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  • 1995-1999  (644)
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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 1-23 
    ISSN: 0271-2091
    Keywords: Transition ; Boundary Layers ; Models of Turbulence ; 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 computational procedure for compressible axisymmetric boundary layers, on bodies of revolution, in transition from laminar to turbulent flow, is introduced. The procedure is an extension of a former method, due to Patankar and Spalding.The flow field is computed by solution of four simultaneous equations for the momentum, the thermal energy, the turbulence energy amplitude and the turbulent scale.The results show good agreement with existing theoretical and experimental data.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 25-42 
    ISSN: 0271-2091
    Keywords: Penalty Method ; Incompressible Flow ; Reduced Quadrature ; Finite Elements ; 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 frequently used reduced integration method for solving incompressible flow problems ‘a la penalty’ is critically examined vis-a-vis the consistent penalty method. For the limited number of quadrilateral and hexahedral elements studied, it is shown that the former method is only equivalent to the latter in certain special cases. In the general case, the consistent penalty method is shown to be more accurate. Finally, we demonstrate significant advantages of a new element, employing biquadratic (2-D) or triquadratic (3-D) velocity and linear pressure over that using the same velocity but employing bilinear (2-D) or trilinear (3-D) pressure approximation.
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  • 4
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 43-60 
    ISSN: 0271-2091
    Keywords: Multigrid ; Iterative Improvement ; Geothermal Model ; Alternating-direction-implicit ; Tau-extrapolation ; Higher-order-accuracy ; 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 considers the multigrid iterative method applied to the solution of finite difference approximations to a linear second-order self-adjoint elliptic equation. It represents an extension of work by Dinar and Brandt. We compare two methods to obtain fourth-order convergence. The first is local error extrapolation developed by Brandt, the second is iterative improvement developed by Lindberg. This work considers non-separable problems, but only on a rectangular domain with Dirichlet boundary conditions. We consider test cases with non-smooth (i.e. discontinuous second derivatives) as well as smooth solutions. We also apply the multigrid method to an elliptic equation with non-separable coefficients which occurs in a geothermal model. In this case an analysis of the error fails to show any advantage in a fourth-order difference scheme over a second-order scheme. However, we do demonstrate that the multigrid iteration performs well on this problem. Also, this example shows that the multigrid iteration can be combined with iterative improvement to create an efficient fourth-order method for a non-separable elliptic equation which is coupled with a marching equation. Other work has found an advantage in this fourth-order scheme for a similar geothermal model.
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  • 5
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 89-112 
    ISSN: 0271-2091
    Keywords: Two Step Scheme ; Selective Lumping Method ; Tidal Flow ; Osaka 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 finite element method for solving shallow water flow problems is presented. The standard Galerkin method is employed for spatial discretization. The numerical integration scheme for the time variation is the explicit two step scheme, which was originated by the authors and their co-workers. However, the original scheme has been improved to remove the erroneous artifical damping effect. Since the improved scheme employs a combination of lumped and unlumped coefficients, the scheme is referred to as a selective lumping scheme. Stability conditions and accuracy are investigated by considering several numerical examples. The method has been applied to the tidal flow in Osaka Bay and Yatsushiro Bay.
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  • 6
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 113-114 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 7
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 61-88 
    ISSN: 0271-2091
    Keywords: Vector ; Differencing ; Finite ; lEement ; Scheme ; Recirculating ; Laminar ; Flow ; False ; Diffusion ; Conservation of Energy ; 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-difference and finite-element techniques have been used to calculate the steady laminar flow over a flat plate normal to an air stream, up to a Reynolds number, Re, based on the plate half-width, of 100. The boundary conditions simulate a central splitter plate downstream of the body, to prevent vortex shedding, so the flow is characterized by a closed recirculation region which grows with increasing Re but at Re = O(100) is very similar in size to the turbulent recirculating region that occurs in the corresponding high Reynolds-number flow. Motivation came, in part, from the increasing efforts of turbulence modellers to calculate complex turbulent flows (containing elliptic regions) and our belief that the numerical methods commonly employed for such work can be inaccurate. The predictions are compared with each other and with some expectations based on classic solutions of the Navier-Stokes equations, and the nature of the numerical errors is demonstrated. It is concluded that effort comparable with that expended in developing turbulence models should be directed to developing higher-order numerical methods, before the numerical accuracy of predictions of, for example, bluff-body flows can be made sufficiently high to sustain detailed discussion of the adequacy of turbulence models in such situations.
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  • 8
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 9
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 115-122 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Free Surface ; Porous 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 inexpensive, finite difference numerical method is developed for the approximate solution of general, free surface, porous flow problems. The method is so designed that the required numerical boundary conditions coincide exactly with the required physical boundary conditions. In the present paper, application is made to prototype, steady state, dam flow problems.
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  • 10
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 151-171 
    ISSN: 0271-2091
    Keywords: Penalty method ; Incompressible Flow ; Finite Elements ; Convergence ; Existence ; 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 penalty function method is reviewed in the general context of solving constrained minimization problems. Mathematical properties, such as the existence of a solution to the penalty problem and convergence of the solution of a penalty problem to the solution of the original problem, are studied for the general case. Then the results are extended to a penalty function formulation of the Stokes and Navier-Stokes equations. Conditions for the equivalence of two penalty-finite element models of fluid flow are established, and the theoretical error estimates are verified in the case of Stokes's problem.
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  • 11
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 123-149 
    ISSN: 0271-2091
    Keywords: Three-dimensional ; Flow ; Computation ; Scheme ; Time ; Marching ; Conventional ; Damping ; Old Time Level ; Current Time Level ; Fourier Perturbation ; Staggered Grid ; 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 stability of a number of computation schemes currently used for three-dimensional, inviscid, compressible flow is analysed using one-dimensional Fourier analysis. Whereas Reference 1 analysed schemes which were modified to render them amenable to simple analysis, the present work analyses the stability of schemes as actually used by Highton,3 Ahrabian,1 Denton2 and Spalding.6 The use of current values of the variables as they become available is shown to bring a general improvement to stability margin. The manner of damping introduced by the time marching formulation is shown to be deleterious to modifications which reduce truncation error. Staggered grid schemes can be formulated to second order accuracy with better stability margin than the corresponding first order scheme. While unstaggered grid schemes can be formulated to second order error and remain stable, their stability margin becomes very small. Agreement of the theory with numerical experiments continues to be of a high order for both one and three-dimensional disturbances.
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  • 12
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 173-184 
    ISSN: 0271-2091
    Keywords: Advection-diffusion ; Characteristics ; Space-time ; Finite ; Elements ; Water Resources ; 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 finite element method is presented for the solution of two-dimensional transport problems. The method is based on a weighted residual formulation in which the method of characteristics is combined with the finite element method. This is achieved by orienting sides of the space-time elements joining the nodes at subsequent time levels along the characteristics of the pure advection equation associated with the transport problem. The method is capable of solving numerically the advection--diffusion equation without generating oscillations or numerical diffusion for the whole spectrum of dispersion from diffusion only through mixed dispersion to pure convection.The utility and accuracy of the method are demonstrated by a number of examples in two space dimensions and a comparison of the numerical results with the exact solution is presented in one case. A very favourable feature of the method is the capability of solving accurately advection dominated transport problems with very large time steps for which the Courant number is well over one.
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  • 13
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 185-207 
    ISSN: 0271-2091
    Keywords: 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, finite-amplitude wave propagation in an inviscid, subsonic, perfect gas medium is analysed by explicit finite-difference methods. A two-step, Lax-Wendroff method and the single-step, Lax-Friedrichs method are used. A prescribed propagating velocity or pressure disturbance is applied along a single row of grid points normal to the stream direction and results in a 'forced' outflow boundary. The inflow boundary is placed far from outflow by utilizing a streamwise expanding grid and uniform inflow is imposed. Side boundaries are spatially periodic. The numerical solutions are compared with analytical small-perturbation solutions; higher-order effects arising from non-linearities are revealed by Fourier analysis. Solutions which closely approached a periodic state were obtained. The Lax-Wendroff method combined with the expanding grid is shown to be accurate and stable, the Lax-Friedrichs scheme produced highly damped solutions.
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  • 14
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 221-221 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 15
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 209-219 
    ISSN: 0271-2091
    Keywords: First Order Equation ; Hyperbolic Conservation Equation ; Discontinuous Solutions ; Least Squares ; Finite Differences ; Finite Elements ; 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: Least square methods have been frequently used to solve fluid mechanics problems. Their specific usefulness is emphasized for the solution of a first-order conservation equation. On the one hand, the least square formulation embeds the first-order problem into equivalent second-order problem, better adapted to discretization techniques due to symmetry and positive-definiteness of the associated matrix. On the other hand, the introduction of a least square functional is convenient for finite element applications.This approach is applied to the model problem of the conservation of mass (the unknown is the density ρ) in a nozzle with a specified velocity field (u, v), possibly including jumps along lines simulating shock waves. This represent a preliminary study towards the solution of the steady Euler equations.A finite difference and a finite element method are presented. The choice of the finite difference scheme and of a continuous finite element representation for the groups of variables (ρu, ρv) is discussed in terms of conservation of mass flux. Results obtained with both methods are compared in two numerical tests with the same mesh system.
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  • 16
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 17
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 222-223 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 18
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 225-238 
    ISSN: 0271-2091
    Keywords: Normal Direction ; Boundary Conditions ; Incompressible ; Mass Conservation ; 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: Various techniques for implementing normal and/or tangential boundary conditions in finite element codes are reviewed. The principle of global conservation of mass is used to define a unique direction for the outward pointing normal vector at any node on an irregular boundary of a domain containing an incompressible fluid. This information permits the consistent and unambiguous application of essential or natural boundary conditions (or any combination thereof) on the domain boundary regardless of boundary shape or orientation with respect to the co-ordinate directions in both two and three dimensions. Several numerical examples are presented which demonstrate the effectiveness of the recommended technique.
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  • 19
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 263-276 
    ISSN: 0271-2091
    Keywords: Finite Elements ; Waves ; Coastline ; Dampers ; 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 problem of truncating nearshore finite element wave models is addressed. Incorrect treatment of the artificial boundaries of the model will cause spurious wave reflections. Three methods for dealing with these boundaries: application of constraints, use of the Smith condition and longshore dampers, are proposed. Numerical results show the dampers to be the best method.
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  • 20
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 239-251 
    ISSN: 0271-2091
    Keywords: Regular ; Discontinuous Boundary Elements ; Fluid 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: The Boundary Element Method is now well established as a valid numerical technique for the solution of field problems, equal to the Finite Element Method in generality and surpassing it in computational efficiency in some cases.1 In this paper is presented a 'Regular Boundary Element Method' as applied to inviscid laminar fluid flow problems. It involves the formation of a system of regular integral equations obtained by moving the singularity outside the domain of the given problem. It is also shown that non-conforming elements may be used whereby freedoms are not defined at the geometric nodes under the boundary element discretization. A linear element is developed here; higher order variants could easily be defined. Satisfactory numerical results have been obtained using the proposed regular method with both conventional (continuous across the boundary) and non-conforming boundary elements for two-dimensional inviscid laminar fluid flow problems having regular and singular solutions.
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  • 21
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 253-261 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; Sloping Shelf ; Moving Shoreline ; Finite-difference Integration ; 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-difference method is described for the numerical integration of the one-dimensional shallow water equations over a sloping shelf that allows for a continuously moving shoreline. An application of the technique is made to the propagation of non-breaking waves towards the shoreline. The results of the computation are compared with an evaluation based upon an exact analytical treatment of the non-linear equations. Excellent agreement is found for both tsunami and tidal scale oscillations.
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  • 22
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    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 23
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 313-315 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 24
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 277-297 
    ISSN: 0271-2091
    Keywords: Advection ; Convection ; Estuary ; Finite ; Element ; Hermite ; Polynomials ; Diffusion ; Dispersion ; Transport ; 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: Space-time finite element solutions of the convection-dispersion equation using higher-order nodal continuity and Hermitian polynomial shape functions are described. Five separate elements ranging from a complete linear element with C0,0 nodal continuity to a complete first-order Hermitian element with C1,1 nodal continuity are subjected to detailed analysis. Wave deformation analyses identify the source of leading or trailing edge oscillations, trailing edge oscillations being the major source of difficulty. These observations are confirmed by numerical experiments which further demonstrate the potential of higher-order nodal continuity. The performance of the complete first-order Hermitian element is quite satisfactory and measurably superior to the linear element.
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  • 25
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 299-311 
    ISSN: 0271-2091
    Keywords: Turbines ; Compressors ; Optimal Design ; Blade Design ; 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: Hamilton's variational principle is applied to derive a system of conditions which expresses the balance of momentum and energy of an ideal gas across the selvadgesThe reviewer of this paper confesses to be unfamiliar with the term 'selvadge(s)' which appears frequently herein. Clearly, however, it (variously) means 'boundary', 'edge', 'projection of edge line' (meridional or axial), 'locus of leading edges', etc. of bladed zones within the flow tracts of turbines. This system provides the background for a correct formulation of optimal design problems for turbines and compressors. The exposition follows the model of a large number of blades when the basic equations can be averaged over the azimuthal co-ordinate.An analysis is given of the obtained conditions and a computational algorithm described.
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  • 26
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 317-330 
    ISSN: 0271-2091
    Keywords: Transonic flow ; Turbomachines ; Finite elements ; 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 work a study of the application of the finite element method to transonic flows in axial turbomachines is undertaken.Solution techniques capable of accurately predicting flows from the incompressible regime up to the establishment of shocks in the transonic regime are presented. In the subsonic and shockless transonic regimes a local linearization method capable of very rapid convergence is used. In the full transonic regime the artificial compressibility method is employed to exclude downstream influences in the supersonic regions. The two approaches can be combined in a unified package and appropriate switches introduced to select the relevant method in any flow regime.
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  • 27
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 331-347 
    ISSN: 0271-2091
    Keywords: Fluid Flow ; Turbulent ; Non-circular Passages ; Secondary 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 difference method has been developed to predict the overall features of the local mean flow in fully developed turbulent non-circular passage flows. The main transport effects of secondary flow have been identified and simulated with diffusion transport in a simple way which eliminates solution of the cross-plane momentum and continuity equations and produces a compact calculation method. Predictions are presented for four different passage shapes and are discussed in relation to experimental measurements and predictions from other more complex methods. Although some minor details were not predicted, the main effects of secondary flow on the mean flow were found to have been quite well simulated, yielding predictions that are in reasonable overall agreement with experiment.
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  • 28
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 349-366 
    ISSN: 0271-2091
    Keywords: Viscous Flow Modelling ; Convection Modelling ; Flow Boundary Treatment ; 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: Stream function-vorticity finite element solution of two-dimensional incompressible viscous flow and natural convection is considered. Steady state solutions of the natural convection problem have been obtained for a wide range of the two independent parameters. Use of boundary vorticity formulae or iterative satisfaction of the no-slip boundary condition is avoided by application of the finite element discretization and a displacement of the appropriate discrete equations. Solution is obtained by Newton-Raphson iteration of all equations simultaneously. The method then appears to give a steady solution whenever the flow is physically steady, but it does not give a steady solution when the flow is physically unsteady. In particular, no form of asymmetric differencing is required. The method offers a degree of economy over primitive variable formulations. Physical results are given for the square cavity convection problem. The paper also reports on earlier work in which the most commonly used boundary vorticity formula was found not to satisfy the no-slip condition, and in which segregated solution procedures were attempted with very minimal success.
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  • 29
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 407-409 
    ISSN: 0271-2091
    Keywords: Incompressible Fluid Flows ; Cavity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 30
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 367-386 
    ISSN: 0271-2091
    Keywords: Free Surface ; Thermocapillary ; Convective Flows ; Curvilinear Co-ordinates ; Interface Equations ; 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 importance of convective flows generated by surface tension gradients, in comparison with the ones generated by other driving forces, has been investigated in connection with space technological applications involving fluid processes. A theoretical model of the boundary conditions at the interface, considered free and diffusive, has been derived in general tensor form to allow for the use of non orthogonal curvilinear co-ordinates. For the study of flow fields contained in enclosures, these co-ordinates are more suitable to fit all teh boundaries, in particular near the contact angle between the interface and the solid walls, thus giving more accurate numerical solutions.A computational procedure to solve the complete set of bulk and surface equations is proposed and applied to a simplified two dimensional flow in a rectangular enclosure with a temperature gradient between the lateral walls. The numerical results show the importance of considering the interface to be deformable and diffusive for an accurate evaluation of the convective flow in the fluid bulk.
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  • 31
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 410-410 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 32
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 387-405 
    ISSN: 0271-2091
    Keywords: Hyperbolic ; Non-standard Finite Elements ; High Order ; Domain of Dependence ; 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 method of non-standard finite elements was used to develop multilevel difference schemes for linear and quasilinear hyperbolic equations with Dirichlet boundary conditions. A closed form equation of kth-order accuracy in space and time (O(Δtk, Δxk)) was developed for one-dimensional systems of linear hyperbolic equations with Dirichlet boundary conditions. This same equation is also applied to quasilinear systems. For the quasilinear systems a simple iteration technique was used to maintain the kth-order accuracy.Numerical results are presented for the linear and non-linear inviscid Burger's equation and a system of shallow water equations with Dirichlet boundary conditions.
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  • 33
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 410-412 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 34
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 57-78 
    ISSN: 0271-2091
    Keywords: parallel processing ; domain partitioning ; hybrid grids ; grid adaptation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A parallel finite volume method for the Navier-Stokes equations with adaptive hybrid prismatic/tetrahedral grids is presented and evaluated in terms of parallel performance. A new method of domain partitioning for complex 3D hybrid meshes is also presented. It is based on orthogonal bisection of a special octree corresponding to the hybrid mesh. The octree is generated automatically and can handle any type of 3D geometry and domain connectivity. One important property of the octree-based partitioning that is exploited is the octree's ability to yield load-balanced partitions that follow the shape of the geometry. This biasing of the octree results in a reduced number of grid elements on the interpartition boundaries and thus fewer data to communicate among processors. Furthermore, the octree-based partitioning gives similar quality of partitions for very different geometries, while requiring minimal user interaction and little computational time. The partitioning method is evaluated in terms of quality of the subdomains as well as execution time. Viscous flow simulations for different geometries are employed to examine the effectiveness of the octree-based partitioning and to test the scalability of parallel execution of the Navier-Stokes solver and hybrid grid adapter on two different parallel systems, the Intel Paragon and the IBM SP2. © 1998 John Wiley & Sons, Ltd.
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  • 35
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 79-100 
    ISSN: 0271-2091
    Keywords: volume-of-fluid method ; free surface flows ; second-order model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: To improve the numerical analysis of free surface convection and interface reconstruction, both first- and second-order algorithms are developed based on the volume-of-fluid method. The methodology applied to the second-order model is to define the second-order linear curve having both face slopes as near horizontal as possible while satisfying the cell's defined volume fraction.The second-order method is compared with the FLAIR method and the first-order method through simulation of the convection for various sizes of circular liquid shapes and solitary waves. For small curvature of the free surface, e.g. circles with large diameter, linear methods such as the FLAIR method and the first-order method show relatively good predictions. However, for large-curvature configurations, e.g. circles with relatively small diameter or solitary waves, the linear approach shows large distortion of the free surface. In contrast, the second-order model always shows powerful prediction capabilities of free surface convection. © 1998 John Wiley & Sons, Ltd.
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  • 36
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 101-121 
    ISSN: 0271-2091
    Keywords: Riemann solvers ; Eulerian schemes ; detonations ; shock tracking ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper compares several high-resolution schemes for the computation of detonation waves in solid explosives. The essential difficulty in comparison with the usual application domain of these schemes is due to the complexity and variety of the equations of state which are used. The HLLC Riemann solver is used in the context of an Eulerian MUSCL scheme and in conjunction with a shock-tracking scheme. The motivation and justification for the various choices in the building of these schemes are discussed. The accuracy of both schemes, full Eulerian and shock-tracking variant, is clearly demonstrated. In addition, the validity of the results is shown. For one-dimensional applications the shock-tracking scheme is very accurate and relatively simple. For multidimensional applications it is recommended that the full Eulerian version be used. © 1998 John Wiley & Sons, Ltd.
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  • 37
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 177-197 
    ISSN: 0271-2091
    Keywords: unsteady flow ; lifting-line ; numerical computation ; Engineering ; Numerical Methods and Modeling
    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 the basis of a computational time-marching approach, for large-aspect ratio lifting systems submitted to unsteady motions, using the lifting-line concept. When engineering requires such an approach, quasi-steady ones are currently encountered, which are based on Prandtl's lifting-line approach for steady flows. The results of recent theoretical works on the unsteady lifting-line, based on the matched asymptotic expansion technique, allow one to improve, on sound theoretical foundations, this quasi-steady approach. The proposed approach solves a first-order approximation of the unsteady outer problem for the time-evolution of the spanwise circulation distribution along the lifting-line. It introduces, in the same kind of process as Prandtl's one, for each span section, an unsteady two-dimensional description of the aerofoil behaviour together with a formulation for the three-dimensional unsteady induced velocity on the lifting-line. The approach's validity is examined through a simple numerical implementation for three wing motion cases. Considering the numerical results it produces, it can be stated that the unsteady lifting-line model implementation can be considered as time-consistent, whereas the quasi-steady one cannot. Furthermore, the approach presented here allows large time steps, even for very unsteady wing motions, and compares favourably with some classical results of R. T. Jones. © 1998 John Wiley & Sons, Ltd.
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  • 38
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 217-247 
    ISSN: 0271-2091
    Keywords: puffs and thermals ; turbulence modelling ; jets and plumes ; environmental fluid mechanics ; vortex flow ; added mass ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The time evolution of a line puff, a turbulent non-buoyant element with significant momentum, is studied using the renormalization group (RNG) k-∊ model. The numerical results show that the puff motion is characterized by a vortex pair flow; the computed flow details and scalar mixing characteristics can be described by self-similar relations beyond a dimensionless time of around 30. The added mass coefficient of the puff motion is found to be approximately unity. The predicted puff flow and mixing rate are substantially similar to those obtained from the standard k-∊ model and are well supported by experimental data. The computed scalar field reveals significant secondary concentration peaks trailing behind in the wake of the puff. The present results suggest that the overall mixing rate of a puff is primarily determined by the large-scale motion and that streamline curvature probably plays a minor role. © 1998 John Wiley & Sons, Ltd.
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  • 39
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 251-280 
    ISSN: 0271-2091
    Keywords: turbulence modelling ; eddy viscosity ; second-moment closure ; tidal flows ; finite volume ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper employs one-point, linear eddy viscosity and differential second-moment (DSM) turbulence closures to predict the turbulent characteristics of both rectilinear and circular tidal flows. The numerical scheme is based on a finite volume approach applied to a non-staggered grid such that all flow variables are stored at one and the same set of nodes. Numerical stability is maintained through the implementation of apparent viscosities and source term linearization, which are essential if eddy viscosity terms are absent. A stable algorithm is devised for the Reynolds stresses which includes a non-linear velocity smoothing in order to stabilise the numerical scheme during flow reversal and relaminarization. Favourable agreement with the experimental rectilinear tidal data of Schröder (Tech. Rep. GK55 87/E/16, GKSS-Forshungszentrum Geesthacht, 1983) and McClean (Turbulence and Sediment Transport Measurements in a North Sea Tidal Inlet (the Jade), Springer, New York, 1987, p. 436) is reported. Numerical calculations of circular tidal flows are also presented which were motivated by the preliminary investigations of Davies and Jones (Int. j. numer. meth. fluids,12, 17 (1991)) and Davies (Continental Shelf. Res., 11, 1313 (1991)), who employed the one-equation, k-l, eddy viscosity turbulence model to simulate rectilinear and circular tidal flows. © 1998 John Wiley & Sons, Ltd.
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  • 40
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 323-343 
    ISSN: 0271-2091
    Keywords: mixed convection ; finite volume algorithm ; eccentricity ; Nusselt number ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A computational study is performed on two-dimensional mixed convection in an annulus between a horizontal outer cylinder and a heated, rotating, eccentric inner cylinder. The computation has been done using a non-orthogonal grid and a fully collocated finite volume procedure. Solutions are iterated to convergence through a pressure correction scheme and the convection is treated by Van Leer's MUSCL scheme. The numerical procedure adopted here can easily eliminate the ‘Numerical leakage’ phenomenon of the mixed convection problem whereby strong buoyancy and centrifugal effects are encountered in the case of a highly eccentric annulus. Numerical results have been obtained for Rayleigh number Ra ranging from 7×103 to 107, Reynolds number Re from 0 to 1200 and Prandtl number Pr from 0.01 to 7. The mixed rotation parameter σ (=Ra/PrRe2) varies from ∞ (pure natural convection) to 0.01 with various eccentricities ε. The computational results are in good agreement with previous works which show that the mixed convection heat transfer characteristics in the annulus are significantly affected by σ and ε. The results indicate that the mean Nusselt number Nu increases with increasing Ra or Pr but decreases with increasing Re. In the case of a highly eccentric annulus the conduction effect becomes predominant in the throat gap. Hence the crucial phenomenon on whereby Nu first decreases and then increases can be found with increasing eccentricity. © 1998 John Wiley & Sons, Ltd.
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  • 41
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 303-322 
    ISSN: 0271-2091
    Keywords: hierarchical grids ; quadtrees ; adaptive remeshing ; separated flows ; Engineering ; Numerical Methods and Modeling
    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 the use of adaptive hierarchical grids to predict incompressible separated flow at low Reynolds number. The grids consist of a quadtree system of hierarchical Cartesian meshes which are generated by recursive subdivision about seeding points. The governing equations are discretized in collocated primitive variable form using finite volumes and solved using a pressure correction scheme. The mesh is locally adapted at each time step, with panel division or removal dependent on the vorticity magnitude. The resulting grids have fine local resolution and are economical in array size. Results are presented for unidirectional, impulsively started flow past a circular and a square cylinder at various Reynolds numbers up to 5000 and 250 respectively. It is clear that hierarchical meshes may offer gains in efficiency when applied to complex flow domains or strongly sheared flows. However, as expected, the stepped approximation to curved boundaries resulting from the Cartesian quadtree representation adversely affects the accuracy of the results for flow past a circular cylinder. © 1998 John Wiley & Sons, Ltd.
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  • 42
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 443-457 
    ISSN: 0271-2091
    Keywords: direct numerical simulation ; 2D temporal disturbance ; plane Poiseuille flow ; finite difference method ; transient non-linear equation ; stream-function-vorticity equation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A direct numerical scheme is developed to study the temporal amplification of a 2D disturbance in plane Poiseuille flow. The transient non-linear Navier-Stokes equations are applied in a region of wavelength moving with the wave propagation speed. The complex amplitude involved in the perturbation functions is considered as the initial input of the non-linear stability equations. In this study a fully implicit finite difference scheme with five points in the flow direction and three points in the normal direction is developed so that numerical simulation of the amplification of a two-dimensional temporal disturbance in plane Poiseuille flow can be investigated. The growth and decay of the disturbance with time are presented and neutral stability curves which are in good agreement with existing solutions can be determined. The critical conditions as a function of the amplitude A0 of the disturbance are presented. Fixing the wavelength, the Navier-Stokes equations are solved up to Re=10,000 a friction factor increasing with Reynolds number is observed. The 2D non-linear behaviour of the streamfunction, vorticity and velocity components at Re=10,000 are also exhibited. © 1998 John Wiley & Sons, Ltd.
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  • 43
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 485-495 
    ISSN: 0271-2091
    Keywords: capillarity ; free surface ; finite elements ; validation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The mathematical formulation of the dynamics of free liquid surfaces including the effects of surface tension is governed by a non-linear system of elliptic differential equations. The major difficulty of getting unique closed solutions only in trivial cases is overcome by numerical methods. This paper considers transient simulations of liquid-gas menisci in vertical capillary tubes and gaps in the presence of gravity. Therefore the CFD code FIDAP 7.52 based on the Galerkin finite element method (FEM) is used. Calculations using the free surface model are presented for a variety of contact angles and cross-sections with experimental and theoretical verification. The liquid column oscillations are compared for numerical accuracy with a mechanical mathematical model, and the sensitivity with respect to the node density is investigated. The efficiency of the numerical treatment of geometric non-trivial problems is demonstrated by a prismatic capillary. Present restrictions limiting efficient transient simulations with irregularly shaped calculational domains are stated. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 533-556 
    ISSN: 0271-2091
    Keywords: mixed finite elements ; finite volumes ; groundwater flow and transport ; biodegradation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical model for the simulation of flow and transport of organic compounds undergoing bacterial oxygen- and nitrate-based respiration is presented. General assumptions regarding microbial population, bacteria metabolism and effects of oxygen, nitrogen and nutrient concentration on organic substrate rate of consumption are briefly described. The numerical solution techniques for solving both the flow and the transport are presented. The saturated flow equation is discretized using a high-order mixed finite element scheme, which provides a highly accurate estimation of the velocity field. The transport equation for a sorbing porous medium is approximated using a finite volume scheme enclosing an upwind TVD shock-capturing technique for capturing concentration-unsteady steep fronts. The performance and capabilities of the present approach in a bio-remediation context are assessed by considering a set of test problems. The reliability of the numerical results concerning solution accuracy and the computational efficiency in terms of cost and memory requirements are also estimated. © 1998 John Wiley & Sons, Ltd.
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  • 45
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 501-517 
    ISSN: 0271-2091
    Keywords: Multiphase ; turbulent ; finite volumes ; structured grids ; compressible flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerically fast algorithm has been developed to solve the viscous two-phase flow in an axisymmetric rocket nozzle. A Eulerian-Eulerian approach is employed in the computation to couple the gas-particle flow. Turbulence closure is achieved using a Baldwin-Lomax model. The numerical procedure employs a multistage time-stepping Runge-Kutta scheme in conjunction with a finite volume method and is made computationally fast for the axisymmetric nozzle. The present numerical scheme is applied to compute the flow field inside JPL and AGARD nozzles. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 627-635 
    ISSN: 0271-2091
    Keywords: arbitrary-order boundary element method ; non-singular formulation ; potential problems ; Engineering ; Numerical Methods and Modeling
    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 general direct integral formulation for potential flows. The singularities of Green's functions are desingularized theoretically, using a subtracting and adding back technique, so that Gaussian quadrature or any other numerical integration methods can be applied directly to evaluate all the integrals without any difficulty. When high-order quadrature formulas are applied globally, the number of unknowns can be reduced. Interpolation functions are not necessary for unknown variables in the present paper. Therefore, the present method is much simpler and more efficient than the conventional one. Several numerical examples are calculated and compared satisfactorily with analytical solutions or published results. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 637-655 
    ISSN: 0271-2091
    Keywords: liquid flow ; energy transport ; electron-beam ; Engineering ; Numerical Methods and Modeling
    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 made of the liquid flow and energy transport in a system to evaporate metals. The energy from an electron-beam heats an axisymmetric metal disk supported by a water-cooled platform. Metal evaporates from the surface of a hot pool of liquid which is surrounded by a shell of its own solid. Flow in the pool is strongly driven by temperature-induced buoyancy and capillary forces, and is located in the transition region between laminar and turbulent flow. The evaporation rate is strongly influenced by the locations of the free boundaries. A modified finite element method is used to calculate the steady state flow and temperature fields coupled with the interface locations. The mesh is structured with spines that stretch and pivot as the interfaces move. The discretized equations are arranged in an ‘arrow’ matrix and are solved using the Newton-Raphson method. The electron-beam power and platform contact resistance are varied for cases involving the evaporation of aluminum. The results reveal the interaction of liquid flow, heat transfer and free interfaces. © 1998 John Wiley & Sons, Ltd.
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  • 48
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 697-712 
    ISSN: 0271-2091
    Keywords: viscoelastic ; boundary conditions ; tube tooling ; cable-coating ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A viscoelastic analysis is presented for model tube tooling, draw-down and combined geometry flows encountered in the cable coating industries. The work investigates the development of stress fields and studies the effect of varying entry flow stress boundary conditions. The analysis takes into account tube tooling and draw-down flow sections individually, and in combination. The flow behaviour of cable-coating grade low density polyethylene is studied assuming a viscoelastic, isothermal flow, and employing a Taylor-Petrov-Galerkin finite element scheme with an exponential Phan-Thien-Tanner constitutive model. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 725-747 
    ISSN: 0271-2091
    Keywords: unsteady two-body interaction ; potential flow theory ; boundary-integral method ; Lagrange's equation of motion ; generalized Taylor's formula ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: On the basis of the potential flow theory, Lagrange's equation of motion is used to study the unsteady ground-effect problem. The forces and moments acting on the moving body are solved in terms of the derivatives of added masses in which the generalized Taylor's formulae are applied. The singular integral equations used to solve the surface source intensities and their derivatives are regularized by the Gauss flux theorem and are therefore amenable to the direct use of the Gaussian quadrature formula. In illustration, the condition of a prolate spheroid moving in the fore-and-aft direction at constant speed past a flat ground with a protrusion is considered. The hydrodynamic forces and moments acting on the moving spheroid are investigated systematically by varying the size of the protrusion and the cruising height of the spheroid. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 791-809 
    ISSN: 0271-2091
    Keywords: open channel ; subcritical and supercritical flows ; TVD schemes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Saint Venant equations for modelling flow in open channels are solved in this paper, using a variety of total variation diminishing (TVD) schemes. The performance of second- and third-order-accurate TVD schemes is investigated for the computation of free-surface flows, in predicting dam-breaks and extreme flow conditions created by the river bed topography. Convergence of the schemes is quantified by comparing error norms between subsequent iterations. Automatically calculated time steps and entropy corrections allow high CFL numbers and smooth transition between different conditions. In order to compare different approaches with TVD schemes, the most accurate of each type was chosen. All four schemes chosen proved acceptably accurate. However, there are important differences between the schemes in the occurrence of clipping, overshooting and oscillating behaviour and in the highest CFL numbers allowed by a scheme. These variations in behaviour stem from the different orders and inherent properties of the four schemes. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 771-789 
    ISSN: 0271-2091
    Keywords: three-dimensional numerical method ; hybrid method ; splitting method ; Eulerian-Lagrangian method ; shallow water equations ; sigma co-ordinate transformation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new efficient numerical method for three-dimensional hydrodynamic computations is presented and discussed in this paper. The method is based on the operator splitting method and combined with Eulerian-Lagrangian method, finite element method and finite difference method. To increase the efficiency and stability of the numerical solutions, the operator splitting method is employed to partition the momentum equations into three parts, according to physical phenomena. A time step is divided into three time substeps. In the first substep, advection and Coriolis force are solved using the explicit Eulerian-Lagrangian method. In the second substep, horizontal diffusion is approximated by implicit FEM in each horizontal layer. In the last substep, the continuity equation is solved by implicit FEM, and vertical diffusion and pressure gradient are discretized by implicit FDM in each nodal column. The stability analysis shows that this method is unconditionally stable. A number of numerical experiments have been performed. The results simulated by the present scheme agree well with analytical solutions and the other documented model results. The method is efficient for 3D shallow water flow computations and fully fits complicated configurations. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 837-850 
    ISSN: 0271-2091
    Keywords: dense gas dispersion ; radiation absorption ; discrete transfer method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical model is presented for the prediction of thermal radiation absorption in dense gas clouds during accidental release in the atmosphere. The model is based on the discrete transfer method (DT method) that was originally developed for modelling radiation in combustion chambers. The radiation model assumes a number of representative rays of predetermined orientation fired from each of the domain boundaries. Each ray is traced through the domain elements until reaching another boundary where it is terminated. Radiation sources are calculated for each element by performing an energy balance across each element for each ray passing through it. The energy sources recovered are fed into the finite element flow solver for every time step in the energy equation. The model proved accurate, and memory and computer time efficient. It showed that accounting for radiation effects lead to improved predictions. It also showed that in certain scenarios, radiation effects could be predominant. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 877-885 
    ISSN: 0271-2091
    Keywords: B-spline basis ; Galerkin method ; Gauss-Newton method ; mixed formulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A mixed Galerkin technique with B-spline basis functions is presented to compute two-dimensional incompressible flow in terms of the primitive variable formulation. To circumvent the Babuska-Brezzi stability criterion, the artificial compressibility formulation of the equation of mass conservation is employed. As a result, the diagonal components of the matrix form in the governing equations are not singular. The B-spline basis is used because it is superior to other splines in providing computer solutions to fluid flow problems. One of the advantages of the B-spline basis is that it has excellent approximation properties. Numerical examples of applications of the mixed formulation are presented to demonstrate the convergence characteristics and accuracy of the present formulation. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 927-957 
    ISSN: 0271-2091
    Keywords: multigrid methods ; finite elements ; finite volumes ; semi-coarsening ; numerical analysis ; turbulent flows ; compressible flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Extending multigrid concepts to the calculation of complex compressible flow is usually not straightforward. This is especially true when non-embedded grid hierarchies or volume agglomeration strategies are used to construct a gradation of unstructured grids. In this work, a multigrid method for solving second-order PDE's on stretched unstructured triangulations is studied. The finite volume agglomeration multigrid technique originally developed for solving the Euler equations is used (M.-H. Lallemand and A. Dervieux, in Multigrid Methods, Theory, Applications and Supercomputing, Marcel Dekker, 337-363 (1988)). First, a directional semi-coarsening strategy based on Poisson's equation is proposed. The second-order derivatives are approximated on each level by introducing a correction factor adapted to the semi-coarsening strategy. Then, this method is applied to solve the Poisson equation. It is extended to the 2D Reynolds-averaged Navier-Stokes equations with appropriate boundary treatment for low-Reynolds number turbulent flows. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 17-37 
    ISSN: 0271-2091
    Keywords: incompressible Navier-Stokes ; parallel finite element method ; Galerkin approximation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A parallel semi-explicit iterative finite element computational procedure for modelling unsteady incompressible fluid flows is presented. During the procedure, element flux vectors are calculated in parallel and then assembled into global flux vectors. Equilibrium iterations which introduce some ‘local implicitness’ are performed at each time step. The number of equilibrium iterations is governed by an implicitness parameter. The present technique retains the advantages of purely explicit schemes, namely (i) the parallel speed-up is equal to the number of parallel processors if the small communication overhead associated with purely explicit schemes is ignored and (ii) the computation time as well as the core memory required is linearly proportional to the number of elements. The incompressibility condition is imposed by using the artificial compressibility technique. A pressure-averaging technique which allows the use of equal-order interpolations for both velocity and pressure, this simplifying the formulation, is employed. Using a standard Galerkin approximation, three benchmark steady and unsteady problems are solved to demonstrate the accuracy of the procedure. In all calculations the Reynolds number is less than 500. At these Reynolds numbers it was found that the physical dissipation is sufficient to stabilize the convective term with no need for additional upwind-type dissipation. © 1998 John Wiley & Sons, Ltd.
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  • 56
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1003-1022 
    ISSN: 0271-2091
    Keywords: steady approach flow ; low Reynolds numbers ; 3D simulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The three-dimensional (3D) unsteady viscous wake of a circular cylinder exposed to a steady approach flow is calculated using a fractional-step finite-difference/spectral-element method. The calculated flow fields at Reynolds numbers of 100 (2D) and 200 (3D) are examined in detail. The flow field at Re = 100 is 2D as expected, while the flow field at Re = 200 has distinct 3D features, with spanwise wavelengths of about 3.75 cylinder diameters. The calculated results produce drag and lift coefficients and Strouhal numbers that agree extremely well with the experimental values. These 3D values at Re = 200 are in better agreement with experimental values than the results of a 2D calculation at Re = 200, which is expected. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1023-1038 
    ISSN: 0271-2091
    Keywords: three-state anemometry ; velocity field ; particle motion equation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An application of a new flow measurement technique is described which allows for the non-intrusive simultaneous measurement of flow velocity, density, and viscosity. The viscosity information can be used to derive the flow field temperature. The combination of the three measured variables and the perfect-gas law then leads to an estimate of the flow field thermodynamic pressure. Thus, the instantaneous state of a flow field can be completely described. Three-state anemometry (3SA), a derivative of particle image velocimetry (PIV), which uses a combination of three monodisperse sizes of styrene seeding particles is proposed. A marker seeding is chosen to follow the flow as closely as possible, while intermediate and large seeding populations provide two supplementary velocity fields, which are also dependent on fluid density and viscosity. A simplified particle motion equation, aimed at turbomachinery applications, is then solved over the whole field to provide both density and viscosity data. The three velocity fields can be separated in a number of ways. The simplest and that proposed in this paper is to dye the different populations and view the region of interest through interferometric filters. The two critical aspects needed to enable the implementation of such a technique are a suitable selection of the diameters of the particle populations, and the separation of the velocity fields. There has been extensive work on the seeding particle behaviour which allows an estimate of the suitable particle diameters to be made. A technique is described in this paper to allow the separation of particles in a range of micrometer sized velocity fields through fluorescence (separation through intensity also being possible). Some preliminary results by direct numerical simulation (DNS) of a 3SA image are also presented. The particle sizes chosen were 1 μm and 5 μm, tested on the near-wake flow past a cylinder to investigate viscosity only, assuming uniform flow density. The accuracy of the technique, derived from simulations of swirling flows, is estimated as 0.5% RMS for velocity, 2% RMS for the density and viscosity, and 4% RMS for the temperature estimate. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1085-1105 
    ISSN: 0271-2091
    Keywords: adaptive ; hybrid grids ; incompressible ; Navier-Stokes ; finite volume ; pressure correction ; 3-D ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Hybrid grids consisting of prisms and tetrahedra are employed for the solution of the 3-D Navier-Stokes equations of incompressible flow. A pressure correction scheme is employed with a finite volume-finite element spatial discretization. The traditional staggered grid formulation has been substituted with a collocated mesh approach which uses fourth-order artificial dissipation. The hybrid grid is refined adaptively in local regions of appreciable flow variations. The scheme operations are performed on an edge-wise basis which unifies treatment of both types of grid elements. The adaptive method is employed for incompressible flows in both single and multiply-connected domains. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 199-215 
    ISSN: 0271-2091
    Keywords: air-conditioning unit ; k-∊ model ; Reynolds stress model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Details are given of a study to obtain experimental data in an idealized environment for the purpose of evaluating the corresponding computational predictions and which supplement parallel measurements made in actual packaged air-conditioning units. The system consisted of a purpose-built low-speed wind tunnel with a working section constructed to reproduce particular features of the real units. In the experiment, both the mean velocity profiles and turbulence properties of the flow are obtained from triple-hot-wire anemometry measurements. A numerical model, based on finite volume methodology, was used to obtain the solution of the Reynolds-averaged Navier-Stokes equations for incompressible isothermal flow. The Reynolds stress terms in the equations are calculated using the standard k-∊ model and second-moment closure (Reynolds stress) models. The accuracy of the two models was evaluated against the experimental measurements made 10 mm downstream of a baffle. The results show that the standard k-∊ model gave the better agreement except in regions of strong recirculation. © 1997 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 235-247 
    ISSN: 0271-2091
    Keywords: confined explosions ; risk assessment ; CFD ; adaptive mesh refinement ; multiple obstacles ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Explosion hazards constitute a significant practical problem for industry. In response to the need for better-resolved predictions for confined explosions, and particularly with a view to advancing safety cases for offshore oil and gas rigs, an existing unstructured, adaptive mesh, finite volume Reynolds-averaged Navier-Stokes computational fluid dynamics code (originally developed to handle non-combusting turbomachinery flows) has been modified to include a one-equation, eddy break-up combustion model. Two benefits accrue from the use of unstructured, solution-adaptive meshes: first, great geometrical flexibility is possible; second, automatic mesh adaptation allows computational effort to be focused on important or interesting areas of the flow by enhancing mesh resolution only where it is required. In the work reported here, the mesh was adaptively refined to achieve flame front capture, and it is shown that this results in a 10%-33% CPU saving for two-dimensional calculations and a saving of between 57% and 70% for three-dimensional calculations. The geometry of the three-dimensional calculations was relatively simple, and it may be expected that the use of unstructured meshes for truly complex geometries will result in CPU savings sufficient to allow an order-of-magnitude increase in either complexity or resolution. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 281-301 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; SIMPLE algorithm ; algebraic multigrid methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The application of standard multigrid methods for the solution of the Navier-Stokes equations in complicated domains causes problems in two ways. First, coarsening is not possible to full extent since the geometry must be resolved by the coarsest grid used. Second, for semi-implicit time-stepping schemes, robustness of the convergence rates is usually not obtained for convection-diffusion problems, especially for higher Reynolds numbers. We show that both problems can be overcome by the use of algebraic multigrid (AMG), which we apply for the solution of the pressure and momentum equations in explicit and semi-implicit time-stepping schemes. We consider the convergence rates of AMG for several model problems and demonstrate the robustiness of the proposed scheme. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 345-364 
    ISSN: 0271-2091
    Keywords: liquid-particle flow ; computational efficiency ; Eulerian-Lagrangian model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The dispersion of solid particles in a turbulent liquid flow impinging on a centrebody through an axisymmetric sudden expansion was investigated numerically using a Eulerian-Lagrangian model. Detailed experimental measurements at the inlet were used to specify the inlet conditions for two-phase flow computations. The anisotropy of liquid turbulence was accounted for using a second-moment Reynold stress transport model. A recently developed stochastic-probabilistic model was used to enhance the computational efficiency of Lagrangian trajectory computations. Numerical results of the stochastic-probabilistic model using 650 particle trajectories were compared with those of the conventional stochastic discrete-delta-function model using 18 000 particle trajectories. In addition, results of the two models were compared with experimental measurements. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 369-401 
    ISSN: 0271-2091
    Keywords: storm surge ; shallow water model ; grid convergence ; coastal ocean ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The focus of this paper is a systematic determination of the relationship between grid resolution and errors associated with computations of hurricane storm surge. A grid structure is sought that provides the spatial resolution necessary to capture pertinent storm surge physics and does not overdiscretize. A set of numerical experiments simulating storm surge generation over 14 grid discretizations of idealized domains examines the influence of grid spacing, shoreline detail, coastline resolution and characteristics of the meteorological forcing on storm surge computations. Errors associated with a given grid are estimated using a Richardson-based error estimator. Analysis of the magnitude and location of estimated errors indicates that underresolution on the continental shelf leads to significant overprediction of the primary storm surge. In deeper waters, underresolution causes smearing or damping of the inverted barometer forcing function, which in turn results in underprediction of the surge elevation. In order to maintain a specified error level throughout the duration of the storm, the highest grid resolution is required on the continental shelf and particularly in nearshore areas. The disparity of discretization requirements between deep waters and coastal regions is best met using a graded grid. Application of the graded gridding strategy to the hindcast of Hurricane Camille reinforces the necessity of using a grid that has high levels of resolution in nearshore regions and areas of complex coastal geometry. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 127-138 
    ISSN: 0271-2091
    Keywords: compressible flow ; supersonic flows ; aerofoils ; Cauchy/Riemann equations ; Crocco's relation ; Engineering ; Numerical Methods and Modeling
    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, alternative formulations of the steady Euler equations for conservation of mass, momentum and energy are adopted for the numerical simulation of compressible flows with shock waves. The total enthalpy is assumed to be constant and hence an isentropic density is calculated in terms of the velocity components. Also, the x- and y-momentum equations written in conservation form are combined to yield the tangential and normal momentum equations. For smooth flows the tangential momentum equation reduces to the entropy transport equation, while the normal momentum equation gives the vorticity in terms of the entropy gradient normal to the flow direction (Crocco's relation). Hence the velocity components can be obtained from the continuity equation and normal momentum equation (Cauchy/Riemann equations), while the entropy correction for the density is obtained from the tangential momentum equation (this correction is not needed in the isentropic flow regions). The present formulation can be easily extended to handle variable total enthalpy. Preliminary results are presented for transonic and supersonic flows over aerofoils and the entropy and vorticity effects are clearly identified. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 139-157 
    ISSN: 0271-2091
    Keywords: hydrodynamic stability ; finite element method ; incompressible cavity flow ; Arnold's method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical methods have been applied to theoretical studies of instability and transition to turbulence. In this study an analysis of the linear stability of incompressible flow is undertaken. By means of the finite element method the two-dimensional base flow is computed numerically over a range of Reynolds numbers and is perturbed with three-dimensional disturbances. The partial differential equations governing the evolution of perturbation are obtained from the non-linear Navier-Stokes equations with a slight compressibility by using linear stability and normal mode analysis. In terms of the finite element discretization a non-singular generalized eigenproblem is formulated from these equations whose solution gives the dispersion relation between complex growth rate and wave number. This study presents stability curves to identify the critical Reynolds number and critical wavelength of the neutral mode and discusses the mechanism of instability. The stability of lid-driven cavity flow is examined. Taylor-Göertler-like vortices in the cavity are obtained by means of reconstruction of three-dimensional flows. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 519-531 
    ISSN: 0271-2091
    Keywords: wavy channel flow ; peristaltic motion ; spectral collocation method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical procedure is developed for the analysis of flow in a channel whose walls describe a travelling wave motion. Following a perturbation method, the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first-order perturbation quantities are calculated using the pseudospectral collocation method. Although limited by the linear analysis, the present approach is not restricted by the Reynolds number of the flow and the wave number and frequency of the wavy-walled channel. Using the computed wall shear stresses, the positions of flow separation and reattachment are determined. The variations in velocity and pressure with frequency of excitation are also presented. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 207-227 
    ISSN: 0271-2091
    Keywords: directional solidification ; multicomponent alloys ; dendritic monocrystals ; Engineering ; Numerical Methods and Modeling
    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 of dendritic solidification of multicomponent alloys is presented that includes solutal convection and is an extension of a previously developed model for solidification of binary alloys. The model is applied to simulation of the solidification of ternary and quaternary Ni-based alloys. The role of solutal convection in the macrosegregation and the formation of freckles is analysed. Calculations show the effects of geometry and material properties on the convection patterns and the attendant segregation. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 1-11 
    ISSN: 0271-2091
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: No Abstract
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 157-186 
    ISSN: 0271-2091
    Keywords: advective transport ; semi-implicit ; conservative ; unconditionally stable ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A one-dimensional scalar transport method which is appropriate for simulations over a wide range of Courant number is described. Von Neumann stability and matrix invertibility are guaranteed for all Courant numbers and the method has less diffusive and dispersive error than simpler implicit methods. It is implemented for vertical scalar transport in a three-dimensional hydrodynamic model, with horizontal transport discretized explicitly. The method is applied and compared with simpler semi-implicit methods in several test cases and used for a simulation of scalar transport in an estuary. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 23-46 
    ISSN: 0271-2091
    Keywords: domain decomposition ; parallel algorithms ; finite element ; Lagrange multipliers ; projected GMRES ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A parallel solver based on domain decomposition is presented for the solution of large algebraic systems arising in the finite element discretization of mechanical problems. It is hybrid in the sense that it combines a direct factorization of the local subdomain problems with an iterative treatment of the interface system by a parallel GMRES algorithm. An important feature of the proposed solver is the use of a set of Lagrange multipliers to enforce continuity of the finite element unknowns at the interface. A projection step and a preconditioner are proposed to control the conditioning of the interface matrix.The decomposition of the finite element mesh is formulated as a graph partitioning problem. A two-step approach is used where an initial decomposition is optimized by non-deterministic heuristics to increase the quality of the decomposition.Parallel simulations of a Navier-Stokes flow problem carried out on a Convex Exemplar SPP system with 16 processors show that the use of optimized decompositions and the preconditioning step are keys to obtaining high parallel efficiencies. Typical parallel efficiencies range above 80%. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 47-72 
    ISSN: 0271-2091
    Keywords: large eddy simulation ; juncture flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Large eddy simulation (LES) results are reported for temporally developing solid-solid and solid-rigid-lid juncture flows. A MacCormack-type scheme that is second-order in time, and fourth-order in space for the convective terms and second-order in space for the viscous terms, is used. The simulations are obtained for a low subsonic Mach number. The subgrid-scale stresses (SGS) are modeled using the dynamic modeling procedure. The turbulent flow field generated on a flat-plate boundary layer is used to initialize the juncture flow simulations. The results of the flat-plate boundary layer simulations are validated with experimental and direct numerical simulations (DNS) data. In juncture flow simulations, the presence of an adjacent solid-wall/rigid-lid boundary altered the mean and the turbulent field, setting up gradients in the anisotropy of normal Reynolds stresses resulting in the formation of turbulence-induced secondary vortices. The relative size of these secondary vortices and the distribution of mean and turbulent quantities are in qualitative agreement with the experimental observations for the solid-solid juncture. The overall distribution of the mean and turbulence quantities showed close resemblance between the solid-solid and the solid-rigid-lid junctures; except for the absence of a second vortical region near the rigid-lid boundary. In agreement with the experimental observations, it was found that the normalized anisotropy term exhibited similarity when plotted against the distance from the boundary, regardless of the type of boundary, i.e. solid-wall or rigid-lid. The turbulent kinetic energy increased near the rigid-lid boundary. While the surface normal velocity fluctuations decreased to zero at the rigid-lid boundary, the other two velocity components showed an increase in their energy, which is also consistent with the experimental observations. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 113-128 
    ISSN: 0271-2091
    Keywords: optimal control ; Burgers' equation ; data assimilation ; adjoint model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In order to use the optimal control techniques in models of geophysical flow circulation, an application to a 1D advection-diffusion equation, the so-called Burgers' equation, is described. The aim of optimal control is to find the best parameters of the model which ensure the closest simulation to the observed values. In a more general case, the continuous problem and the corresponding discrete form are formulated. Three kinds of simulation are realized to validate the method. Optimal control processes by initial and boundary conditions require an implicit discretization scheme on the first time step and a decentered one for the non-linear advection term on boundaries. The robustness of the method is tested with a noised dataset and random values of the initial controls. The optimization process of the viscosity coefficient as a time- and space-dependent variable is more difficult. A numerical study of the model sensitivity is carried out. Finally, the numerical application of the simultaneous control by the initial conditions, the boundary conditions and the viscosity coefficient allows a possible influence between controls to be taken into account. These numerical experiments give methodological rules for applications to more complex situations. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 143-156 
    ISSN: 0271-2091
    Keywords: turbine ; spiral casing ; finite element method ; Galerkin weighted residual technique ; Gauss-Legendre quadrature ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Flow through the spiral casing of a hydraulic turbine was analyzed. Reynolds averaged Navier-Stokes equations were solved using a finite element method. The physical domain was divided into a number of hexahedral elements which are isoparametrically mapped onto standard cubic elements. Numerical integration for the unsteady momentum equation is performed over such hexahedral elements to obtain a provisional velocity field. Compliance with the mass conservation equation and determination of the pressure correction are accomplished through an iterative procedure. The velocity distribution inside the spiral casing corroborates the results available in literature. The static pressure at the midplane generally decreases from the outside wall towards the exit of the spiral casing. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 201-213 
    ISSN: 0271-2091
    Keywords: curved surface ; shallow water ; non-hydrostatic ; spillway ; finite element ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In Part I a detailed derivation of a more general shallow water equation set was developed via a perturbation analysis. A finite element computational model of these more general equations is now constructed and the model behavior is compared with conventional shallow water formulations applied to an outletworks flume. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 225-242 
    ISSN: 0271-2091
    Keywords: turbulent flow ; non-linear turbulence modelling ; secondary flow ; rectangular duct ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Details of the turbulent flow in a 1:8 aspect ratio rectangular duct at a Reynolds number of approximately 5800 were investigated both numerically and experimentally. The three-dimensional mean velocity field and the normal stresses were measured at a position 50 hydraulic diameters downstream from the inlet using laser doppler velocimetry (LDV). Numerical simulations were carried out for the same flow case assuming fully developed conditions by imposing cyclic boundary conditions in the main flow direction. The numerical approach was based on the finite volume technique with a non-staggered grid arrangement and the SIMPLEC algorithm. Results have been obtained with a linear and a non-linear (Speziale) k-ε model, combined with the Lam-Bremhorst damping functions for low Reynolds numbers. The secondary flow patterns, as well as the magnitude of the main flow and overall parameters predicted by the non-linear k-ε model, show good agreement with the experimental results. However, the simulations provide less anisotropy in the normal stresses than the measurements. Also, the magnitudes of the secondary velocities close to the duct corners are underestimated. © 1998 John Wiley & Sons, Ltd.
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  • 76
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 317-336 
    ISSN: 0271-2091
    Keywords: algebraic multigrid ; elementary restriction/prolongation ; minimum residual methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An algebraic multigrid (AMG) scheme is presented for the efficient solution of large systems of coupled algebraic equations involving second-order discrete differentials. It is based on elementary (zero-order) intergrid transfer operators but exhibits convergence rates that are independent of the system bandwidth. Inconsistencies in the coarse-grid approximation are minimised using a global scaling approximation which requires no explicit geometrical information. Residual components of the error spectrum that remain poorly represented in the coarse-grid approximations are reduced by exploiting Krylof subspace methods. The scheme represents a robust, simple and cost-effective approach to the problem of slowly converging eigenmodes when low-order prolongation and restriction operators are used in multigrid algorithms. The algorithm investigated here uses a generalised conjugate residual (GCR) accelerator; it might also be described as an AMG preconditioned GCR method. It is applied to two test problems, one based on a solution of a discrete Poisson-type equation for nodal pressures in a pipe network, the other based on coupled solutions to the discrete Navier-Stokes equations for flows and pressures in a driven cavity. © 1998 John Wiley & Sons, Ltd.
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  • 77
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 293-315 
    ISSN: 0271-2091
    Keywords: Euler equations ; free surface ; gravity waves ; finite volume method ; fractional step method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A fractional step method is developed for solving the time dependent two-dimensional Euler equations with full non-linear free-surface boundary conditions. The geometry of the free surface is described by a height function, and its evolution is tracked by integrating in time the kinematic boundary conditions based on the free-surface volume flux. The fluid domain is discretised by adapting a time-varying curvilinear grid to all boundaries, including the free surface. Mass and momentum equations are discretised by a conservative finite volume formulation, taking into account the time dependency of the grid. A fractional step type method is developed for integrating the fluid motion in time. The method is applied to a non-linear standing wave in a square container, testing for compliance with mass and energy conservation and comparing computed wave period with other results. Non-linear travelling waves are simulated in channels with either constant depth or varying depth and non-linear wave processes involving both triad interactions and quartet interactions are studied. Results are compared with both experimental data and theoretical results and excellent agreement is found. Interaction of waves and currents is studied. The blocking of waves in an opposing current is simulated and found to show good agreement with theoretical results. The method is intended to be a first step towards a full description of wave dynamics interacting with structures and currents. © 1998 John Wiley & Sons, Ltd.
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  • 78
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 395-418 
    ISSN: 0271-2091
    Keywords: compressible liquid ; Riemann solvers ; approximate Riemann solvers ; Tammann equation of state ; Tait equation of state ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A number of Riemann solvers are proposed for the solution of the Riemann problem in a compressible liquid. Both the Tait and Tammann equations of state are used to describe the liquid. Along with exact Riemann solvers, a detailed description of a primitive variable Riemann solver, a two-shock Riemann solver, a two-rarefaction Riemann solver and an extension to the HLL Riemann solver, namely the HLLC Riemann solver, are presented. It is shown how these Riemann solvers may be implemented into Godunov-type numerical methods. The appropriateness of each of the Riemann solvers for a number of flow situations is demonstrated by applying Godunov's method to some revealing shock tube test problems. © 1998 John Wiley & Sons, Ltd.
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  • 79
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 419-442 
    ISSN: 0271-2091
    Keywords: finite element analysis ; design sensitivity analysis ; optimization ; mold filling ; free surface ; turbulence ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A novel, fully-analytical design sensitivity formulation for transient, turbulent, free surface flows is derived and implemented in the context of finite element analysis. The time-averaged, turbulent form of the Navier-Stokes equations are solved using a mixing length model, in conjunction with the volume of fluid (VOF) method to model the free surface movement. The design derivatives of these governing equations are computed and solved to find the analytical sensitivities of the fluid position, velocity and pressure fields with respect to shape design variables. The computational efficiency produced by evaluating the sensitivities analytically is demonstrated. The design of the runner and gating system of a simple block casting is presented as an example application for using sensitivity information in design. The analytical sensitivity routine is coupled to a numerical optimizer to yield an automated method for optimal design of the casting rigging system. The results produce runner shapes which eliminate mold-gas aspiration. © 1998 John Wiley & Sons, Ltd.
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  • 80
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 477-499 
    ISSN: 0271-2091
    Keywords: natural convection ; tilted cavity ; partial cooling ; storage tanks ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two-dimensional numerical simulations of laminar natural convection in a partially cooled, differentially heated inclined cavities are performed. One of the cavity walls is entirely heated to a uniformly high temperature (heat source) while the opposite wall is partially cooled to a lower temperature (heat sink). The remaining walls are adiabatic. The tilt angle of the cavity is varied from 0° (heated from left) to -90° (heated from top). The fast false implicit transient scheme (FITS) algorithm, developed earlier by the same authors, is modified to solve the derived variables vorticity-streamfunction formulation. The effects of aspect ratio (AR), sink-source ratio and tilt angle on the average Nusselt number are examined through a parametric study; solutions are obtained for two Grashof numbers, 105 and 107. Flow patterns and isotherms are used to investigate the heat transfer and fluid flow mechanisms inside the cavity. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 523-540 
    ISSN: 0271-2091
    Keywords: non-reflecting boundary conditions ; numerical simulation ; compression wave ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In simulations of propagating blast waves the effects of artificial reflections at open boundaries can seriously degrade the accuracy of the computations. In this paper, a boundary condition based on a local approximation by a plane traveling wave is presented. The method yields small artificial reflections at open boundaries. The derivation and the theory behind these so-called plane-wave boundary conditions are presented. The method is conceptually simple and is easy to implement in two and three dimensions. These non-reflecting boundary conditions are employed in the three-dimensional computational fluid dynamics (CFD) solver FLACS, capable of simulating gas explosions and blast-wave propagation in complex geometries. Several examples involving propagating waves in one and two dimensions, shock tube and an example of a simulation of a propagating blast wave generated by an explosion in a compressor module are shown. The numerical simulations show that artificial reflections due to the boundary conditions employed are negligible. © 1998 John Wiley & Sons, Ltd.
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  • 82
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 565-568 
    ISSN: 0271-2091
    Keywords: fundamental solution method ; integral equation method ; Navier-Stokes equations ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A complete boundary integral formulation for incompressible Navier-Stokes equations with time discretization by operator splitting is developed using the fundamental solutions of the Helmholtz operator equation with different order. The numerical results for the lift and the drag hysteresis associated with a NACA0012 aerofoil oscillating in pitch show good agreement with available experimental data. © 1998 John Wiley & Sons, Ltd.
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  • 83
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 719-736 
    ISSN: 0271-2091
    Keywords: front tracking ; mesh adaptation ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented in this paper: the broken dam problem and the Rayleigh-Taylor instability. Good agreement has been obtained in the comparison of the numerical results with theory or available experimental data. © 1998 John Wiley & Sons, Ltd.
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  • 84
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 601-616 
    ISSN: 0271-2091
    Keywords: turbulence modeling ; CFD ; finite volume method ; vortex shedding ; two-layer approach ; Engineering ; Numerical Methods and Modeling
    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 the results of numerical simulations of vortex shedding past a free-standing square cylinder at ReD=22 000, obtained with different turbulence models. Using wall functions, the standard k-ε model is compared with a modification suggested by Kato and Launder (Proc. 9th Symp. Turbulent Shear Flows, Kyoto, 10-4-1 (1993)). In addition, both versions are used in a two-layer approach, in which the flow close to the cylinder is computed with a locally more suitable one-equation turbulence model and only outside the viscous near-wall layer with the two mentioned high-Re model versions. To allow a comparison, the simulations are performed first using the same computational domain and boundary conditions as in previous investigations. Then results are presented that were obtained on a computational domain and with boundary conditions more suitable for a comparison with the experiments. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1155-1180 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; averaged volume transport equations ; void wave propagation speed ; interfacial effects ; two-phase flow ; finite difference method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A one-dimensional, time-dependent, isothermal, incompressible, Newtonian fluid, two-phase volume averaging model was developed to study momentum interaction effects in vertical ducts with bubble flow regime. For the evaluation of averaged description, potential inviscid flow around bubbles was considered in order to get closure relationships. The linear dynamic analysis is based on the eigenvalue technique, determining the domain of the hyperbolic behavior and the void fraction wave velocity, which are compared with previous models and experimental data. The solution to the partial differential equations is based on the finite difference technique implicit scheme. These schemes serve to demonstrate the numerical solution procedure. The numerical results are compared with analytical solution and experimental data for void fraction wave propagation. The importance of the surface tension effect in the behavior of the phases in transient conditions is shown. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1181-1203 
    ISSN: 0271-2091
    Keywords: trapezoidal cylinder ; laminar flow ; Reynolds number ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Characteristics of the developing recirculation region behind a tapered trapezoidal cylinder and its interaction with the separating shear layer from the leading edges were studied numerically for an impulsively started laminar flow. An unsteady stream function-vorticity formulation was used. The Reynolds numbers considered range from 25 to 1000. Pressure contours, surface pressure coefficient, wake length and drag coefficient were studied through the streamline flow field. Main flow and subflow regimes were identified by an analysis of the evolution of the flow characteristics. It was found that typically, for a given trapezoidal cylinder, flow starts with no separation. As time advances, the symmetrical standing zone of recirculation develops aft of the trapezoidal cylinder. The rate of growth in width, length and structure of the aft end eddies depends on the Reynolds number. In time, separated flow from the leading edges of the trapezoidal cylinder also develops and forms growing separation bubbles on the upper and lower inclined surfaces of the trapezoidal cylinder. As time advances, the separation bubbles on the upper and lower inclined surfaces of the cylinder grow towards the downstream regions and eventually merge with the swelling symmetrical eddies aft of the cylinder. This merging of the flows creates a complex flow regime with a disturbed tertiary flow zone near the merging junction. Eventually, depending on the Reynolds number and the tapered angle of the trapezoidal cylinder, the flow develops into a specific category of symmetrical standing recirculatory flow with its own distinct characteristics. Comparisons with the available results of other investigators showed very good agreement. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 33-39 
    ISSN: 0271-2091
    Keywords: error estimation ; Stokes flow ; adaptivity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We describe in this paper an algebraic technique for estimating local and pollution errors in finite element approximations of Stokesian flows. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1053-1071 
    ISSN: 0271-2091
    Keywords: turbulence modeling ; internal flow ; flow separation ; shock-boundary layer interaction ; finite volume method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The existence of shock-turbulent boundary layer interactions lead to very complicated flow phenomena and pose a challenge for numerical simulation. In this paper, two turbulence models, the Baldwin-Lomax (B-L) model and the Johnson-King (J-K) model, which were originally developed for simple external flow simulation, are modified to model complex high-speed internal separated flows. The full Navier-Stokes solver used in this paper is based on a cell-centered finite volume method and multistepping time marching scheme. Both implicit residual smoothing and local time stepping techniques are incorporated to accelerate the convergence rate. To ensure the numerical stability with the present explicit scheme, a point-implicit treatment to the source term in the ordinary differential equation (ODE) of the J-K model has been developed and has proved to be very effective in modeling such a complex flow. An arc-bump channel flow case has been studied. Comparisons of computed results with experimental data show that the present solver, with the modified turbulence models, predicts the shock and the flow separation very well. The J-K model is found to predict the size of the separation bubble with a higher accuracy. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1093-1108 
    ISSN: 0271-2091
    Keywords: boundary conditions ; Euler equations ; finite volume ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The implementation of boundary conditions at rigid, fixed wall boundaries in inviscid Euler solutions by upwind, finite volume methods is considered. Some current methods are reviewed. Two new boundary condition procedures, denoted as the symmetry technique and the curvature-corrected symmetry technique are then presented. Their behaviour in relation to the problem of the subsonic flow about blunt and slender elliptic bodies is analysed. The subsonic flow inside the Stanitz elbow is then computed. The symmetry technique is proven to be as accurate as one of the current methods, second-order pressure extrapolation technique. Finally, for arbitrary curved geometries, dramatic advantages of the curvature-corrected symmetry technique over the other methods are shown. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1139-1158 
    ISSN: 0271-2091
    Keywords: non-linear Reynolds stresses ; k-ε turbulence model ; higher-order convective scheme ; pressure correction ; direct sparse matrix solver ; incompressible duct flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A non-linear modelling of the Reynolds stresses has been incorporated into a Navier-Stokes solver for complex three-dimensional geometries. A k-ε model, adopting a modelling of the turbulent transport which is not based on the eddy viscosity, has been written in generalised co-ordinates and solved with a finite volume approach, using both a GMRES solver and a direct solver for the solution of the linear systems of equations. An additional term, quadratic in the main strain rate, has been introduced into the modelling of the Reynolds stresses to the basic Boussinesq's form; the corresponding constant has been evaluated through comparison with the experimental data. The computational procedure is implemented for the flow analysis in a 90° square section bend and the obtained results show that with the non-linear modelling a much better agreement with the measured data is obtained, both for the velocity and the pressure. The importance of the convection scheme is also discussed, showing how the effect of the non-linear correction added to the Reynolds stresses is effectively hidden by the additional numerical diffusion introduced by a low-order convection scheme as the first-order upwind scheme, thus making the use of higher order schemes necessary. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 1421-1440 
    ISSN: 0271-2091
    Keywords: parallel ; conjugate gradient ; least squares ; FEM ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this study we consider parallel conjugate gradient solution of sparse systems arising from the least-squares mixed finite element method. Of particular interest are transport problems involving convection. The least-squares approach leads to a symmetric positive system and the conjugate gradient scheme is directly applicable. The scheme is applied to both the convection-diffusion equation and to the stationary Navier-Stokes equations. Here we demonstrate parallel solution and performance studies for a representative MIMD parallel computer with hypercube architecture. © 1998 John Wiley & Sons, Ltd.
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  • 92
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. i 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 93
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 21-46 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: An analysis is presented of the non-linear creep effects around a deep circular tunnel driven in ‘squeezing’ ground. The time-dependent behaviour of the geotechnical medium is described by means of a simple viscoplastic rheological model capable of approximating primary, secondary and tertiary creep behaviours. It is shown that tertiary creep can be allowed for by providing a suitable law governing the variation of some material parameters (such as viscosity) with stresses and strains. The basic operations of the ‘evolutive’ procedure adopted for time integration are outlined. Along each time integration step, quadratic variations of the stress and strain fields and linear variations of the material parameters are assumed. The results of various finite element analyses are presented concerning both lined and unlined cases. For the lined cases, the influence of the liner stiffness and of the time elapsed between the end of excavation and the liner installation is considered.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 47-76 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: In this paper, the ability of a displacement-type finite element analysis to predict collapse loads accurately is investigated. For the usual assumptions of ideal plasticity and infinitesimal deformations, attention is focused on undrained geotechnical problems. The theoretical criterion originally developed by Nagtegaal et al.1 is applied to each member of the serendipidity quadrilateral and triangular family of elements, up to and including those with a quartic displacement expansion. This method of assessing the suitability of a particular type of element is shown to be valid for any constitutive law which attempts to enforce the constant volume condition at failure, such as critical state type soil models. The method is also generalized to permit an assessment, a priori, of the suitability of any given mesh which is composed of a finite number of elements of the same type. It is postulated that the 15-noded, cubic strain triangle is theoretically capable of accurate computations in the fully plastic range for undrained geotechnical situations which involve axial symmetry or plane strain. This prediction is verified by a series of numerical experiments on footing problems. Extending the work of Nagtegaal et al., 1 it is established theretically that if lower order finite elements are employed rigorously for non-trivial undrained problems with axial symmetry, then it is impossible to predict the exact limit load accurately, regardless of how refined the mesh may be.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 77-94 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: It is commonly accepted that the mechanical behaviour of granular masses is strongly affected by their microstructure, namely the relative arrangement of voids and particles, i.e. the granular fabric. Therefore, parameters which characterize the granular fabric are of paramount importance in a fundamental description of the overall macroscopic stresses and deformation measures. In this paper several measures of granular fabric are introduced for a random assembly of spherical granules, using a statistical approach. In particular, a second-order symmetric tensor, Fij, emerges from this consideration, which seems to be of fundamental importance for the description of fabric, and which is closely related to the distribution of the contact normals in the assembly. The relation between fabric measures presented here and those discussed by other investigators is also discussed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 141-145 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A mapping finite element method is proposed for the solution of elastic problems in two-dimensions. This method, based on the logarithmic condensation of physical space, is found to give significantly greater accuracy than when the problem is solved in the physical plane using the standard FEM. Logarithmic condensation of space also permits the solution of large aspect-ratio problems of this type, accurately and economically.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 129-139 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Collapse loads are overestimated by finite-element or finite-difference procedures when the material discretization does not allow locally incompressible plastic flow: for example, constant-strain triangles or tetrahedra give unacceptable results. The use of different discretizations for the isotropic and deviatoric parts of the strain tensor is advocated for preventing this problem. The technique can be easily implemented in existing two- and three-dimensional computer programs. Its effectiveness is demonstrated by several examples.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 148-148 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 148-149 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
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