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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 1-1 
    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 1 (1981), S. 129-144 
    ISSN: 0271-2091
    Keywords: Vorticity Conditions ; Integral Conditions Incompressible Navier-Stokes Equations ; Computation of 2D Viscous Flows ; Vorticity/Stream Function Splitting ; Noniterative Algorithms ; 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 establishing appropriate conditions for the vorticity transport equation is considered. It is shown that, in viscous incompressible flows, the boundary conditions on the velocity imply conditions of an integral type on the vorticity. These conditions determine a projection of the vorticity field on the linear manifold of the harmonic vector fields. Some computational consequences of the above result in two-dimensional calculations by means of the nonprimitive variables, stream function and vorticity, are examined. As an example of the application of the discrete analogue of the projection conditions, numerical solutions of the driven cavity problem are reported.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 145-169 
    ISSN: 0271-2091
    Keywords: Numerical Model ; Estuary ; Open Boundary Condition ; Three dimensional ; Hydrothermal Biscayne 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 three-dimensional time dependent free-surface model has been used to simulate the velocity and temperature distributions in Biscayne Bay, an estuarine basin in South Florida. Comparisons with tide gauge data and airborne infrared temperature data have been made. Analyses of three-dimensional velocity structure, phase relationships of velocity with depth and horizontal location have been conducted.One of the major concerns with three-dimensional models is the specification of conditions at open-boundaries, since it is rare that complete time dependent variations of variables at these boundaries are available. Two sets of approximate boundary conditions at the Biscayne Bay-Atlantic Ocean interface have been used for computations. It was found that specification of averaged surface height variation at open boundaries yield significantly better results than specification of estimated values of velocity.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 205-206 
    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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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981) 
    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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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 291-291 
    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
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 1 (1981), S. 237-272 
    ISSN: 0271-2091
    Keywords: Diffraction ; Refraction ; Gravity Water Waves ; Wave Equation ; Homma's Island Tsunamis ; 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 linear wave equation correct to first order in bed slope is used to calculate the wave field in the sea around an idealized island. This is of circular cylindrical shape and is situated on a paraboloidal shoal in an ocean of constant depth (Figure 1). The sides of the island are assumed fully reflecting. The incident waves are plane and periodic. Wave periods up to 30 min are investigated, and the Coriolis force is neglected. The solution of the wave equation is represented by a finite Fourier series, and a large number of very accurate numerical computations are carried through. The results appear partly in figures showing amplitude and phase angle curves (in some cases extending to the water area of constant depth outside the shoal), partly in figures showing amplitude vs wave period in fixed points. Comparison with solutions to the linearized long-wave equation is made, and the validity range of the corresponding shallow water theory is given. The influence of the shoal is studied by investigating the wave field around an island in an ocean of constant depth. New criteria are given for the applicability of a geometrical optics approach (i. e. refraction). Complete numerical refraction solutions for points at the shoreline (corresponding to many wave orthogonals ending at the point) for shallows water waves, as for the general case, demonstrate the inadequacy of this approach for long-period waves (seismic seawaves: tsunamis). All non-linear effects, including dissipation, are excluded.
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  • 8
    Electronic Resource
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    Chichester : Wiley-Blackwell
    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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  • 9
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    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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  • 10
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    Chichester : Wiley-Blackwell
    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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  • 11
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 137-163 
    ISSN: 0271-2091
    Keywords: Selective Lumping Scheme ; High Reynolds Number ; Vortex Shedding ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents the finite element method for the analysis of unsteady viscous flow of fluid at high Reynolds numbers. The method is based on the explicit numerical integration scheme in time and uses three node triangular finite elements. For the convenience of the formulation, slight compressibility is considered. For the explicit scheme, the selective lumping two step scheme has been successfully employed. Vortex shedding behind a cylinder has been computed and compared with the conventional experimental results. The results agree favourably when both schemes are compared.
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  • 12
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 209-212 
    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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  • 13
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983) 
    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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  • 14
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 179-200 
    ISSN: 0271-2091
    Keywords: Wave ; Run-up ; Hydrodynamics ; Moving-boundary ; Finite-element Model ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element model to tackle the moving boundary problem of wave run-up on moderately steep slopes is developed. The special aspects considered in this study are (1) the modification of shallow water equations to accommodate the effect of vertical accelerations and (2) the use of Lagrangian acceleration coupled with an element that adapts itself to the moving boundary closely. The pressure term in the one-dimensional momentum equation is derived using the Eulerian equation in the vertical direction. This takes care of the vertical accelerations which are significant during the motion of a wave on moderately steep slopes. The element near the boundary is allowed to change its dimension so that the fluid boundary is closely followed. Such a flexible element precludes the need for approximation of the variables with regard to the indefinite position of the boundary. This element is split into two when its dimension becomes unduly large compared to the unchanging elements. The need for such a splitting is shown by an examination of the entries in the global matrix. Results of water profile as a wave runs up a structure are given. A brief history of the work on similar problems is outlined.
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  • 15
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 201-208 
    ISSN: 0271-2091
    Keywords: Aquifer Model ; Leakage ; Noise ; Averaging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Previous papers12 have drawn attention to the sustained oscillations (‘noise’) in the solution by successive over-relaxation of the equations from the finite difference approximation of regional groundwater flow including ephemeral streams. This paper shows that the trouble can be avoided by introducing an averaging step in the algorithm; the trouble can also be avoided by ‘under-relaxation’ but this is far less efficient than averaging.
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  • 16
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 213-216 
    ISSN: 0271-2091
    Keywords: Burgers' Equations ; Exact Solution ; 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
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  • 17
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 217-225 
    ISSN: 0271-2091
    Keywords: Cathodic Reduction ; Convection-Diffusion-Reaction ; Characteristics ; Finite Differences ; 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 derives the convection-diffusion-reaction equation governing the reaction between the dissolved oxygen in sea-water and the steel walls of a pulsating crack. By the neglect of the diffusion term it is shown that an exact solution of the convection-reaction equation can be obtained. A numerical method for the solution of the complete convection-diffusion-reaction equation is derived by the use of finite differences. The numerical computation of the initial transient and the final periodic steady-state values is also discussed.
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  • 18
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 265-282 
    ISSN: 0271-2091
    Keywords: Optimization ; Finite Elements ; Partial Differential 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: Described in this paper is a methodology for solving a particular class of optimum design problems in Fluid Mechanics, namely optimum design problems for aerofoils when the corresponding fluid flow is potential. The methods described in this paper operate directly in the physical space, and take advantage of the variational formulation of the partial differential equation modelling the flow. The techniques of optimal control, optimization and the finite element method are used. Numerical examples are also given.
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  • 19
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 283-293 
    ISSN: 0271-2091
    Keywords: Random Vortex Method Model ; Multiple Jet Flow ; Two-Stroke Uniflow Diesel ; Intake Process ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical model is developed to study the interactions of multiple angled jet flows in the inlet port plane of the Detroit Diesel 6V-92 two-stroke engine cylinder. The random vortex method is used in two dimensions.Results show axisymmetric swirl initially. As flow develops, the centre of the swirl moves to the mid-radius region and begins to precess about the cylinder centre. The flow becomes progressively more chaotic as time progresses.
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  • 20
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    International Journal for Numerical Methods in Fluids 3 (1983) 
    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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  • 21
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 315-317 
    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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  • 22
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    International Journal for Numerical Methods in Fluids 3 (1983), S. i 
    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 3 (1983), S. 333-345 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; Liquid Column Collapse ; 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 shallow-water equations in radial symmetry are solved numerically to simulate the collapse of a cylindrical liquid column into an area surrounded by a concentric dike. The following three subcases of this problem are considered: a liquid column collapsing onto a layer of the same liquid, a liquid column collapsing onto a solid surface, and a column of lighter liquid collapsing onto a heavier liquid (i.e. liquefied natural gas (LNG) spilled onto water). The results for the three categories are compared and the differences and similarities between them are analysed.
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  • 24
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 363-375 
    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: Heat transfer associated with forced convection between bundles of cylindrical fuel rods is analysed using the finite element method. A subchannel technique is employed and the numerical results are compared with previous experimental and numerical values. The solid and fluid zones are analysed, for temperature distribution, as a single domain.
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  • 25
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 347-361 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; LNG Pool Spreading ; Continuous and Instantaneous Spills ; 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 simple numerical model based on the shallow water equations in radial symmetry is used to simulate both instantaneous and continuous spills of liquefied natural gas (LNG) onto a water surface. Using the computed results, a study is made of the similarities and differences in the pool structure resulting from the two types of spills. For instantaneous spills a relation linear on a logarithmic plot is suggested between the maximum pool size and the spill volume. The effects of shear forces and surface cohesivity on the evolution of the spill are also examined.
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  • 26
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 319-331 
    ISSN: 0271-2091
    Keywords: Convection Diffusion Equation ; Linearized Burger's Equation ; Finite Difference Schemes ; Accuracy Convection Dominated Flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a survey of several finite difference schemes for the steady-state convection-diffusion equation in one and two dimensions. Most difference schemes have O(h2) truncation error. The behaviour of these schemes on a one-dimensional model problem is analysed in detail, especially for the case when convection dominates diffusion. It is concluded that none of these schemes is universally second order. One recently proposed scheme is found to yield highly inaccurate solutions for the case of practical interest, i.e. when convection dominates diffusion. Extensions to two and threedimensions are also discussed.
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  • 27
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 171-204 
    ISSN: 0271-2091
    Keywords: Finite Element ; Navier-Stokes ; Incompressible Flows ; Penalty Methods ; Pressure Filters ; 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 spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier-Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two-dimensions and one element in three-dimensions. The automatic pressure filter associated with the penalty method is also explained. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.
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  • 28
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    International Journal for Numerical Methods in Fluids 1 (1981), S. i 
    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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  • 29
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 207-223 
    ISSN: 0271-2091
    Keywords: Numerical Solution ; Integrated Compartment Method ; Fluid Dynamics ; Incompressible Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The most common numerical methods that are used by physical scientists to approximate partial differential equations employ finite differences and/or finite elements. In addition, compartment analyses have been adopted by ecological system analysts to simulate the evolution of processes governed by differential equations without spatial derivatives. An integrated compartment method (ICM) is proposed to combine the merits of these three numerical techniques. The basic procedures of the ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. These procedures are applied to the Navier-Stokes equations to yield the computational algorithm from which computer programs can be coded. The computer code is designed to solve one-, two-, or three-dimensional problems as desired. The program is applied to two simple cases: wake formation behind an obstacle in a channel and circulatory motion of a body of fluid in the square cavity. These preliminary applications have shown promising results.
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  • 30
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 225-235 
    ISSN: 0271-2091
    Keywords: Turbulence ; Fluid Flow ; Mathematical Models ; Reynolds Stresses ; Channels Lateral Motion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The solution for the stress transport turbulence model equations for the situation where the flow is unidirectional is now commonly applied to flows with weak secondary currents in closed ducts, open channels, and rod bundles in nuclear reactor channels. Here, perturbations to the unidirectional flow solutions are studied by solving the exact equations using an iterative procedure. Now the equations also contain the small lateral velocity gradients formerly neglected. The applicability as well as the limitation of the use of the unidirectional flow turbulence model for the description of channel flow with lateral motion are discussed. Modifications for weak lateral motion are suggested.
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  • 31
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 273-290 
    ISSN: 0271-2091
    Keywords: Large Eddy ; Simulation ; Isotropic ; Turbulence ; Filtering ; 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: HOMTY, a code for Large Eddy Simulation of homogeneous isotropic turbulence is proven by successful simulation of two experiments. The role of each term in the equations of motion and the concept of filtering is examined. It is shown that ‘prefiltering’ is unnecessary, and the resulting additional term in the equations, instead of transferring energy to the subgrid scales, backscatters energy from the resolved large wavenumerbers to the small ones. The kinetic energy decay exponent is shown to depend on the low wavenumber part of the velocity spectrum. Pressure statistics are computed and found to be in agreement with previous computations.
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  • 32
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 291-294 
    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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  • 33
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 295-304 
    ISSN: 0271-2091
    Keywords: Numerical Methods ; Turbulence ; Separation ; 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: Flow over a downstream-facing step is predicted using the F.E.M. A two-equation model of turbulence is employed where the transport of turbulence kinetic energy and dissipation rate are depicted using transport-type equations, i.e. the two-equation model of turbulence. The results obtained are compared with other models and experimental results. Generally, the model was found to be under-predictive with regard to the reattachment length when previous empirical data was used in the transport equations.
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  • 34
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    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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  • 35
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    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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  • 36
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 61-70 
    ISSN: 0271-2091
    Keywords: Tides ; Residual Currents ; Finite Elements ; Modal Separation ; 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: From the linearized, time-independent, constant depth, shallow water tidal equations in an f-plane for a two-layer estuary, two independent modal Helmholtz equations are derived. These modal equations are solved using a fifth-degree finite element technique. The first and second space derivatives of the complex modal tidal elevations, and thus the modal currents and their first derivatives, are evaluated directly from the solution at each node of the finite element mesh.The Stokes drift, which is the major part of the residual tidal flow, is evaluated from these nodal values of the currents and their derivatives. Good agreement is obtained with the exact analytical solution for a wedge-shaped estuary with a wedge angle of π/3, using a mesh of 64 equilateral triangles with sides approximately 1/10 of the wavelength 2πC2/σ of a Kelvin wave solution for the short-wavelength mode.
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  • 37
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 99-101 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 38
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 33-60 
    ISSN: 0271-2091
    Keywords: Vertical ; Eddy ; Viscosity ; Galerkin ; Method ; Hydrodynamic ; Model ; Eigenfunction ; Currents ; Roughness length ; 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 three dimensional linear hydrodynamic equations which describe wind induced flow in a sea are solved using the Galerkin method. A basis set of eigenfunctions is used in the calculation. These eigenfunctions are determined numerically using an expansion of B-splines.Using the Galerkin method the problem of wind induced flow in a rectangular basin is examined in detail. A no-slip bottom boundary condition with a vertically varying eddy viscosity distribution is employed in the calculation. With a low (of order 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s near the sea bed together with high current shear in this region are physically realistic and have been observed in the sea.In order to accurately compute the eigenfunctions associated with large (of order 2000 cm2/s at the sea surface to 1 cm2/s at the sea bed) vertical variation of viscosity, an expansion of the order of thirty-five B-splines has to be used. The spline functions are distributed through the vertical so as to give the maximum resolution in the high shear region near the sea bed.Calculations show that in the case of a no-slip bottom boundary condition, with an associated region of high current shear near the sea bed, the Galerkin method with a basis set of the order of ten eigenfunctions (a Galerkin-eigenfunction method) yields an accurate solution of the hydrodynamic equations. However, solving the same problem using the Galerkin method with a basis set of B-splines, requires an expansion of the order of thirty-five spline functions in order to obtain the same accuracy.Comparisons of current profiles and time series of sea surface elevation computed using a model with a slip bottom boundary condition and a model with a no-slip boundary condition have been made. These comparisions show that consistent solutions are obtained from the two models when a physically relistic coefficient of bottom friction is used in the slip model, and a physically realistic bottom roughness length and thickness of the bottom boundary layer are employed in the no-slip model.
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  • 39
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 93-98 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 40
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 71-92 
    ISSN: 0271-2091
    Keywords: Boundary Elements ; Hamel Flow ; Free Surface ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A formulation of the boundary element method for the solution of non-zero Reynolds number incompressible flows in which the non-linear terms are lumped together to form a forcing function is presented. Solutions can be obtained at low to moderate Reynolds numbers. The method was tested using the flow of a fluid in a two-dimensional converging channel (Hamel flow) for which an exact solution is available. An axisymmetric formulation is demonstrated by examining the drag experienced by a sphere held stationary in uniform flow. Performance of the method was satisfactory. New results for an axisymmetric free jet at zero Reynolds number obtained using the boundary element method are also included. The method is ideal for this type of free-surface problem.
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  • 41
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 165-177 
    ISSN: 0271-2091
    Keywords: Viscoelastic Flow ; Non-Newtonian Flow ; Memory Fluids ; Memory Integral Fluids ; Maxwell Fluids ; Generalized Maxwell Fluids ; Convective Integration ; Metal Rolling ; Residence Time ; 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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  • 42
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 295-305 
    ISSN: 0271-2091
    Keywords: Primitive Variables ; Navier-Stokes ; Central Difference ; Upwind Difference ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The use of the velocity-pressure formulation of the Navier-Stokes equations for the numerical solution of fluid flow problems is favoured for free-surface problems, more involved flow configurations, and three-dimensional flows. Many engineering problems involve such features in addition to strong inertial effects. The computational instabilities arising from central-difference schemes for the convective terms of the governing equations impose serious limitations on the range of Reynolds numbers that can be investigated by the numerical method. Solutions for higher Reynolds numbers Re 〉 1000 could be reached using upwind-difference schemes. A comparative study of both schemes using a method based on the primitive variables is presented. The comparison is made for the model problem of the driven flow in a square cavity. Using a central scheme stable solutions of the pressure and velocity fields were obtained for Reynolds numbers up to 5000. The streamfunction and vorticity fields were calculated from the resulting velocity field and compared with previous solutions. It is concluded that total upwind differencing results in a considerable change in the flow pattern due to the false diffusion. For practical calculations, by a proper choice of a small amount of partial upwind differencing the vorticity diffusion near the walls and the global features of the solutions are not sigificantly altered.
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  • 43
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    International Journal for Numerical Methods in Fluids 1 (1981) 
    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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  • 44
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 3-16 
    ISSN: 0271-2091
    Keywords: Vector Upstream ; Differencing Scheme ; Significant Sources ; False Diffusion ; Spatial Oscillation ; Steady-state Linear Systems ; Convective Flow ; Rod Bundle Geometry ; Temperature Prediction ; 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 a finite difference scheme for modelling the convection/diffusion equation in strongly convective flow regimes including circumstances in which significant source terms are present.The main objective is to provide an alternative approach to central and/or upwind difference methods which for various reasons are unsatisfactory. To illustrate the main features of the scheme, an assessment of its accuracy is made by means of a Taylor expansion analysis and a study of its performance in two model problems. As a demonstration of its generality for use in large-scale practical problems, some numerical results are presented for the prediction of the temperature distribution in a flow through a partially blocked heated rod bundle.The main conclusions are that in almost all practical circumstances results obtained using the scheme are not susceptible to false diffusion or spatial oscillations, which are, respectively, the inherent weaknesses in many upwind and central difference scheme formulations, and in general its use results in improved overall accuracy.
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  • 45
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 45-61 
    ISSN: 0271-2091
    Keywords: Two Layer Flow ; Periodic Galerkin Method ; Mixed Interpolation ; Niigata Port ; 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 aim of this paper is to present the finite element method and its application to quasi-steady periodic two-layer tidal flow in estuaries and coastal seas. Formulating the weighted residual equations, using quadratic polynomials for velocity and linear polynomials for water elevation as interpolation functions and employing the periodic Galerkin method, the nonlinear simultaneous equations can be derived. The present method is used for the simulation analysis of the Niigata Port redevelopment planning.
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  • 46
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 17-43 
    ISSN: 0271-2091
    Keywords: Finite Element ; Navier-Stokes ; Incompressible Flows ; Penalty Methods ; Pressure Filters ; 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 spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier-Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of both mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two-dimensions and one element in three-dimensions. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.
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  • 47
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 63-79 
    ISSN: 0271-2091
    Keywords: Heat Transfer ; Convection Finite ; Element Method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A simple method is proposed to generate high-order accurate convection operators for lumped-explicit schemes based on linear or multilinear finite elements. The basic idea is to reduce the truncation error on the first-order spatial derivatives by exploiting the consistent mass matrix of the finite element method in a purely explicit multistep procedure. The effectiveness of the method is demonstrated on pure convection problems in one and two dimensions.
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  • 48
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    International Journal for Numerical Methods in Fluids 1 (1981) 
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    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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  • 49
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 81-97 
    ISSN: 0271-2091
    Keywords: Waves ; Mixed Finite Element ; Shallow Water ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents new finite element formulations of the shallow-water wave equations which use different basis functions for the velocity and height fields. These arrangements are analysed with the Fourier transform technique which was developed by Schoenstadt,1 and they are also compared with other finite difference and finite element schemes. The new schemes are integrated in time for two initial states and compared with analytic solutions and numerical solutions from other schemes. The behaviour of the new forms is excellent and they are also convenient to apply in two dimensions with triangular elements.
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  • 50
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 99-100 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 51
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 101-115 
    ISSN: 0271-2091
    Keywords: Subsidence ; Finite Elements ; Reservoirs ; Hydrocarbons ; Pore Pressure ; Consolidation ; Aquifer ; Waterdrive ; Permeability ; 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 fully coupled consolidation model has been developed for the simulation of the surface subsidence above gas reservoirs. The model is based on the Biot Theory and the material balance equation for hydrocarbon reservoirs. The model is extremely versatile and can handle such complex situations as vertical cross-sections where several gas reservoirs and aquifers are exploited at different levels. Computer runs were used to generate several reservoir formation profiles and the surface subsidence bowl for a variety of conditions. These results indicate the importance of various parameters which are disregarded in proelasticity models.
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 117-127 
    ISSN: 0271-2091
    Keywords: Finite Elements ; Conservation Forms ; Inviscid Boussinesq 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 finite element discretization of the inviscid Boussinesq equations is studied with particular emphasis on the conservation properties of the discrete equations. Methods which conserve the total energy, total temperature and total temperature squared, or two of the above mentioned quantities, are presented. The effect of time discretization, and other numerical errors, on the conservation laws is considered. Finally, the theory is supported and illustrated by several numerical experiments.
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  • 53
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    International Journal for Numerical Methods in Fluids 1 (1981) 
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    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 305-322 
    ISSN: 0271-2091
    Keywords: Diffusion ; Convection ; Heat Transfer ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Scope of this paper is to develop the basic equations for a variational formulation which can be used to solve problems related to convection and/or diffusion dominated flows. The formulation is based on the introduction of a generalized quantity defined as the hear displacement. The governing equation is expressed in terms of this quantity and a variational formulation is developed which leads to a system of equations similar in form to Lagrange's equations of mechanics. These equations can be used for obtaining approximate solutions, though they are of particular interest for application of the finite element method.As an example of the formulation two finite element models are derived for solving convectiondiffusion boundary value problems. The performance of the two models is investigated and numerical results are given for different cases of convection and diffusion with two types of boundary conditions. The applications of the developed formulations are not limited to convection-diffusion problems but can also be applied to other types of problems such as mass transfer, hydrodynamics and wave propagation.
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 323-346 
    ISSN: 0271-2091
    Keywords: Finite Element ; Incompressible Material ; Divergence-free Bases ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Explicit basis functions are constructed for 9-node biquadratic velocity fields which guarantee that a weak form of the continuity equation is satisfied. The corresponding pressure approximations are either piecewise constant, piecewise linear or piecewise bilinear. These results are extended to give bases for bilinear velocity/piecewise constant pressure elements and also to some three-dimensional brick elements.
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 347-364 
    ISSN: 0271-2091
    Keywords: Incompressible Flows ; Pressure Modes ; Vortices ; Finite Element ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents some seemingly new elements for the computation of two and three-dimensional incompressible flow. We want to obtain elements satisfying the Babǔska-Brezzi condition for mixed methods and thus introducing no spurious pressure modes (cf. Sani et al.1). In order to present clearly the advantages and disadvantages of our new elements we compare them on a qualitative basis with more standard ones. Of particular importance for incompressible flow is the size and shape of vortices that can be produced by the elements. We shall try to describe this as precisely as possible. The conclusion is that the elements introduced here should be quite competitive on a cost/precision scale.
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 389-392 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 59
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    International Journal for Numerical Methods in Fluids 1 (1981), S. 365-387 
    ISSN: 0271-2091
    Keywords: Lagrangian Advective Schemes ; Numerical Diffusion ; Navier-Stokes ; 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 one-dimensional transport test applied to some conventional advective Eulerian schemes shows that linear stability analyses do not guarantee the actual performances of these schemes. When adopting the Lagrangian approach, the main problem raised in the numerical treatment of advective terms is a problem of interpolation or restitution of the transported function shape from discrete data. Several interpolation methods are tested. Some of them give excellent results and these methods are then extended to multi-dimensional cases.The Lagrangian formulation of the advection term permits an easy solution to the Navier-Stokes equations in primitive variables V, p, by a finite difference scheme, explicit in advection and implicit in diffusion.As an illustration steady state laminar flow behind a sudden enlargement is analysed using an upwind differencing scheme and a Lagrangian scheme. The importance of the choice of the advective scheme in computer programs for industrial application is clearly apparent in this example.
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    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
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    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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  • 61
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    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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    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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  • 63
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    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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  • 64
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 185-207 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    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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  • 65
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 221-221 
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    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 66
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 222-223 
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    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 67
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    International Journal for Numerical Methods in Fluids 2 (1982) 
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    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 68
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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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  • 69
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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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  • 70
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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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  • 71
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 313-315 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 72
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    International Journal for Numerical Methods in Fluids 2 (1982) 
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    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 73
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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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    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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  • 75
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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
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    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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    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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    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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  • 78
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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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    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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    International Journal for Numerical Methods in Fluids 2 (1982), S. 410-412 
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    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 410-410 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983), S. i 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983), S. i 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 125-135 
    ISSN: 0271-2091
    Keywords: Gas Networks ; Computational Methods ; Simulation ; Optimization ; 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 methods for solving the linear model describing unsteady state flow in pipelines are considered in the present paper. These methods are compared with each other in order to determine the best one, which meets the criteria of accuracy and relatively small computation time.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 103-123 
    ISSN: 0271-2091
    Keywords: Aquifers ; Convection ; Dispersion ; Finite Difference ; Finite Element ; Mass Transport ; Numerical Solutions ; Unconfined 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: Two numerical methods for solving the problem of solute transport in unsteady flow in unconfined aquifers are studied. They are the method of characteristics (MOC) based on the finite difference method (FDM), and the finite element method (FEM). The FEM is further subdivided into four schemes: moving mesh, pseudo-Lagrangian (FEM1); stationary mesh, pseudo-Lagrangian (FEM2); pseudo saturated-unsaturated, Eulerian (FEM3); and non-stationary element, Eulerian (FEM4).Experiments on a one-dimensional flow case are performed to illustrate the schemes and to determine the effect of discretization on accuracy. In two-dimensional flow the above methods are compared with experimental results from a sand box model. Results indicate that for a similar degree of accuracy, the FEM requires less computational effort than the MOC. Among the four FEM schemes, FEM4 appears to be most attractive as it is the most efficient and most convenient to apply.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 249-264 
    ISSN: 0271-2091
    Keywords: Natural Convection ; Numerical Methods ; Bench Mark Solution ; Square 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
    Notes: Details are given of the computational method used to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls. Second-order, central difference approximations were used. Mesh refnement and extrapolation led to solutions for 103≤Ra≤10 6 which are believed to be accurate to better than 1 per cent at the highest Rayleigh number and down to one-tenth of that at the lowest value.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 481-491 
    ISSN: 0271-2091
    Keywords: Boundary Elements ; Lifting Aerofoil ; Potential Flow ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The bbundary integral formulation and boundary element method are extended to include lifting flow problems. This involves inclusion of a branch cut in the flow field and imposition of a Kutta condition to determine the circulation, Γ Additional boundary integral contributions arise from the cut surface. Techniques for calculating Γ are developed and we treat, in particular, a superposition procedure which permits very efficient computation. Numerical results are presented for an NACA0012 aerofoil at several angles of attack.
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  • 90
    ISSN: 0271-2091
    Keywords: Finite Element ; Quasi-three-dimensional ; Interconnected Aquifer Systmes ; Fluid Mass Balance ; Iterated Frontal Method ; Predictor-Corrector Method ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The quasi-three-dimensional equations controlling the groundwater flow in heterogeneous and interconnected aquifer systems are discretized by finite elements, considering also the aquifer branching. A new method for fluid mass balance evaluation based on the equivalent nodal source (E.N.S.) concept allows one to express the balance in conservative terms, and interpret finite element equations as nodal balance equations. The solution of the system is based on the frontal method. Use of substructures limits the frontal increase in correspondence to the aquifer branching. In the steady state, the frontal method is integrated with an iterative solution technique to eliminate the frontal increase caused by the presence of aquitards. It converges very rapidly, using a forcing technique with an automatic parameter definition. In the unsteady case the same scope is achieved using a predictor-corrector procedure which employs the Crank-Nicolson method in the corrector phase.This very stable procedure permits use of fairly long time-steps and concerns the case of source terms depending on piezometry (problem of interaction between water table and river). This method has been tested with several fairly complex cases.
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  • 91
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    International Journal for Numerical Methods in Fluids 1 (1981), S. i 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 1-23 
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    Keywords: Transition ; Boundary Layers ; Models of Turbulence ; Engineering ; Engineering General
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    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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    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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    International Journal for Numerical Methods in Fluids 2 (1982), S. 113-114 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 2 (1982) 
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    Keywords: Engineering ; Engineering General
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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.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
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  • 97
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 1-21 
    ISSN: 0271-2091
    Keywords: Turbomachines ; Finite Elements ; Transonic Flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical approximation is taken to the solution of the complex flows existing in gas turbine engines with transonic blading. The quasi-3D approach decouples the problem into through-flow and blade-to-blade solutions. An industrially practical finite element through-flow solution is developed and for blade-to-blade solutions a transonic finite areas method is utilized. The finite element code developed is capable of operating in an analysis or a design mode. In both modes a dynamic relaxation factor is employed and considerable reduction in solution time can be achieved. Comparisons to streamline curvature methods are carried out for simple analytical and complex industrial problems.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 23-31 
    ISSN: 0271-2091
    Keywords: Finite Element ; Navier-Stokes ; Incompressible Flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A variational formulation for the solution of two dimensional, incompressible viscous flows has been developed by one of the authors.1 The main objective of the present paper is to demonstrate the applicability of this approach for the solution of practical problems and in particular to investigate the introduction of boundary conditions to the Navier-Stokes equations through a variational formulation. The application of boundary conditions for typical internal and external flow problems is presented. Sample cases include flow around a cylinder and flow through a stepped channel.Quadrilateral, bilinear isoparametric elements are utilized in the formulation. A single-step, implicit, and fully coupled numerical integration scheme based on the variational principle is employed. Presented results include sample cases with different Reynolds numbers for laminar and turbulent flows. Turbulence is modelled using a simple mixing length model. Numerical results show good agreement with existing solutions.
    Additional Material: 5 Ill.
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  • 99
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 227-248 
    ISSN: 0271-2091
    Keywords: Comparison ; Natural Convection ; Numerical Methods ; Validation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A number of contributed solutions to the problem of laminar natural convection in a square cavity have been compared with what is regarded as a solution of high accuracy. The purposes of this exercise have been to confirm the accuracy of the bench mark solution and to provide a basis for the assessment of the various methods and computer codes used to obtain the contributed solutions.
    Additional Material: 1 Ill.
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  • 100
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 314-315 
    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
    Type of Medium: Electronic Resource
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