problems, namely (1) two-dimensional laminar flow inside a wall-driven cavity, (2) two-dimensional laminar flow over a backward-facing step and (3) two-dimensional turbulent flow over a backward-facing step, are presented. The consistent integration penalty finite element method is used with Q2/P1 (nine-node biquadratic velocity with linear discontinuous pressure) finite elements. Results of FIDAP on the above problems are compared with other numerical solutions and experimental data to evaluate its numerical accuracy. The influence of streamline upwinding is also investigated for all the test cases.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650081202
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  • 49
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    Lagrangian finite element analysis applied to viscous free surface fluid flow (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 953-984 
    Details
    ISSN: 0271-2091
    Keywords: Navier - Stokes equations ; Lagrangian method ; Finite element method ; Galerkin formulatiion ; Linear interpolation ; Free surface ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new Lagrangian finite element formulation is presented for time-dependent incompressible free surface fluid flow problems described by the Navier-Stokes equations. The partial differential equations describing the continuum motion of the fluid are discretized using a Galerkin procedure in conjunction with the finite element approximation. Triangular finite elements are used to represent the dependent variables of the problem. An effective time integration procedure is introduced and provides a viable computational method for solving problems with equality of representation of the pressure and velocity fields. Its success has been attributed to the strict enforcement of the continuity constraint at every stage of the iterative process. The capabilities of the analysis procedure and the computer programs are demonstrated through the solution of several problems in viscous free surface fluid flow. Comparisons of results are presented with previous theoretical, numerical and experimental results.
    Additional Material: 24 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070906
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  • 50
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    Finite elements for exterior problems using integral equations (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 1229-1234 
    Details
    ISSN: 0271-2091
    Keywords: Finite element method ; Integral equations ; Coupling ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present some integral methods for exterior problems for the Laplace equation. Then we give finite element approximations for these equations and some errors estimates. Finally, we indicate how these integral equations can be coupled with a usual finite element method on a bounded domain to solve an exterior non-linear problem which is linear far away.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650071106
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