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  • Articles  (14)
  • Incompressible flow  (14)
  • Wiley-Blackwell  (14)
  • Annual Reviews
  • 1990-1994  (14)
  • 1980-1984
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (14)
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  • Articles  (14)
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  • Wiley-Blackwell  (14)
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  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (14)
  • 1
    Electronic Resource
    Electronic Resource
    Iterative stabilization of the bilinear velocity-constant pressure element (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 125-140 
    Details
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Finite element ; Stability ; 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: Some finite element approximations of incompressible flows, such as those obtained with the bilinear velocity-constant pressure element (Q1-P0), are well known to be unstable in pressure while providing reasonable results for the velocity.We shall see that there exists a subspace of piecewise constant pressures that leads to a stable approximation. The main drawback associated with this subspace is the necessity of assembling groups of elements, the so-called ‘macro-elements’, which increases dramatically the bandwidth of the system.We study a variant of Uzawa's method which enables us to work in the desired subspace without increasing the bandwidth of the system. Numerical results show that this method is efficient and can be made to work at a low extra cost. The method can easily be generalized to other problems and is very attractive in three-dimensional cases.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100202
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  • 2
    Electronic Resource
    Electronic Resource
    On a network method for unsteady incompressible fluid flow on triangular grids (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 1383-1406 
    Details
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Co-volume method ; Upwind ; Voronoi tessellation ; Networks ; 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 dual variable method for Delaunay triangulations is a network-theoretic method that transforms a set of primitive variable finite difference or finite element equations for incompressible flow into an equivalent system which is one-fifth the size of the original. Additionally, it eliminates the pressures from the system and produces velocities that are exactly discretely divergence-free. In this paper new discretizations of the convection term are presented for Delaunay triangulations, the dual variable method is extended to tessellations that contain obstacles, and an efficient algorithm for the solution of the dual variable system is described.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650151203
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  • 3
    Electronic Resource
    Electronic Resource
    On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1: Theory (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 587-620 
    Details
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Navier-Stokes equations ; Projection methods ; Splitting methods ; Fractional step methods ; 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: Ever since the time of Chorin's classic 1968 paper on projection methods, there have been lingering and poorly understood issues related to the best - or even proper or appropriate - boundary conditions (BCs) that should be (or could be) applied to the ‘intermediate’ velocity when the viscous terms in the incompressible Navier-Stokes equations are treated with an implicit time integration method and a Poisson equation is solved as part of a ‘time step’. These issues also pervade all related methods that uncouple the equations by ‘splitting’ the pressure computation from that of the velocity - at least in the presence of solid boundaries and (again) when implicit treatment of the viscous terms is employed. This paper is intended to clarify these issues by showing which intermediate BCs are ‘best’ and why some that are not work well anyway. In particular we show that all intermediate BCs must cause problems related to the regularity of the solution near boundaries, but that a near-miraculous recovery occurs such that accurate results are nevertheless achieved beyond the spurious boundary layer introduced by such methods. The mechanism for this ‘miracle’ is related to the existence of a higher-order equation that is actually satisfied by the pressure. All that is required then for projection (splitting, fractional step, etc.) methods to work well is that the spurious boundary layer be thin - as has been largely observed in practice.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110509
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  • 4
    Electronic Resource
    Electronic Resource
    Using a segregated finite element scheme to solve the incompressible Navier-Stokes equations (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 81-92 
    Details
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Finite element methods ; 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 segregated finite element scheme for the solution of the incompressible Navier-Stokes equations is proposed which is simpler in form than previously reported formulations. A pressure correction equation is derived from the momentum and continuity equations, and equal-order interpolation is used for both the velocity components and pressure. Algorithms such as this have been known to lead to checkerboard pressure oscillations; however, the pressure correction equation of this scheme should not produce these oscillations. The method is applied to several laminar flow situations, and details of the methods used to achieve converged solutions are given.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120106
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  • 5
    Electronic Resource
    Electronic Resource
    Multivariant finite elements for three-dimensional simulation of viscous incompressible flows (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 557-585 
    Details
    ISSN: 0271-2091
    Keywords: Multivariant finite element ; Incompressible flow ; Pressure modes ; Shape functions ; 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: Within multivariant elements, which have restricted degrees of freedom at some nodes, different velocity components have different variations. Shape functions for the multivariant elements Q1+ Po and R2+ Po are developed. With such shape functions the value of a velocity component within a multivariant element is shown to depend upon all the independent components of velocity at the nodes of the element.The use of the Q1 P0 element to simulate flows with discontinuous boundary conditions generated disturbance throughout the flow domain, giving erroneous pressure and velocity distributions. The Q1+ Po element restricted the disturbance due to such discontinuities to a small region near the singular points, whereas the P2+ Po element completely eliminated the fluctuations. Flows with discontinuous boundary conditions were simulated with reasonable accuracy by partially relaxing the no-slip condition on the Q1 Po elements near the singular points.
    Additional Material: 23 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140505
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  • 6
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    The PROSPER General Circulation Model, an adapted form of the Sandia Ocean Modelling method: A numerical description (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 251-263 
    Details
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Hydrostatic approximation ; Pressure Poisson Equation ; Staggered grid ; Numerical diffusion ; 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 PROSPER General Circulation Model (PGCM) is a three-dimensional model based on the incompressible Navier-Stokes equations, an equation of state and the heat equation. The hydrostatic approximation and the rigid lid approximation are used. The system of equations is converted into an equivalent form in which the surface pressure is more directly expressed in terms of a two-dimensional Poisson equation. The finite difference method is described and analysed. In particular, the iteration method within every time step to determine the new surface pressure and velocity components, and numerical diffusion aspects due to the use of the staggered Arakawa-C grid are looked at. Since part of the development of the PGCM code is a result of studying the Sandia Ocean Modelling System (SOMS), a comparison is made with respect to the concepts used in both models.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130208
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  • 7
    Electronic Resource
    Electronic Resource
    Numerical simulation of an isolated vortex and shear flow interaction (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 683-696 
    Details
    ISSN: 0271-2091
    Keywords: Collocation ; Incompressible flow ; Shear layer ; Unbounded region ; Vortex ; 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 solution for the Navier-Stokes equations in the unbounded region is considered for the interaction of an isolated vortex and shear flow. A Chebyshey collocation method in space and finite-difference method for temporal discretization are used. The results of the numerical experiments for the interaction are discussed. It is shown that shear flow can both increase and decrease the vortex dissipation rate.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650160803
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  • 8
    Electronic Resource
    Electronic Resource
    A numerical method for 3D viscous incompressible flows using non-orthogonal grids (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 449-469 
    Details
    ISSN: 0271-2091
    Keywords: Body-fitted co-ordinates ; Non-orthogonal grids ; Physical geometric quantities ; Incompressible flow ; Coupled equation solver ; 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 method for fluid flow in complex three-dimensional geometries using a body-fitted co-ordinate system. A new second-order-accurate scheme for the cross-derivative terms is proposed to describe the non-orthogonal components, allowing parts of these terms to be treated implicitly without increasing the number of computational molecules. The physical tangential velocity components resulting from the velocity expansion in the unit tangent vector basis are used as dependent variables in the momentum equations. A coupled equation solver is used in place of the complicated pressure correction equation associated with grid non-orthogonality. The co-ordinate-invariant conservation equations and the physical geometric quantities of control cells are used directly to formulate the numerical scheme, without reference to the co-ordinate derivatives of transformation. Several two- and three-dimensional laminar flows are computed and compared with other numerical, experimental and analytical results to validate the solution method. Good agreement is obtained in all cases.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650180503
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  • 9
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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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  • 10
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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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  • 11
    Electronic Resource
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    Locally mass-conserving Taylor-Hood elements for two- and three-dimensional flow (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 341-353 
    Details
    ISSN: 0271-2091
    Keywords: Finite element techniques ; 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: By supplementing the pressure space for Taylor-Hood elements, elements that satisfy continuity locally are produced. These elements are shown to satisfy the Babuska-Brezzi compatibility condition by using the patch argument.Two examples are presented, one illustrating the convergence rates and the other illustrating a difficulty with a Taylor-Hood element that is overcome by the element presented here.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110307
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  • 12
    Electronic Resource
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    Turbulent flow through bifurcated nozzles (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 23-47 
    Details
    ISSN: 0271-2091
    Keywords: Finite-element method ; Incompressible flow ; K-∊ turbulence model ; Continuous casting ; Bifurcated submerged entry nozzles ; FIDAP ; Steel ; 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 model has been used to study steady-state turbulent flow through bifurcated submerged-entry nozzles with oversized ports typical of those used in the continuous casting of steel. Both 2D and 3D simulations have been performed with the commercial code FIDAP, using the standard K-∊ turbulence model. Predicted velocities from 3D simulations compare reasonably with experimental measurements using a hot-wire anemometer conducted in a physical water model, where severe turbulent fluctuations are present. Results show that a 2D simulation can also capture the main flow characteristics of the jet existing the nozzle and requires two orders of magnitude less computer time than the 3D simulation. A model combining the nozzle and mould was set up to study the effect of the outlet boundary conditions of the nozzle on the jet characteristics. This modelling technique will assist in the design of submerged-entry nozzles, especially as applied to enhance steel quality in the continuous casting process. Further, the model will provide appropriate inlet boundary conditions for a separate numerical model of the mould.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170104
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  • 13
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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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  • 14
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    Is the steady viscous incompressible two-dimensional flow over a backward-facing step at Re = 800 stable? (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 501-541 
    Details
    ISSN: 0271-2091
    Keywords: Backward-facing step ; Flow stability ; 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: A detailed case study is made of one particular solution of the 2D incompressible Navier-Stokes equations. Careful mesh refinement studies were made using four different methods (and computer codes): (1) a high-order finite-element method solving the unsteady equations by time-marching; (2) a high-order finite-element method solving both the steady equations and the associated linear-stability problem; (3) a second-order finite difference method solving the unsteady equations in streamfunction form by time-marching; and (4) a spectral-element method solving the unsteady equations by time-marching. The unanimous conclusion is that the correct solution for flow over the backward-facing step at Re = 800 is steady - and it is stable, to both small and large perturbations.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170605
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