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  • Engineering  (1,006)
  • 1995-1999  (644)
  • 1980-1984  (362)
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  • 1984  (362)
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  • 1980-1984  (362)
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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984) 
    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
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 1-12 
    ISSN: 0271-2091
    Keywords: Review ; Finite Elements ; Meteorology ; 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 application of the finite-element method to the simulation of meterological fluid flow problems is reviewed. Early studies were aimed primarily at demonstrating the viability of the method for one- and two-dimensional flows, whereas more recent studies have been aimed at demonstrating the efficiency and viability of the method for more complex three-dimensional simulations. There has also been a shift towards exploiting such models to better understand and predict the underlying meteorological phenomena, rather than restricting attention to the development of the algorithms.
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  • 3
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 105-105 
    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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  • 4
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 147-158 
    ISSN: 0271-2091
    Keywords: Finite Element ; Incompressible Flow ; Pressure-specification-point ; 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 discontinuity of a finite-element pressure field that is sometimes present in the neighbourhood of the pressure-specification-point is shown to arise either from round-off, or from mistakes in modelling. The implications of this are considered. In particular it restricts grid refinement near the pressure-specification-point. The analysis can be extended to finite-difference calculations, and to other fields governed by equations similar to Poisson's equation.
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  • 5
    Electronic Resource
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 109-125 
    ISSN: 0271-2091
    Keywords: Finite elements ; Navier-Stokes ; Vorticity-stream function ; Time-dependent ; flows ; Boundary conditions ; Incompressible viscous flows ; Two-dimensional 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 new finite element method for solving the time-dependent incompressible Navier-Stokes equations with general boundary conditions is presented. The two second-order partial differential equations for the vorticity and the stream function are factorized, apart from the non-linear advection term, by eliminating the coupling due to the double specification on the stream function at (a part of) the boundary. This is achieved by reducing the no-slip boundary conditions to projection integral conditions for the vorticity field and by evaluating the relevant quantities involved according to an extension of the method of Glowinski and Pironneau for the biharmonic problem. Time integration schemes and iterative algorithms are introduced which require the solution only of banded linear systems of symmetric type. The proposed finite element formulation is compared with its finite difference equivalent by means of a few numerical examples. The results obtained using 4-noded bilinear elements provide an illustration of the superiority of the finite element based spatial discretization.
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  • 6
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984) 
    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
    ISSN: 0271-2091
    Keywords: Polymer Flows ; Non-Newtonian ; Moving Boundary ; 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: Recent progress in the simulation of polymeric flows of two key problems in the injection moulding process, carried out by a team at Cornell University, is briefly described. For the filling of cooled thin cavities, the fluid is characterized by a power-law viscosity with exponential temperature dependence, and interaction between the transient thermal boundary-layer and the core flow in a domain with moving boundary is essential. The earlier procedure of Hieber and Shen is modified in two aspects: a boundary-integral formulation replaces the finite-element treatment of the pressure, and an ‘energy integral’ approach is used for the transient temperature. The second problem is the steady visco-elastic flow in the juncture region where sudden changes of the geometry and large strain rates occur. The constitutive equation is postulated according to the Leonov model. The main features in the numerical implementation are: integration along a streamline to determine the elastic deformation tensors for a given velocity field, and finite-element treatment (in time-dependent form) of the pressure and fields for given stresses. In an example where the contraction ratio is 7:1, results for nominal Deborah number exceeding 100 show no numerical instability. (However, for this problem, the true Weissenberg number, i.e. the ratio of local first-normal-stress difference to shear stress turns out to be generally O(10).) The predictions also correlate very well with experimental birefringence measurements.
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  • 8
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 303-319 
    ISSN: 0271-2091
    Keywords: Finite Element ; Turbulent 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: Although the finite-element (FE) method has been successful in analysing complex laminar flows, a number of difficulties can arise when two-equation turbulence models (e.g. the k-∊ model) are incorporated. This work describes a particular FE discretization of the k-∊ model and reports its performance in recirculating flow. Severe problems encountered in attempts to obtain convergence of the numerical scheme are isolated and analysed, and methods by which the problems can be overcome are suggested.Insight gained in this work has enabled a practical turbulent flow FE code to be constructed which is robust and efficient. This code is the subject of a further paper.
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  • 9
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 321-336 
    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: Incorporation of the k-∊ turbulence model into Galerkin finite-element fluid-flow codes (which, unlike upwind finite-difference codes, have no artificial damping) can lead to severe iterative convergence difficulties. This paper introduces an alternative turbulence model (the q-f model) and an associated finite-element discretization method which are designed to overcome these problems. The new model forms the basis of a finite-element fluid-flow code which is robust and efficient. Furthermore, it is demonstrated on a practical example that the code can give good agreement with experiment on fairly coarse meshes.
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  • 10
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 399-419 
    ISSN: 0271-2091
    Keywords: Laminar Boundary Layers ; Finite Element Method ; Finite Difference Method ; Spectral Method Convergence ; Computational Efficiency ; 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 Dorodnitsyn boundary later formulation is given a finite element interpretation and found to generate very accurate and economical solutions when combined with an implicit, non-iterative marching scheme in the downstream direction. The algorithm is of order (Δ2u, Δx) whether linear or quadratic elements are used across the boundary layer. Solutions are compared with a Dorodnitsyn spectral formulation and a conventional finite difference formulation for three Falkner-Skan pressure gradient cases and the flow over a circular cylinder. With quadratic elements the Dorodnitsyn finite element formulation is approximately five times more efficient than the conventional finite difference formulation.
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  • 11
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 421-439 
    ISSN: 0271-2091
    Keywords: Laminar Flow ; Turbulent Flow ; Compressible Flow ; Separation ; Time-split Method ; Finite Element Method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The time-split finite element method is extended to compute laminar and turbulent flows with and without separation. The examples considered are the flows past trailing edges of a flat plate and a backward-facing step. Eddy viscosity models are used to represent effects of turbulence. It is found that the time-split method produces results in agreement with previous experimental and computational results. The eddy viscosity models employed are found to give accurate predictions in all regions of flow except downstream of reattachment.
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  • 12
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 441-457 
    ISSN: 0271-2091
    Keywords: Finite Element Method ; Dip Coating ; Newtonian Fluid ; 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 finite element simulation of the dip coating process based on a discretization of the continuum with discontinuous pressure elements is presented. The algorithm computes the flow field from natural boundary conditions while an extra condition provided by the existence of free surface is employed to displace the meniscus location towards the actual position. The process is iterative and uses a pseudo-time stepping technique coupled to a cubic spline fitting of the free surface. Numerical predictions exhibit good agreement with experimental data for Newtonian fluids in the case of flat plate dip coating as well as in the case of wire dip coating.
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  • 13
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 459-475 
    ISSN: 0271-2091
    Keywords: Augmented Lagrangian ; Finite Element Method ; Dip Coating ; Non-Newtonian Fluids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We apply in this paper the augmented Lagrangian method to the study of various non-Newtonian fluid flow problems, and in particular the dip coating process. We only present in this second part the treatment specific to the non-linearities involved in the constitutive equations, the first part having largely been concerned with the general description of the approximation used.Two rheological models illustrating different rheological behaviours are used to simulate dip coating process: the Carreau-A model for shear-thinning properties of the viscosity and a truncated second-order model for a Newtonian behaviour in viscosity with elastic properties.Numerical predictions show a very good agreement with experimental data for the second-order model. The discrepancy observed in the other case can be explained qualitatively by the elastic properties exhibited by the shear-thinning fluids used: this elasticity is not taken into account in the Carreau-A model.
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  • 14
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 667-683 
    ISSN: 0271-2091
    Keywords: Rotating Flow ; Finite Differences ; Numerical Stability ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A computer program has been developed to predict laminar source-sink flow in a rotating cylindrical cavity. Although the program is based on a standard finite difference technique for recirculating flow, it incorporates two novel features. Step changes in grid size are employed to obtain sufficient resolution in the boundary layers and special treatment is given to the solution of the pressure correction equations, in the ‘SIMPLE’ algorithm, in order to improve the convergence properties of the method. Results are presented both for the flow in an infinite rotating cylindrical annulus and a finite rotating cylindrical cavity, with the inner cylindrical surface acting as a uniform source and the outer cylinder as a sink. These show good agreement with existing analytical solutions and illustrate some of the problems associated with the computation of rapidly rotating flows.
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  • 15
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 685-699 
    ISSN: 0271-2091
    Keywords: Stokes 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 family of simple Stokes flows involving sliding surfaces adjacent to surfaces at rest is considered. Principally, two specific flow configurations are investigated: (i) that arising when parts of the boundary of an infinitely long circular cylinder are rotating about the axis while other parts of the boundary are at rest, and (ii) the flow produced when a cap of a sphere is held at rest while the remainder of the sphere rotates about the symmetry axis. In each case computer plots of streamlines or constant velocity lines are presented to give a general impression of the resulting flow pattern.
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  • 16
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 708-708 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 17
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 709-709 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 18
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 765-780 
    ISSN: 0271-2091
    Keywords: Diffraction ; Hydrodynamics ; Ocean Engineering ; Underwater Structures ; Wave Forces ; Offshore Structures ; Velocity Potential ; Boundary 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 fluid forces resulting from wave interaction with large submerged structures may be calculated using numerical procedures based on the solution of the associated boundary-value problem. In this paper, the analysis of wave interaction with a fixed submerged object of arbitrary cross-section and infinite length using a two-dimensional boundary value formation based on linear diffraction theory is summarized. Subsequently, the application of the boundary element method to obtain a solution is presented. The numerical considerations are emphasized with particular reference to computational efficiency.Numerical results are presented in the form of dimensionless wave force plots for various structural shapes. In the case of a bottom-seated half cylinder, for which there exists a closed-form solution, comparisons are made between results generated using both boundary element and equivalent finite element approaches. In the case of a submerged cylinder, comparisons are made between boundary element derived values and experimental results. The boundary element results compare well with both the closed-form solution and the experimental values.
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  • 19
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    International Journal for Numerical Methods in Fluids 4 (1984) 
    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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  • 20
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 931-947 
    ISSN: 0271-2091
    Keywords: Two-layer Flow ; Two-step Scheme ; Selective Lumping Method ; Ishikari 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 the analysis of two-layer density flows is presented in this paper. The standard Galerkin method based on linear interpolation functions is used to yield discrete spatial variables. For numerical integration in time, an explicit two-step selective lumping method is used. Here it is applied to a flow analysis of Ishikari Bay, at the mouth of Ishikari River. This case demonstrates a procedure that yields a numerically stable solution.
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  • 21
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 949-969 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Discrete Fourier Transform ; Finite Difference ; Short Convolutions ; No-slip Boundary Condition ; Far Field Condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A mixed discrete Fourier transform-Finite difference algorithm is developed and used for the calculation of rapidly changing viscous fluid flows past a circular cylinder. The numerical approach has been designed to overcome certain difficulties arising for high Reynolds number simulations. The foremost advantage of the technique lies in its fast calculations of the convolution sums portraying the convective terms of the governing equations. Third-order spatial discretizations and fourth-order time marching are implemented.New schemes are proposed for the boundary conditions at the solid wall and at large distances. The techniques are tested on a case study with other schemes (summarized by Roache1) in order to obtain an optimal choice. Definite indications on the stability and accuracy of boundary condition schemes are achieved. Support for the statement of dominant importance of boundary conditions is also given.A comparison of computational results with experimental data is presented for the case study of the flow past an impulsively started cylinder at Reynolds number 20.The time development of the symmetrical zone of recirculation, which is formed at an early stage of the flow, has been studied for 300 ≤ Re ≤ 9500 by means of the proposed algorithm. Computational results, comparisons with experimental data2 and discussion of upper limits of validity of the procedure will be presented in a companion paper.
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  • 22
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 997-998 
    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 4 (1984), S. 999-999 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 24
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 989-996 
    ISSN: 0271-2091
    Keywords: Galerkin ; Spline ; Stability ; Disk ; 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 perturbation equations which characterize the stability of flow over a rotating infinite disk are derived via strict order of magnitude analysis. These equations contain viscous terms not considered by Stuart,1 curvature and Coriolis terms not considered by Brown,2 and axial velocity terms not considered by Kobayashi et al.3 The strategy for reducing the problem to an algebraic system is Galerkin's method with B-spline discretization. In comparison with the Poiseuille flow solutions of Orszag,4 the method is shown to perform well without placing undue demands on computing capability. Critical values of Reynolds number, wave length, vortex orientation and number of spiral vortices calculated by the present method compare favourably with experimental data of Kobayashi et al.
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  • 25
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1001-1012 
    ISSN: 0271-2091
    Keywords: Compressible Fluid Flow ; Numerical Analysis ; Pressure Method ; von Kármán Vortex Street ; 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 pressure method for incompressible fluid flow simulation is extended and applied to the numerical simulation of compressible fluid flow. The governing equations, obtained from the physical principles of conservation of momentum, mass and energy, are first studied from a characteristic point of view. Then they are discretized with a semi-implicit finite difference technique in such a fashion that stability is achieved independently of the speed of sound. The resulting algorithm is fast, accurate and particularly efficient in subsonic flow calculations. As an example, the computer simulation of the von Kármán vortex street is described and discussed.
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  • 26
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 13-24 
    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: A technique is presented for calculating the transient flow in high pressure transportation systems where both simple systems (without compressors) and systems with compressors have been taken into consideration. A partial differential equation characterizing the dynamic gas flow through a pipeline and a numerical scheme for its solution are considered. A method of computing node pressures is also characterized.
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  • 27
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 106-108 
    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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  • 28
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    International Journal for Numerical Methods in Fluids 4 (1984) 
    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 4 (1984), S. 127-145 
    ISSN: 0271-2091
    Keywords: Finite Element ; Bénard Connection ; Bifurcation ; Continuation ; 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 fluid motion in a cavity with rigid sidewalls that is heated uniformly from below is studied by the finite-element method. The techniques of parameter-stepping and monitoring the determinant of the Jacobian matrix to find bifurcations are used. Results are presented for width-to-height ratios in the range 1 to 4, and for three different boundary conditions on the horizontal surfaces, namely both rigid, both free, and rigid bottom with free top. The non-linear branches above the critical Rayleigh number are examined. Extensions to non-Boussinesq flow are trivial.
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  • 30
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 203-205 
    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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  • 31
    ISSN: 0271-2091
    Keywords: Potential Flows ; Navier-Stokes Problems ; 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 approach for the numerical solution of flow problems based on the concept of fundamental solutions of differential equations is described. This approach uses the finite element methodology but does not rely on the concept of variational principle or that of residuals. The approach is shown to be well-suited for many types of flow problems. Various applications of this approach are discussed in this paper, with particular emphasis placed on the solution of potential flows and viscous flows containing appreciable regions of separation.
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  • 32
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 247-269 
    ISSN: 0271-2091
    Keywords: Finite Elements ; Navier-Stokes ; Driven Cavity ; Flow Past a Cylinder ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present a simple and efficient finite element method to solve the Navier-Stokes equations in primitive variables V, p. It uses (a) an explicit advection step, by upwind differencing. Improvement with regard to the classical upwind differencing scheme of the first order is realized by accurate calculation of the characteristic curve across several elements, and higher order interpolation; (b) an implicit diffusion step, avoiding any theoretical limitation on the time increment, and (c) determination of the pressure field by solving the Poisson equation. Two laminar flow calculations are presented and compared to available numerical and experimental results.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 271-281 
    ISSN: 0271-2091
    Keywords: Collocation ; Moving Mesh ; Advection-Diffusion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A collocation method based on multiple regions with moving boundaries placed in a flow field in which convection effects dominate, is proposed. By making the moving boundaries of the regions coincide with moving sharp fronts present in the solution of convection dominated problems, and thereby allowing higher concentration of meshes to be placed about the fronts, the proposed method is able to achieve very high accuracy. By having a moving mesh, the Peclet number characterizing the flow field depends upon velocity relative to a moving mesh in a region. Consequently by choosing proper velocities of the moving boundaries, the value of this Peclet number can be made as small as desired. The traditional collocation method based on centred discretization, when applied to each region in the field, produces oscillation free solutions even when the values of Peclet number based on absolute velocity are extremely large. In view of these characteristics the method appears to be an excellent candidate for the solution of any two-phase flow problem containing sharp fronts.
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    International Journal for Numerical Methods in Fluids 4 (1984) 
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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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  • 35
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 283-290 
    ISSN: 0271-2091
    Keywords: Prandtl's Equation ; Singular Integrodifferential Equations ; Quadrature Method ; Natural Interpolation Formula ; Principal Value Integrals ; Gauss- and Lobatto-Chebyshev Quadrature Rules ; 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: Prandtl's singular integrodifferential equation and related equations appear in problems of aerofoil and propeller theory in fluid mechanics. Here a natural interpolation formula for the approximation to the unknwon function of Prandtl's equation when this is solved numerically by the direct quadrature method, based on the Gauss- and Lobatto-Chebyshev quadrature rules, is proposed. This interpolation formula is analogous to Nyström's natural interpolation formula for Fredholm integral equations of the second kind and the corresponding formula for singular integral equations. Numerical applications of the same formula are also made.
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  • 36
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 291-302 
    ISSN: 0271-2091
    Keywords: Finite Elements ; MHD 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 finite element method is given to obtain the numerical solution of the coupled equations in velocity and magnetic field for unsteady MHD flow through a pipe having arbitrarily conducting walls. Pipes of rectangular, circular and triangular sections have been taken for illustration. Computations have been carried out for different Hartmann numbers and wall conductivity at various time levels. It is found that if the wall conductivity increases, the flux through a section decreases. The same is the effect of increasing the Hartmann number. It is also observed that the steady state is approached at a faster rate for larger Hartmann numbers or larger wall conductivity. Selected graphs are given showing the behaviour of velocity, induced magnetic field and flux across a section.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 497-497 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984) 
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    Keywords: Engineering ; Engineering General
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  • 39
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 477-496 
    ISSN: 0271-2091
    Keywords: Gas Dynamics ; Finite Difference Schemes ; Shock Localization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We consider a problem on shock wave localization in the numerical solution of one-dimensional unsteady problems of gas dynamics in Eulerian variables obtained on the basis of finite difference shock-capturing schemes. An optimization method for strong discontinuity localization proposed previously by Miranker and Pironneau is investigated by means of methods of classical variational calculus. This method may be difficult to implement when the entropy condition is included in the formulation of Miranker and Pironneau's optimization problem as an active constraint. In this connection we suggest an alternative optimization problem using artificial viscosity in the variational principle. It is shown theoretically that the application of such a variational principle yields a trajectory which coincides with the true discontinuity trajectory in the case of a shock wave moving at a constant speed. On the basis of this modification one more algorithm is proposed which reduces the shock localization problem to a problem of minimization of a univariate function. Numerical tests corroborate completely the theoretical conclusions. In particular, a higher shock localization accuracy is obtained on the basis of the proposed algorithms as compared to the original Miranker-Pironneau method.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. i 
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    Keywords: Engineering ; Engineering General
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  • 41
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    International Journal for Numerical Methods in Fluids 4 (1984), S. i 
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    Keywords: Engineering ; Engineering General
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  • 42
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 499-509 
    ISSN: 0271-2091
    Keywords: Critical Flow Rate ; Finite Elements ; Free Surface ; Weir ; 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: Computing critical flows in hydraulics involves three problems in one: the internal flow problem, the location of the free surface and the determination of the critical flow rate. The subject can involve such difficulties as non-uniqueness, non-existence, ill-conditioning and catastrophes.This paper discusses the difficulties relating to computing critical flows over weirs. A new rapidly convergent method of determining the critical flow rate is presented and various results are shown using it with finite element discretization and with a new streamline shifting method. Numerical results are in good agreement with published data, both numerical and experimental.
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  • 43
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 511-517 
    ISSN: 0271-2091
    Keywords: Approximation ; Cubic Splines ; Orthogonal Collocation ; 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 well-known Stokes problem is discussed by a cubic spline collocation method. Two consecutive cubic splines are obtained for the problem. The results by this method are compared with those of an orthogonal collocation method. The selection of the length of the subintervals of the range of the boundary value problem is also justified. The results obtained by these two methods are compared with the analytic solution. The methods involve simple algebra, and hence the calculations do not require the help of a computer. Necessary error analysis has been carried out.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 519-537 
    ISSN: 0271-2091
    Keywords: Boundary-Fitted Co-ordinates ; Incompressible Flow ; 2D and 3D ; 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: For three-dimensional fluid flows in complex geometries, it is convenient to make predictions using a non-orthogonal boundary-fitted mesh. The present paper describes an economical method of solving the equations of motion for two and three dimensional problems using such meshes. The locations on the mesh at which the depenent variables are calculated, and the methods used to solve the equations, are key issues in the development of a successful algorithm; these are discussed in the present paper. Results obtained when the proposed method is applied to several problems are also described. The method is intended for flows in which compressibility effects do not dominate.
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    International Journal for Numerical Methods in Fluids 4 (1984) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 710-710 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 711-724 
    ISSN: 0271-2091
    Keywords: Finite-Volume Method ; Numerical Diffusion ; Upstream Weighted Differencing ; Skew Upstream Differencing ; Turbulent Recirculating Flow ; Turbulence 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: Predictions are reported for two-dimensional, steady, incompressible flows over rearward-facing steps for both laminar and turbulent conditions. The standard k-∊ turbulence model was used for the turbulent flow. Attention was focused on obtaining accurate solutions to the differential equations. It is concluded that some of the serious discrepancies that have occurred between prediction and observation, and attributed in earlier studies to the inadequacy of the turbulence model, may have been due to the inaccuracy of the solution.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 749-764 
    ISSN: 0271-2091
    Keywords: Hyperbolic Conservation Equation ; 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: Several explicit schemes are presented for triangular P0 and P1 finite elements. A first-order accurate upwind P0 scheme is compared to a FLIC type method. A second-order accurate Richtmyer scheme is constructed. Applications are given for the Euler system of conservation laws in the 2-dimensional case.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 725-747 
    ISSN: 0271-2091
    Keywords: Ray Methods ; Water Waves ; Refraction ; Diffraction ; Coasts ; Harbours ; 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: Ray methods are used in coastal and harbour wave disturbance investigations where the area to be modelled is large compared to the wavelength. The interpretation of forward-plotted ray diagrams, once obtained, has always been a difficult problem. The technique described in this paper calculates wave amplitudes during the ray plotting process and requires only minor modifications to existing ray plotting programs. The idea is to superimpose a grid of square elements over the entire sea area under study, and to perform a spatial averaging of the rays crossing each square element. This ‘square-averaging’ technique has a number of advantages. It smooths the rapid amplitude variations near caustics, calculates the interference of several wave trains, and generates amplitudes automatically in a square array covering the whole studied sea area. Two types of sensitivity tests are carried out. These tests are designed to determine the accuracy of the predicted wave amplitudes with respect to: (1) the square size per wavelength, and (2) the ray density. These two factors largely determine the computing storage, time and cost of a ray model. An upper limit on the square size per wavelength and a lower limit on the ray density are obtained.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 801-801 
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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 4 (1984), S. 802-802 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1013-1025 
    ISSN: 0271-2091
    Keywords: Stream Function ; Viscous Flow ; Non-conforming Elements ; Interface Penalties ; Reduced 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 element method for solution of the stream function formulation of Stokes flow is developed. The method involves complete cubic non-conforming (C0) triangular Hermite elements. This element fails the patch test. To correct the element and produce a convergent method we employ a penalty method to weakly enforce the desired continuity constraint on the normal derivative across the inter-element boundaries. Successful use of the method is demonstrated to require reduced integration of the inter-element penalty with a 1-point Gauss rule. Error estimates relate the optimal choice of penalty parameter to mesh size and are corroborated by numerical convergence studies. The need for reduced integration is interpreted using rank relations for an associated hybrid method.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1097-1098 
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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 4 (1984), S. 1083-1095 
    ISSN: 0271-2091
    Keywords: Turbomachines ; Finite Volume ; Consistency ; 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 contribution is to investigate the consistency and order of accuracy of different control surfaces used for finite area blade-to-blade flow calculations. The following cases will be treated: a hexagonal element, a trapezoidal element, a bitrapezoidal element and a quadrilateral element. Finally, the consistency conditions will be discussed and compared with respect to a cascade flow application.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1099-1099 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1117-1136 
    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: We describe in this paper some new methods for solving the shallow water flow problem; this problem is composed of two coupled non-linear equations. First a fractional step method is used to decouple the difficulties due to the convection and the propagation. The diffusion propagation step amounts to solving two coupled linear equations on the water depth and the fluxes. We used then some quasi-direct decomposition techniques to decouple the unknowns, leading to symmetric systems only. In addition some non-trivial boundary conditions on the flux are examined. Particularly we are interested to get decoupled systems on the two components of the flux. Numerical tests are presented to enlighten the behaviour and the capabilities of the method. Finally an industrial example is treated on the Dunkirk harbour.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1101-1115 
    ISSN: 0271-2091
    Keywords: Numerical Solution ; Navier-Stokes Equations ; 2-D Steady, Laminar Flows ; ADI Method ; Spline Interpolating Polynomials ; 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 present paper provides an improved alternating direction implicit (ADI) technique as well as high-order-accurate spline ADI method for the numerical solution of steady two-dimensional incompressible viscous flow problems. The vorticity-stream function Navier-Stokes equations are considered in a general curvilinear coordinate system, which maps an arbitrary two-dimensional flow domain in the physical plane into a rectangle in the computational plane. The stream function equation is parabolized in time by means of a relaxation-like time derivative and the steady state solution is obtained by a time-marching ADI method requiring to solve only 2 × 2 block-tridiagonal linear systems. The difference equations are written in incremental form; upwind differences are used for the incremental variables, for stability, whereas central differences approximate the non-incremental terms, for accuracy, so that, at convergence, the solution is free of numerical viscosity and second-order accurate. The high-order-accurate spline ADI technique proceeds in the same manner; in addition, at the end of each two-sweep ADI cycle, the solution is corrected by means of a fifth-order spline interpolating polynomial along each row and column of the computational grid, explicitly. The validity and the efficiency of the present methods are demonstrated by means of three test problems.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1137-1148 
    ISSN: 0271-2091
    Keywords: Free Surface Flows ; Computation ; Kantorovich 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: Computing free surface gravity flows involves basically two coupled problems, namely, the location of the free surface position and the determination of the internal flow field (for assumed values H0 and Q of the total head and discharge, respectively).Solution techniques are invariably based on iterative procedures, but those that iterate between the two coupled problems may become unstable.In this paper we present a computational method in which the coupling is kept throughout the process of iteration. This is achieved by converting the coupled problems (by means of the Kantorovich method) into the single problem of finding a set of streamlines, including that of the free surface. These streamlines are moved (iteratively) to satisfy the stationary conditions of the governing variational principle.The algorithm is very stable and converges rapidly. It is also easy to implement to solve various types of steady flows with a free surface under gravity.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1149-1163 
    ISSN: 0271-2091
    Keywords: Stokes Problem ; Chebyshev Approximation ; Spectral Method ; Penalty Formulation ; Splitting Scheme ; 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: To investigate the influences of time scheme, pressure treatment and initial conditions in incompressible fluid dynamics, a Stokes problem is solved numerically on a slab geometry within the framework of spectral approximation in space. Four algorithms are examined: splitting schemes, influence matrix method, penalty formulation and pseudo-spectral space-time technique. It is shown that splitting schemes are less accurate than the other processes. Furthermore, the initial field should respect a compatibility condition to avoid singularities at the initial time. If it is not possible to build such a compatible field, the numerical procedure has to present good damping properties at the first steps of the time integration.
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1186-1187 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1185-1185 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 4 (1984), S. 1165-1184 
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    Keywords: Turbulence ; Buoyancy ; Swirl ; 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-parameter model of turbulence applicable to free boundary layers has been developed and applied for the prediction of axisymmetric turbulent swirling flows in uniform and stagnant surroundings under the action of buoyancy forces. The turbulent momentum and heat fluxes appearing in the time-averaged equations for the mean motion have been determined from algebraic expressions, derived by neglecting the convection and diffusion terms in the differential transport equations for these quantities, which relate the turbulent fluxes to the kinetic energy of turbulence, k, the dissipation length scale of turbulence, L, and the temperature covariance, T′2. Differential transport equations have been used to determine these latter quantities. The governing equations have been solved using fully implicit finite difference schemes. The turbulence model is capable of reproducing the gross features of pure jet flows, buoyant flows and swirling flows for weak and moderate swirl.The behaviour of a turbulent buoyant swirling jet has been found to depend solely on exit swirl and Froude numbers. The predicted results indicate that the incorporation of buoyancy can cause significant changes in the behaviour of a swirling jet, particularly when the buoyancy strength is high. The jet exhibits similarity behaviour in the initial region for weak swirl and weak buoyancy strengths only, and the asymptotic case of a swirling jet under the action of buoyancy forces is a pure plume in the far field. The predicted results have been found to be in satisfactory agreement with the available experimental data and in good qualitative agreement with other predicted results.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 57-78 
    ISSN: 0271-2091
    Keywords: parallel processing ; domain partitioning ; hybrid grids ; grid adaptation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A parallel finite volume method for the Navier-Stokes equations with adaptive hybrid prismatic/tetrahedral grids is presented and evaluated in terms of parallel performance. A new method of domain partitioning for complex 3D hybrid meshes is also presented. It is based on orthogonal bisection of a special octree corresponding to the hybrid mesh. The octree is generated automatically and can handle any type of 3D geometry and domain connectivity. One important property of the octree-based partitioning that is exploited is the octree's ability to yield load-balanced partitions that follow the shape of the geometry. This biasing of the octree results in a reduced number of grid elements on the interpartition boundaries and thus fewer data to communicate among processors. Furthermore, the octree-based partitioning gives similar quality of partitions for very different geometries, while requiring minimal user interaction and little computational time. The partitioning method is evaluated in terms of quality of the subdomains as well as execution time. Viscous flow simulations for different geometries are employed to examine the effectiveness of the octree-based partitioning and to test the scalability of parallel execution of the Navier-Stokes solver and hybrid grid adapter on two different parallel systems, the Intel Paragon and the IBM SP2. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 79-100 
    ISSN: 0271-2091
    Keywords: volume-of-fluid method ; free surface flows ; second-order model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: To improve the numerical analysis of free surface convection and interface reconstruction, both first- and second-order algorithms are developed based on the volume-of-fluid method. The methodology applied to the second-order model is to define the second-order linear curve having both face slopes as near horizontal as possible while satisfying the cell's defined volume fraction.The second-order method is compared with the FLAIR method and the first-order method through simulation of the convection for various sizes of circular liquid shapes and solitary waves. For small curvature of the free surface, e.g. circles with large diameter, linear methods such as the FLAIR method and the first-order method show relatively good predictions. However, for large-curvature configurations, e.g. circles with relatively small diameter or solitary waves, the linear approach shows large distortion of the free surface. In contrast, the second-order model always shows powerful prediction capabilities of free surface convection. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 101-121 
    ISSN: 0271-2091
    Keywords: Riemann solvers ; Eulerian schemes ; detonations ; shock tracking ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper compares several high-resolution schemes for the computation of detonation waves in solid explosives. The essential difficulty in comparison with the usual application domain of these schemes is due to the complexity and variety of the equations of state which are used. The HLLC Riemann solver is used in the context of an Eulerian MUSCL scheme and in conjunction with a shock-tracking scheme. The motivation and justification for the various choices in the building of these schemes are discussed. The accuracy of both schemes, full Eulerian and shock-tracking variant, is clearly demonstrated. In addition, the validity of the results is shown. For one-dimensional applications the shock-tracking scheme is very accurate and relatively simple. For multidimensional applications it is recommended that the full Eulerian version be used. © 1998 John Wiley & Sons, Ltd.
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  • 67
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 177-197 
    ISSN: 0271-2091
    Keywords: unsteady flow ; lifting-line ; numerical computation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents the basis of a computational time-marching approach, for large-aspect ratio lifting systems submitted to unsteady motions, using the lifting-line concept. When engineering requires such an approach, quasi-steady ones are currently encountered, which are based on Prandtl's lifting-line approach for steady flows. The results of recent theoretical works on the unsteady lifting-line, based on the matched asymptotic expansion technique, allow one to improve, on sound theoretical foundations, this quasi-steady approach. The proposed approach solves a first-order approximation of the unsteady outer problem for the time-evolution of the spanwise circulation distribution along the lifting-line. It introduces, in the same kind of process as Prandtl's one, for each span section, an unsteady two-dimensional description of the aerofoil behaviour together with a formulation for the three-dimensional unsteady induced velocity on the lifting-line. The approach's validity is examined through a simple numerical implementation for three wing motion cases. Considering the numerical results it produces, it can be stated that the unsteady lifting-line model implementation can be considered as time-consistent, whereas the quasi-steady one cannot. Furthermore, the approach presented here allows large time steps, even for very unsteady wing motions, and compares favourably with some classical results of R. T. Jones. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 217-247 
    ISSN: 0271-2091
    Keywords: puffs and thermals ; turbulence modelling ; jets and plumes ; environmental fluid mechanics ; vortex flow ; added mass ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The time evolution of a line puff, a turbulent non-buoyant element with significant momentum, is studied using the renormalization group (RNG) k-∊ model. The numerical results show that the puff motion is characterized by a vortex pair flow; the computed flow details and scalar mixing characteristics can be described by self-similar relations beyond a dimensionless time of around 30. The added mass coefficient of the puff motion is found to be approximately unity. The predicted puff flow and mixing rate are substantially similar to those obtained from the standard k-∊ model and are well supported by experimental data. The computed scalar field reveals significant secondary concentration peaks trailing behind in the wake of the puff. The present results suggest that the overall mixing rate of a puff is primarily determined by the large-scale motion and that streamline curvature probably plays a minor role. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 251-280 
    ISSN: 0271-2091
    Keywords: turbulence modelling ; eddy viscosity ; second-moment closure ; tidal flows ; finite volume ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper employs one-point, linear eddy viscosity and differential second-moment (DSM) turbulence closures to predict the turbulent characteristics of both rectilinear and circular tidal flows. The numerical scheme is based on a finite volume approach applied to a non-staggered grid such that all flow variables are stored at one and the same set of nodes. Numerical stability is maintained through the implementation of apparent viscosities and source term linearization, which are essential if eddy viscosity terms are absent. A stable algorithm is devised for the Reynolds stresses which includes a non-linear velocity smoothing in order to stabilise the numerical scheme during flow reversal and relaminarization. Favourable agreement with the experimental rectilinear tidal data of Schröder (Tech. Rep. GK55 87/E/16, GKSS-Forshungszentrum Geesthacht, 1983) and McClean (Turbulence and Sediment Transport Measurements in a North Sea Tidal Inlet (the Jade), Springer, New York, 1987, p. 436) is reported. Numerical calculations of circular tidal flows are also presented which were motivated by the preliminary investigations of Davies and Jones (Int. j. numer. meth. fluids,12, 17 (1991)) and Davies (Continental Shelf. Res., 11, 1313 (1991)), who employed the one-equation, k-l, eddy viscosity turbulence model to simulate rectilinear and circular tidal flows. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 323-343 
    ISSN: 0271-2091
    Keywords: mixed convection ; finite volume algorithm ; eccentricity ; Nusselt number ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A computational study is performed on two-dimensional mixed convection in an annulus between a horizontal outer cylinder and a heated, rotating, eccentric inner cylinder. The computation has been done using a non-orthogonal grid and a fully collocated finite volume procedure. Solutions are iterated to convergence through a pressure correction scheme and the convection is treated by Van Leer's MUSCL scheme. The numerical procedure adopted here can easily eliminate the ‘Numerical leakage’ phenomenon of the mixed convection problem whereby strong buoyancy and centrifugal effects are encountered in the case of a highly eccentric annulus. Numerical results have been obtained for Rayleigh number Ra ranging from 7×103 to 107, Reynolds number Re from 0 to 1200 and Prandtl number Pr from 0.01 to 7. The mixed rotation parameter σ (=Ra/PrRe2) varies from ∞ (pure natural convection) to 0.01 with various eccentricities ε. The computational results are in good agreement with previous works which show that the mixed convection heat transfer characteristics in the annulus are significantly affected by σ and ε. The results indicate that the mean Nusselt number Nu increases with increasing Ra or Pr but decreases with increasing Re. In the case of a highly eccentric annulus the conduction effect becomes predominant in the throat gap. Hence the crucial phenomenon on whereby Nu first decreases and then increases can be found with increasing eccentricity. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 303-322 
    ISSN: 0271-2091
    Keywords: hierarchical grids ; quadtrees ; adaptive remeshing ; separated flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper describes the use of adaptive hierarchical grids to predict incompressible separated flow at low Reynolds number. The grids consist of a quadtree system of hierarchical Cartesian meshes which are generated by recursive subdivision about seeding points. The governing equations are discretized in collocated primitive variable form using finite volumes and solved using a pressure correction scheme. The mesh is locally adapted at each time step, with panel division or removal dependent on the vorticity magnitude. The resulting grids have fine local resolution and are economical in array size. Results are presented for unidirectional, impulsively started flow past a circular and a square cylinder at various Reynolds numbers up to 5000 and 250 respectively. It is clear that hierarchical meshes may offer gains in efficiency when applied to complex flow domains or strongly sheared flows. However, as expected, the stepped approximation to curved boundaries resulting from the Cartesian quadtree representation adversely affects the accuracy of the results for flow past a circular cylinder. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 443-457 
    ISSN: 0271-2091
    Keywords: direct numerical simulation ; 2D temporal disturbance ; plane Poiseuille flow ; finite difference method ; transient non-linear equation ; stream-function-vorticity equation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A direct numerical scheme is developed to study the temporal amplification of a 2D disturbance in plane Poiseuille flow. The transient non-linear Navier-Stokes equations are applied in a region of wavelength moving with the wave propagation speed. The complex amplitude involved in the perturbation functions is considered as the initial input of the non-linear stability equations. In this study a fully implicit finite difference scheme with five points in the flow direction and three points in the normal direction is developed so that numerical simulation of the amplification of a two-dimensional temporal disturbance in plane Poiseuille flow can be investigated. The growth and decay of the disturbance with time are presented and neutral stability curves which are in good agreement with existing solutions can be determined. The critical conditions as a function of the amplitude A0 of the disturbance are presented. Fixing the wavelength, the Navier-Stokes equations are solved up to Re=10,000 a friction factor increasing with Reynolds number is observed. The 2D non-linear behaviour of the streamfunction, vorticity and velocity components at Re=10,000 are also exhibited. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 485-495 
    ISSN: 0271-2091
    Keywords: capillarity ; free surface ; finite elements ; validation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The mathematical formulation of the dynamics of free liquid surfaces including the effects of surface tension is governed by a non-linear system of elliptic differential equations. The major difficulty of getting unique closed solutions only in trivial cases is overcome by numerical methods. This paper considers transient simulations of liquid-gas menisci in vertical capillary tubes and gaps in the presence of gravity. Therefore the CFD code FIDAP 7.52 based on the Galerkin finite element method (FEM) is used. Calculations using the free surface model are presented for a variety of contact angles and cross-sections with experimental and theoretical verification. The liquid column oscillations are compared for numerical accuracy with a mechanical mathematical model, and the sensitivity with respect to the node density is investigated. The efficiency of the numerical treatment of geometric non-trivial problems is demonstrated by a prismatic capillary. Present restrictions limiting efficient transient simulations with irregularly shaped calculational domains are stated. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 533-556 
    ISSN: 0271-2091
    Keywords: mixed finite elements ; finite volumes ; groundwater flow and transport ; biodegradation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical model for the simulation of flow and transport of organic compounds undergoing bacterial oxygen- and nitrate-based respiration is presented. General assumptions regarding microbial population, bacteria metabolism and effects of oxygen, nitrogen and nutrient concentration on organic substrate rate of consumption are briefly described. The numerical solution techniques for solving both the flow and the transport are presented. The saturated flow equation is discretized using a high-order mixed finite element scheme, which provides a highly accurate estimation of the velocity field. The transport equation for a sorbing porous medium is approximated using a finite volume scheme enclosing an upwind TVD shock-capturing technique for capturing concentration-unsteady steep fronts. The performance and capabilities of the present approach in a bio-remediation context are assessed by considering a set of test problems. The reliability of the numerical results concerning solution accuracy and the computational efficiency in terms of cost and memory requirements are also estimated. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 501-517 
    ISSN: 0271-2091
    Keywords: Multiphase ; turbulent ; finite volumes ; structured grids ; compressible flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerically fast algorithm has been developed to solve the viscous two-phase flow in an axisymmetric rocket nozzle. A Eulerian-Eulerian approach is employed in the computation to couple the gas-particle flow. Turbulence closure is achieved using a Baldwin-Lomax model. The numerical procedure employs a multistage time-stepping Runge-Kutta scheme in conjunction with a finite volume method and is made computationally fast for the axisymmetric nozzle. The present numerical scheme is applied to compute the flow field inside JPL and AGARD nozzles. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 627-635 
    ISSN: 0271-2091
    Keywords: arbitrary-order boundary element method ; non-singular formulation ; potential problems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a general direct integral formulation for potential flows. The singularities of Green's functions are desingularized theoretically, using a subtracting and adding back technique, so that Gaussian quadrature or any other numerical integration methods can be applied directly to evaluate all the integrals without any difficulty. When high-order quadrature formulas are applied globally, the number of unknowns can be reduced. Interpolation functions are not necessary for unknown variables in the present paper. Therefore, the present method is much simpler and more efficient than the conventional one. Several numerical examples are calculated and compared satisfactorily with analytical solutions or published results. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 637-655 
    ISSN: 0271-2091
    Keywords: liquid flow ; energy transport ; electron-beam ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical analysis is made of the liquid flow and energy transport in a system to evaporate metals. The energy from an electron-beam heats an axisymmetric metal disk supported by a water-cooled platform. Metal evaporates from the surface of a hot pool of liquid which is surrounded by a shell of its own solid. Flow in the pool is strongly driven by temperature-induced buoyancy and capillary forces, and is located in the transition region between laminar and turbulent flow. The evaporation rate is strongly influenced by the locations of the free boundaries. A modified finite element method is used to calculate the steady state flow and temperature fields coupled with the interface locations. The mesh is structured with spines that stretch and pivot as the interfaces move. The discretized equations are arranged in an ‘arrow’ matrix and are solved using the Newton-Raphson method. The electron-beam power and platform contact resistance are varied for cases involving the evaporation of aluminum. The results reveal the interaction of liquid flow, heat transfer and free interfaces. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 697-712 
    ISSN: 0271-2091
    Keywords: viscoelastic ; boundary conditions ; tube tooling ; cable-coating ; finite elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A viscoelastic analysis is presented for model tube tooling, draw-down and combined geometry flows encountered in the cable coating industries. The work investigates the development of stress fields and studies the effect of varying entry flow stress boundary conditions. The analysis takes into account tube tooling and draw-down flow sections individually, and in combination. The flow behaviour of cable-coating grade low density polyethylene is studied assuming a viscoelastic, isothermal flow, and employing a Taylor-Petrov-Galerkin finite element scheme with an exponential Phan-Thien-Tanner constitutive model. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 725-747 
    ISSN: 0271-2091
    Keywords: unsteady two-body interaction ; potential flow theory ; boundary-integral method ; Lagrange's equation of motion ; generalized Taylor's formula ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: On the basis of the potential flow theory, Lagrange's equation of motion is used to study the unsteady ground-effect problem. The forces and moments acting on the moving body are solved in terms of the derivatives of added masses in which the generalized Taylor's formulae are applied. The singular integral equations used to solve the surface source intensities and their derivatives are regularized by the Gauss flux theorem and are therefore amenable to the direct use of the Gaussian quadrature formula. In illustration, the condition of a prolate spheroid moving in the fore-and-aft direction at constant speed past a flat ground with a protrusion is considered. The hydrodynamic forces and moments acting on the moving spheroid are investigated systematically by varying the size of the protrusion and the cruising height of the spheroid. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 791-809 
    ISSN: 0271-2091
    Keywords: open channel ; subcritical and supercritical flows ; TVD schemes ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Saint Venant equations for modelling flow in open channels are solved in this paper, using a variety of total variation diminishing (TVD) schemes. The performance of second- and third-order-accurate TVD schemes is investigated for the computation of free-surface flows, in predicting dam-breaks and extreme flow conditions created by the river bed topography. Convergence of the schemes is quantified by comparing error norms between subsequent iterations. Automatically calculated time steps and entropy corrections allow high CFL numbers and smooth transition between different conditions. In order to compare different approaches with TVD schemes, the most accurate of each type was chosen. All four schemes chosen proved acceptably accurate. However, there are important differences between the schemes in the occurrence of clipping, overshooting and oscillating behaviour and in the highest CFL numbers allowed by a scheme. These variations in behaviour stem from the different orders and inherent properties of the four schemes. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 771-789 
    ISSN: 0271-2091
    Keywords: three-dimensional numerical method ; hybrid method ; splitting method ; Eulerian-Lagrangian method ; shallow water equations ; sigma co-ordinate transformation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new efficient numerical method for three-dimensional hydrodynamic computations is presented and discussed in this paper. The method is based on the operator splitting method and combined with Eulerian-Lagrangian method, finite element method and finite difference method. To increase the efficiency and stability of the numerical solutions, the operator splitting method is employed to partition the momentum equations into three parts, according to physical phenomena. A time step is divided into three time substeps. In the first substep, advection and Coriolis force are solved using the explicit Eulerian-Lagrangian method. In the second substep, horizontal diffusion is approximated by implicit FEM in each horizontal layer. In the last substep, the continuity equation is solved by implicit FEM, and vertical diffusion and pressure gradient are discretized by implicit FDM in each nodal column. The stability analysis shows that this method is unconditionally stable. A number of numerical experiments have been performed. The results simulated by the present scheme agree well with analytical solutions and the other documented model results. The method is efficient for 3D shallow water flow computations and fully fits complicated configurations. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 837-850 
    ISSN: 0271-2091
    Keywords: dense gas dispersion ; radiation absorption ; discrete transfer method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical model is presented for the prediction of thermal radiation absorption in dense gas clouds during accidental release in the atmosphere. The model is based on the discrete transfer method (DT method) that was originally developed for modelling radiation in combustion chambers. The radiation model assumes a number of representative rays of predetermined orientation fired from each of the domain boundaries. Each ray is traced through the domain elements until reaching another boundary where it is terminated. Radiation sources are calculated for each element by performing an energy balance across each element for each ray passing through it. The energy sources recovered are fed into the finite element flow solver for every time step in the energy equation. The model proved accurate, and memory and computer time efficient. It showed that accounting for radiation effects lead to improved predictions. It also showed that in certain scenarios, radiation effects could be predominant. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 877-885 
    ISSN: 0271-2091
    Keywords: B-spline basis ; Galerkin method ; Gauss-Newton method ; mixed formulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A mixed Galerkin technique with B-spline basis functions is presented to compute two-dimensional incompressible flow in terms of the primitive variable formulation. To circumvent the Babuska-Brezzi stability criterion, the artificial compressibility formulation of the equation of mass conservation is employed. As a result, the diagonal components of the matrix form in the governing equations are not singular. The B-spline basis is used because it is superior to other splines in providing computer solutions to fluid flow problems. One of the advantages of the B-spline basis is that it has excellent approximation properties. Numerical examples of applications of the mixed formulation are presented to demonstrate the convergence characteristics and accuracy of the present formulation. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 927-957 
    ISSN: 0271-2091
    Keywords: multigrid methods ; finite elements ; finite volumes ; semi-coarsening ; numerical analysis ; turbulent flows ; compressible flows ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Extending multigrid concepts to the calculation of complex compressible flow is usually not straightforward. This is especially true when non-embedded grid hierarchies or volume agglomeration strategies are used to construct a gradation of unstructured grids. In this work, a multigrid method for solving second-order PDE's on stretched unstructured triangulations is studied. The finite volume agglomeration multigrid technique originally developed for solving the Euler equations is used (M.-H. Lallemand and A. Dervieux, in Multigrid Methods, Theory, Applications and Supercomputing, Marcel Dekker, 337-363 (1988)). First, a directional semi-coarsening strategy based on Poisson's equation is proposed. The second-order derivatives are approximated on each level by introducing a correction factor adapted to the semi-coarsening strategy. Then, this method is applied to solve the Poisson equation. It is extended to the 2D Reynolds-averaged Navier-Stokes equations with appropriate boundary treatment for low-Reynolds number turbulent flows. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 17-37 
    ISSN: 0271-2091
    Keywords: incompressible Navier-Stokes ; parallel finite element method ; Galerkin approximation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A parallel semi-explicit iterative finite element computational procedure for modelling unsteady incompressible fluid flows is presented. During the procedure, element flux vectors are calculated in parallel and then assembled into global flux vectors. Equilibrium iterations which introduce some ‘local implicitness’ are performed at each time step. The number of equilibrium iterations is governed by an implicitness parameter. The present technique retains the advantages of purely explicit schemes, namely (i) the parallel speed-up is equal to the number of parallel processors if the small communication overhead associated with purely explicit schemes is ignored and (ii) the computation time as well as the core memory required is linearly proportional to the number of elements. The incompressibility condition is imposed by using the artificial compressibility technique. A pressure-averaging technique which allows the use of equal-order interpolations for both velocity and pressure, this simplifying the formulation, is employed. Using a standard Galerkin approximation, three benchmark steady and unsteady problems are solved to demonstrate the accuracy of the procedure. In all calculations the Reynolds number is less than 500. At these Reynolds numbers it was found that the physical dissipation is sufficient to stabilize the convective term with no need for additional upwind-type dissipation. © 1998 John Wiley & Sons, Ltd.
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1003-1022 
    ISSN: 0271-2091
    Keywords: steady approach flow ; low Reynolds numbers ; 3D simulation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The three-dimensional (3D) unsteady viscous wake of a circular cylinder exposed to a steady approach flow is calculated using a fractional-step finite-difference/spectral-element method. The calculated flow fields at Reynolds numbers of 100 (2D) and 200 (3D) are examined in detail. The flow field at Re = 100 is 2D as expected, while the flow field at Re = 200 has distinct 3D features, with spanwise wavelengths of about 3.75 cylinder diameters. The calculated results produce drag and lift coefficients and Strouhal numbers that agree extremely well with the experimental values. These 3D values at Re = 200 are in better agreement with experimental values than the results of a 2D calculation at Re = 200, which is expected. © 1998 John Wiley & Sons, Ltd.
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  • 87
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1023-1038 
    ISSN: 0271-2091
    Keywords: three-state anemometry ; velocity field ; particle motion equation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An application of a new flow measurement technique is described which allows for the non-intrusive simultaneous measurement of flow velocity, density, and viscosity. The viscosity information can be used to derive the flow field temperature. The combination of the three measured variables and the perfect-gas law then leads to an estimate of the flow field thermodynamic pressure. Thus, the instantaneous state of a flow field can be completely described. Three-state anemometry (3SA), a derivative of particle image velocimetry (PIV), which uses a combination of three monodisperse sizes of styrene seeding particles is proposed. A marker seeding is chosen to follow the flow as closely as possible, while intermediate and large seeding populations provide two supplementary velocity fields, which are also dependent on fluid density and viscosity. A simplified particle motion equation, aimed at turbomachinery applications, is then solved over the whole field to provide both density and viscosity data. The three velocity fields can be separated in a number of ways. The simplest and that proposed in this paper is to dye the different populations and view the region of interest through interferometric filters. The two critical aspects needed to enable the implementation of such a technique are a suitable selection of the diameters of the particle populations, and the separation of the velocity fields. There has been extensive work on the seeding particle behaviour which allows an estimate of the suitable particle diameters to be made. A technique is described in this paper to allow the separation of particles in a range of micrometer sized velocity fields through fluorescence (separation through intensity also being possible). Some preliminary results by direct numerical simulation (DNS) of a 3SA image are also presented. The particle sizes chosen were 1 μm and 5 μm, tested on the near-wake flow past a cylinder to investigate viscosity only, assuming uniform flow density. The accuracy of the technique, derived from simulations of swirling flows, is estimated as 0.5% RMS for velocity, 2% RMS for the density and viscosity, and 4% RMS for the temperature estimate. © 1998 John Wiley & Sons, Ltd.
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  • 88
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 1085-1105 
    ISSN: 0271-2091
    Keywords: adaptive ; hybrid grids ; incompressible ; Navier-Stokes ; finite volume ; pressure correction ; 3-D ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Hybrid grids consisting of prisms and tetrahedra are employed for the solution of the 3-D Navier-Stokes equations of incompressible flow. A pressure correction scheme is employed with a finite volume-finite element spatial discretization. The traditional staggered grid formulation has been substituted with a collocated mesh approach which uses fourth-order artificial dissipation. The hybrid grid is refined adaptively in local regions of appreciable flow variations. The scheme operations are performed on an edge-wise basis which unifies treatment of both types of grid elements. The adaptive method is employed for incompressible flows in both single and multiply-connected domains. © 1998 John Wiley & Sons, Ltd.
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  • 89
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 199-215 
    ISSN: 0271-2091
    Keywords: air-conditioning unit ; k-∊ model ; Reynolds stress model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Details are given of a study to obtain experimental data in an idealized environment for the purpose of evaluating the corresponding computational predictions and which supplement parallel measurements made in actual packaged air-conditioning units. The system consisted of a purpose-built low-speed wind tunnel with a working section constructed to reproduce particular features of the real units. In the experiment, both the mean velocity profiles and turbulence properties of the flow are obtained from triple-hot-wire anemometry measurements. A numerical model, based on finite volume methodology, was used to obtain the solution of the Reynolds-averaged Navier-Stokes equations for incompressible isothermal flow. The Reynolds stress terms in the equations are calculated using the standard k-∊ model and second-moment closure (Reynolds stress) models. The accuracy of the two models was evaluated against the experimental measurements made 10 mm downstream of a baffle. The results show that the standard k-∊ model gave the better agreement except in regions of strong recirculation. © 1997 John Wiley & Sons, Ltd.
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  • 90
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 235-247 
    ISSN: 0271-2091
    Keywords: confined explosions ; risk assessment ; CFD ; adaptive mesh refinement ; multiple obstacles ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Explosion hazards constitute a significant practical problem for industry. In response to the need for better-resolved predictions for confined explosions, and particularly with a view to advancing safety cases for offshore oil and gas rigs, an existing unstructured, adaptive mesh, finite volume Reynolds-averaged Navier-Stokes computational fluid dynamics code (originally developed to handle non-combusting turbomachinery flows) has been modified to include a one-equation, eddy break-up combustion model. Two benefits accrue from the use of unstructured, solution-adaptive meshes: first, great geometrical flexibility is possible; second, automatic mesh adaptation allows computational effort to be focused on important or interesting areas of the flow by enhancing mesh resolution only where it is required. In the work reported here, the mesh was adaptively refined to achieve flame front capture, and it is shown that this results in a 10%-33% CPU saving for two-dimensional calculations and a saving of between 57% and 70% for three-dimensional calculations. The geometry of the three-dimensional calculations was relatively simple, and it may be expected that the use of unstructured meshes for truly complex geometries will result in CPU savings sufficient to allow an order-of-magnitude increase in either complexity or resolution. © 1998 John Wiley & Sons, Ltd.
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  • 91
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 281-301 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; SIMPLE algorithm ; algebraic multigrid methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The application of standard multigrid methods for the solution of the Navier-Stokes equations in complicated domains causes problems in two ways. First, coarsening is not possible to full extent since the geometry must be resolved by the coarsest grid used. Second, for semi-implicit time-stepping schemes, robustness of the convergence rates is usually not obtained for convection-diffusion problems, especially for higher Reynolds numbers. We show that both problems can be overcome by the use of algebraic multigrid (AMG), which we apply for the solution of the pressure and momentum equations in explicit and semi-implicit time-stepping schemes. We consider the convergence rates of AMG for several model problems and demonstrate the robustiness of the proposed scheme. © 1998 John Wiley & Sons, Ltd.
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  • 92
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 345-364 
    ISSN: 0271-2091
    Keywords: liquid-particle flow ; computational efficiency ; Eulerian-Lagrangian model ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The dispersion of solid particles in a turbulent liquid flow impinging on a centrebody through an axisymmetric sudden expansion was investigated numerically using a Eulerian-Lagrangian model. Detailed experimental measurements at the inlet were used to specify the inlet conditions for two-phase flow computations. The anisotropy of liquid turbulence was accounted for using a second-moment Reynold stress transport model. A recently developed stochastic-probabilistic model was used to enhance the computational efficiency of Lagrangian trajectory computations. Numerical results of the stochastic-probabilistic model using 650 particle trajectories were compared with those of the conventional stochastic discrete-delta-function model using 18 000 particle trajectories. In addition, results of the two models were compared with experimental measurements. © 1998 John Wiley & Sons, Ltd.
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  • 93
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 369-401 
    ISSN: 0271-2091
    Keywords: storm surge ; shallow water model ; grid convergence ; coastal ocean ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The focus of this paper is a systematic determination of the relationship between grid resolution and errors associated with computations of hurricane storm surge. A grid structure is sought that provides the spatial resolution necessary to capture pertinent storm surge physics and does not overdiscretize. A set of numerical experiments simulating storm surge generation over 14 grid discretizations of idealized domains examines the influence of grid spacing, shoreline detail, coastline resolution and characteristics of the meteorological forcing on storm surge computations. Errors associated with a given grid are estimated using a Richardson-based error estimator. Analysis of the magnitude and location of estimated errors indicates that underresolution on the continental shelf leads to significant overprediction of the primary storm surge. In deeper waters, underresolution causes smearing or damping of the inverted barometer forcing function, which in turn results in underprediction of the surge elevation. In order to maintain a specified error level throughout the duration of the storm, the highest grid resolution is required on the continental shelf and particularly in nearshore areas. The disparity of discretization requirements between deep waters and coastal regions is best met using a graded grid. Application of the graded gridding strategy to the hindcast of Hurricane Camille reinforces the necessity of using a grid that has high levels of resolution in nearshore regions and areas of complex coastal geometry. © 1998 John Wiley & Sons, Ltd.
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  • 94
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 127-138 
    ISSN: 0271-2091
    Keywords: compressible flow ; supersonic flows ; aerofoils ; Cauchy/Riemann equations ; Crocco's relation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper, alternative formulations of the steady Euler equations for conservation of mass, momentum and energy are adopted for the numerical simulation of compressible flows with shock waves. The total enthalpy is assumed to be constant and hence an isentropic density is calculated in terms of the velocity components. Also, the x- and y-momentum equations written in conservation form are combined to yield the tangential and normal momentum equations. For smooth flows the tangential momentum equation reduces to the entropy transport equation, while the normal momentum equation gives the vorticity in terms of the entropy gradient normal to the flow direction (Crocco's relation). Hence the velocity components can be obtained from the continuity equation and normal momentum equation (Cauchy/Riemann equations), while the entropy correction for the density is obtained from the tangential momentum equation (this correction is not needed in the isentropic flow regions). The present formulation can be easily extended to handle variable total enthalpy. Preliminary results are presented for transonic and supersonic flows over aerofoils and the entropy and vorticity effects are clearly identified. © 1998 John Wiley & Sons, Ltd.
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  • 95
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 139-157 
    ISSN: 0271-2091
    Keywords: hydrodynamic stability ; finite element method ; incompressible cavity flow ; Arnold's method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical methods have been applied to theoretical studies of instability and transition to turbulence. In this study an analysis of the linear stability of incompressible flow is undertaken. By means of the finite element method the two-dimensional base flow is computed numerically over a range of Reynolds numbers and is perturbed with three-dimensional disturbances. The partial differential equations governing the evolution of perturbation are obtained from the non-linear Navier-Stokes equations with a slight compressibility by using linear stability and normal mode analysis. In terms of the finite element discretization a non-singular generalized eigenproblem is formulated from these equations whose solution gives the dispersion relation between complex growth rate and wave number. This study presents stability curves to identify the critical Reynolds number and critical wavelength of the neutral mode and discusses the mechanism of instability. The stability of lid-driven cavity flow is examined. Taylor-Göertler-like vortices in the cavity are obtained by means of reconstruction of three-dimensional flows. © 1998 John Wiley & Sons, Ltd.
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  • 96
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    International Journal for Numerical Methods in Fluids 26 (1998), S. 519-531 
    ISSN: 0271-2091
    Keywords: wavy channel flow ; peristaltic motion ; spectral collocation method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical procedure is developed for the analysis of flow in a channel whose walls describe a travelling wave motion. Following a perturbation method, the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first-order perturbation quantities are calculated using the pseudospectral collocation method. Although limited by the linear analysis, the present approach is not restricted by the Reynolds number of the flow and the wave number and frequency of the wavy-walled channel. Using the computed wall shear stresses, the positions of flow separation and reattachment are determined. The variations in velocity and pressure with frequency of excitation are also presented. © 1998 John Wiley & Sons, Ltd.
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  • 97
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 207-227 
    ISSN: 0271-2091
    Keywords: directional solidification ; multicomponent alloys ; dendritic monocrystals ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element model of dendritic solidification of multicomponent alloys is presented that includes solutal convection and is an extension of a previously developed model for solidification of binary alloys. The model is applied to simulation of the solidification of ternary and quaternary Ni-based alloys. The role of solutal convection in the macrosegregation and the formation of freckles is analysed. Calculations show the effects of geometry and material properties on the convection patterns and the attendant segregation. © 1998 John Wiley & Sons, Ltd.
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  • 98
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    International Journal for Numerical Methods in Fluids 27 (1998), S. 1-11 
    ISSN: 0271-2091
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: No Abstract
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  • 99
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 157-186 
    ISSN: 0271-2091
    Keywords: advective transport ; semi-implicit ; conservative ; unconditionally stable ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A one-dimensional scalar transport method which is appropriate for simulations over a wide range of Courant number is described. Von Neumann stability and matrix invertibility are guaranteed for all Courant numbers and the method has less diffusive and dispersive error than simpler implicit methods. It is implemented for vertical scalar transport in a three-dimensional hydrodynamic model, with horizontal transport discretized explicitly. The method is applied and compared with simpler semi-implicit methods in several test cases and used for a simulation of scalar transport in an estuary. © 1998 John Wiley & Sons, Ltd.
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  • 100
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    International Journal for Numerical Methods in Fluids 28 (1998), S. 23-46 
    ISSN: 0271-2091
    Keywords: domain decomposition ; parallel algorithms ; finite element ; Lagrange multipliers ; projected GMRES ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A parallel solver based on domain decomposition is presented for the solution of large algebraic systems arising in the finite element discretization of mechanical problems. It is hybrid in the sense that it combines a direct factorization of the local subdomain problems with an iterative treatment of the interface system by a parallel GMRES algorithm. An important feature of the proposed solver is the use of a set of Lagrange multipliers to enforce continuity of the finite element unknowns at the interface. A projection step and a preconditioner are proposed to control the conditioning of the interface matrix.The decomposition of the finite element mesh is formulated as a graph partitioning problem. A two-step approach is used where an initial decomposition is optimized by non-deterministic heuristics to increase the quality of the decomposition.Parallel simulations of a Navier-Stokes flow problem carried out on a Convex Exemplar SPP system with 16 processors show that the use of optimized decompositions and the preconditioning step are keys to obtaining high parallel efficiencies. Typical parallel efficiencies range above 80%. © 1998 John Wiley & Sons, Ltd.
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