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  • Engineering General
  • 1985-1989
  • 1980-1984  (541)
  • 1983  (281)
  • 1982  (260)
  • 1
    ISSN: 0271-2091
    Keywords: Finite Element ; Quasi-three-dimensional ; Interconnected Aquifer Systmes ; Fluid Mass Balance ; Iterated Frontal Method ; Predictor-Corrector 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 quasi-three-dimensional equations controlling the groundwater flow in heterogeneous and interconnected aquifer systems are discretized by finite elements, considering also the aquifer branching. A new method for fluid mass balance evaluation based on the equivalent nodal source (E.N.S.) concept allows one to express the balance in conservative terms, and interpret finite element equations as nodal balance equations. The solution of the system is based on the frontal method. Use of substructures limits the frontal increase in correspondence to the aquifer branching. In the steady state, the frontal method is integrated with an iterative solution technique to eliminate the frontal increase caused by the presence of aquitards. It converges very rapidly, using a forcing technique with an automatic parameter definition. In the unsteady case the same scope is achieved using a predictor-corrector procedure which employs the Crank-Nicolson method in the corrector phase.This very stable procedure permits use of fairly long time-steps and concerns the case of source terms depending on piezometry (problem of interaction between water table and river). This method has been tested with several fairly complex cases.
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  • 2
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 493-506 
    ISSN: 0271-2091
    Keywords: Modified ; Dodge ; Algorithm ; Parabolized ; Navier-Stokes ; Computational Fluid Dynamics ; Low Speed Flow ; Channel Flow ; Zebra Algorithm ; Mass Balancing ; 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 revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow has been developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (chequerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A chequerboard iteration is ued to solve the resulting implicit non-linear systems of finite-difference equations which govern stepwise transition. Qualitive agreement with analytical predictions and experimental results has been obtained for some flows with well-known solutions.
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  • 3
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 529-542 
    ISSN: 0271-2091
    Keywords: Strongly Rotating ; Incompressible ; Free-surface ; Finite-difference ; Coriolis ; 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 flow of an incompressible fluid in a rapidly rotating right circular cylinder is considered. A source/sink mass distribution at the lateral wall, which is azimuthally uniform and symmetric across the midplane, causes a deviation from wheel flow. The container is only partially full and the inner free surface is allowed to deviate slightly from the vertical. A finite-difference solution of the full axisymmetric, non-linear governing equations was used to obtain the flow field. A special implicit technique for the Coriolis terms which maintains geostrophy was developed and is described. The results obtained for a low Rossby number flow compare quite favourably with the linearized solution. Results are also presented for a case wherein the non-linear terms are important.
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  • 4
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 567-581 
    ISSN: 0271-2091
    Keywords: Advection ; Convection ; Estuary ; Fractional ; Step ; Diffusion ; Dispersion ; Moving ; Co-ordinates Transport ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A successful and economical fractional step algorithm for the convection-dispersion-reaction equation is described. Exact solutions are adopted for the reaction and convection steps, the latter by the introduction of a moving co-ordinate system. The dispersion step uses an optimized finite difference algorithm which specifically accommodates the grid non-uniformity. The excellent performance of the algorithm is confirmed by numerical experiments together with computations of the Fourier response and integrated square error characteristics.
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  • 5
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 583-590 
    ISSN: 0271-2091
    Keywords: QUICK ; Finite Difference ; Free Surface Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The spatially third-order accurate QUICK finite difference technique is applied to the solution of the depth-integrated equations of motion for steady, subcritical, free surface flow in a wide, shallow, rectangular channel with and without an abrupt expansion. The conservative, control-volume discretization of the equations of motion and the use of QUICK in approximating required cell and cell face average quantities is discussed. Results presented show that it is possible to obtain stable solutions for advective free surface flows without resorting to implicit numerical smoothing.
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  • 6
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 591-604 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; Finite Element Method ; Wave Equation ; Numerical Noise ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical noise has been a problem with finite element solutions to the shallow water equations. Two methods used to reduce the noise level are evaluated, and these results are compared with published results for equal-order interpolations. The two methods are mixed-interpolation (quadratic interpolation for velocity and linear interpolation for sea level) and a spectral form of the wave equation. Whereas mixed interpolation removes the troublesome sea level mode, it can still have considerable noise in velocity. The spectral wave equation is efficient and does not contain the spurious eigenmodes which contribute to high noise levels.
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  • 7
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 605-622 
    ISSN: 0271-2091
    Keywords: Natural ; Convection ; Stream ; Function ; Finite ; Element ; Formulation ; C1 ; Continuity ; Truncated ; Quintic ; Restricted Variational Principle ; 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 stream function formulation is presented for the solution to the two-dimensional double-glazing problem. Laminar flow with constant properties is considered and the Boussinesq approximation used. A restricted variational principle is used, in conjunction with a triangular finite element of C1 continuity, to discretize the two coupled governing partial differential equations (4th order in stream function and second order in temperature). The resulting non-linear system of equations is solved in a segregated (decoupled) manner by the Newton-Raphson linearizing technique.Results are produced for the standard test case of an upright square cavity. These are for Rayleigh numbers in the range 103-105, with a Prandtl number of 0.71. Comparisons are made with benchmark results presented at the 1981 International Comparison study in Venice. In the discussion of results, emphasis is placed on the variation of local Nusselt number along the isothermal walls, particularly near the corner. This reveals a noticeable source of error in the evaluation of the maximum Nusselt number by lower order discretization methods.
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  • 8
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    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 9
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 1-23 
    ISSN: 0271-2091
    Keywords: Transition ; Boundary Layers ; Models of Turbulence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A computational procedure for compressible axisymmetric boundary layers, on bodies of revolution, in transition from laminar to turbulent flow, is introduced. The procedure is an extension of a former method, due to Patankar and Spalding.The flow field is computed by solution of four simultaneous equations for the momentum, the thermal energy, the turbulence energy amplitude and the turbulent scale.The results show good agreement with existing theoretical and experimental data.
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  • 10
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 25-42 
    ISSN: 0271-2091
    Keywords: Penalty Method ; Incompressible Flow ; Reduced Quadrature ; Finite Elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The frequently used reduced integration method for solving incompressible flow problems ‘a la penalty’ is critically examined vis-a-vis the consistent penalty method. For the limited number of quadrilateral and hexahedral elements studied, it is shown that the former method is only equivalent to the latter in certain special cases. In the general case, the consistent penalty method is shown to be more accurate. Finally, we demonstrate significant advantages of a new element, employing biquadratic (2-D) or triquadratic (3-D) velocity and linear pressure over that using the same velocity but employing bilinear (2-D) or trilinear (3-D) pressure approximation.
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  • 11
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 43-60 
    ISSN: 0271-2091
    Keywords: Multigrid ; Iterative Improvement ; Geothermal Model ; Alternating-direction-implicit ; Tau-extrapolation ; Higher-order-accuracy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper considers the multigrid iterative method applied to the solution of finite difference approximations to a linear second-order self-adjoint elliptic equation. It represents an extension of work by Dinar and Brandt. We compare two methods to obtain fourth-order convergence. The first is local error extrapolation developed by Brandt, the second is iterative improvement developed by Lindberg. This work considers non-separable problems, but only on a rectangular domain with Dirichlet boundary conditions. We consider test cases with non-smooth (i.e. discontinuous second derivatives) as well as smooth solutions. We also apply the multigrid method to an elliptic equation with non-separable coefficients which occurs in a geothermal model. In this case an analysis of the error fails to show any advantage in a fourth-order difference scheme over a second-order scheme. However, we do demonstrate that the multigrid iteration performs well on this problem. Also, this example shows that the multigrid iteration can be combined with iterative improvement to create an efficient fourth-order method for a non-separable elliptic equation which is coupled with a marching equation. Other work has found an advantage in this fourth-order scheme for a similar geothermal model.
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  • 12
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 89-112 
    ISSN: 0271-2091
    Keywords: Two Step Scheme ; Selective Lumping Method ; Tidal Flow ; Osaka Bay ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element method for solving shallow water flow problems is presented. The standard Galerkin method is employed for spatial discretization. The numerical integration scheme for the time variation is the explicit two step scheme, which was originated by the authors and their co-workers. However, the original scheme has been improved to remove the erroneous artifical damping effect. Since the improved scheme employs a combination of lumped and unlumped coefficients, the scheme is referred to as a selective lumping scheme. Stability conditions and accuracy are investigated by considering several numerical examples. The method has been applied to the tidal flow in Osaka Bay and Yatsushiro Bay.
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  • 13
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 113-114 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 14
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 61-88 
    ISSN: 0271-2091
    Keywords: Vector ; Differencing ; Finite ; lEement ; Scheme ; Recirculating ; Laminar ; Flow ; False ; Diffusion ; Conservation of Energy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Finite-difference and finite-element techniques have been used to calculate the steady laminar flow over a flat plate normal to an air stream, up to a Reynolds number, Re, based on the plate half-width, of 100. The boundary conditions simulate a central splitter plate downstream of the body, to prevent vortex shedding, so the flow is characterized by a closed recirculation region which grows with increasing Re but at Re = O(100) is very similar in size to the turbulent recirculating region that occurs in the corresponding high Reynolds-number flow. Motivation came, in part, from the increasing efforts of turbulence modellers to calculate complex turbulent flows (containing elliptic regions) and our belief that the numerical methods commonly employed for such work can be inaccurate. The predictions are compared with each other and with some expectations based on classic solutions of the Navier-Stokes equations, and the nature of the numerical errors is demonstrated. It is concluded that effort comparable with that expended in developing turbulence models should be directed to developing higher-order numerical methods, before the numerical accuracy of predictions of, for example, bluff-body flows can be made sufficiently high to sustain detailed discussion of the adequacy of turbulence models in such situations.
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  • 15
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    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 16
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 115-122 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Free Surface ; Porous Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An inexpensive, finite difference numerical method is developed for the approximate solution of general, free surface, porous flow problems. The method is so designed that the required numerical boundary conditions coincide exactly with the required physical boundary conditions. In the present paper, application is made to prototype, steady state, dam flow problems.
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  • 17
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 151-171 
    ISSN: 0271-2091
    Keywords: Penalty method ; Incompressible Flow ; Finite Elements ; Convergence ; Existence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper the penalty function method is reviewed in the general context of solving constrained minimization problems. Mathematical properties, such as the existence of a solution to the penalty problem and convergence of the solution of a penalty problem to the solution of the original problem, are studied for the general case. Then the results are extended to a penalty function formulation of the Stokes and Navier-Stokes equations. Conditions for the equivalence of two penalty-finite element models of fluid flow are established, and the theoretical error estimates are verified in the case of Stokes's problem.
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  • 18
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 123-149 
    ISSN: 0271-2091
    Keywords: Three-dimensional ; Flow ; Computation ; Scheme ; Time ; Marching ; Conventional ; Damping ; Old Time Level ; Current Time Level ; Fourier Perturbation ; Staggered Grid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The numerical stability of a number of computation schemes currently used for three-dimensional, inviscid, compressible flow is analysed using one-dimensional Fourier analysis. Whereas Reference 1 analysed schemes which were modified to render them amenable to simple analysis, the present work analyses the stability of schemes as actually used by Highton,3 Ahrabian,1 Denton2 and Spalding.6 The use of current values of the variables as they become available is shown to bring a general improvement to stability margin. The manner of damping introduced by the time marching formulation is shown to be deleterious to modifications which reduce truncation error. Staggered grid schemes can be formulated to second order accuracy with better stability margin than the corresponding first order scheme. While unstaggered grid schemes can be formulated to second order error and remain stable, their stability margin becomes very small. Agreement of the theory with numerical experiments continues to be of a high order for both one and three-dimensional disturbances.
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  • 19
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 173-184 
    ISSN: 0271-2091
    Keywords: Advection-diffusion ; Characteristics ; Space-time ; Finite ; Elements ; Water Resources ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new finite element method is presented for the solution of two-dimensional transport problems. The method is based on a weighted residual formulation in which the method of characteristics is combined with the finite element method. This is achieved by orienting sides of the space-time elements joining the nodes at subsequent time levels along the characteristics of the pure advection equation associated with the transport problem. The method is capable of solving numerically the advection--diffusion equation without generating oscillations or numerical diffusion for the whole spectrum of dispersion from diffusion only through mixed dispersion to pure convection.The utility and accuracy of the method are demonstrated by a number of examples in two space dimensions and a comparison of the numerical results with the exact solution is presented in one case. A very favourable feature of the method is the capability of solving accurately advection dominated transport problems with very large time steps for which the Courant number is well over one.
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  • 20
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 185-207 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two-dimensional, finite-amplitude wave propagation in an inviscid, subsonic, perfect gas medium is analysed by explicit finite-difference methods. A two-step, Lax-Wendroff method and the single-step, Lax-Friedrichs method are used. A prescribed propagating velocity or pressure disturbance is applied along a single row of grid points normal to the stream direction and results in a 'forced' outflow boundary. The inflow boundary is placed far from outflow by utilizing a streamwise expanding grid and uniform inflow is imposed. Side boundaries are spatially periodic. The numerical solutions are compared with analytical small-perturbation solutions; higher-order effects arising from non-linearities are revealed by Fourier analysis. Solutions which closely approached a periodic state were obtained. The Lax-Wendroff method combined with the expanding grid is shown to be accurate and stable, the Lax-Friedrichs scheme produced highly damped solutions.
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  • 21
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 221-221 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 22
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 209-219 
    ISSN: 0271-2091
    Keywords: First Order Equation ; Hyperbolic Conservation Equation ; Discontinuous Solutions ; Least Squares ; Finite Differences ; Finite Elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Least square methods have been frequently used to solve fluid mechanics problems. Their specific usefulness is emphasized for the solution of a first-order conservation equation. On the one hand, the least square formulation embeds the first-order problem into equivalent second-order problem, better adapted to discretization techniques due to symmetry and positive-definiteness of the associated matrix. On the other hand, the introduction of a least square functional is convenient for finite element applications.This approach is applied to the model problem of the conservation of mass (the unknown is the density ρ) in a nozzle with a specified velocity field (u, v), possibly including jumps along lines simulating shock waves. This represent a preliminary study towards the solution of the steady Euler equations.A finite difference and a finite element method are presented. The choice of the finite difference scheme and of a continuous finite element representation for the groups of variables (ρu, ρv) is discussed in terms of conservation of mass flux. Results obtained with both methods are compared in two numerical tests with the same mesh system.
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  • 23
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    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 24
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 222-223 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 25
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 225-238 
    ISSN: 0271-2091
    Keywords: Normal Direction ; Boundary Conditions ; Incompressible ; Mass Conservation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Various techniques for implementing normal and/or tangential boundary conditions in finite element codes are reviewed. The principle of global conservation of mass is used to define a unique direction for the outward pointing normal vector at any node on an irregular boundary of a domain containing an incompressible fluid. This information permits the consistent and unambiguous application of essential or natural boundary conditions (or any combination thereof) on the domain boundary regardless of boundary shape or orientation with respect to the co-ordinate directions in both two and three dimensions. Several numerical examples are presented which demonstrate the effectiveness of the recommended technique.
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  • 26
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 263-276 
    ISSN: 0271-2091
    Keywords: Finite Elements ; Waves ; Coastline ; Dampers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The problem of truncating nearshore finite element wave models is addressed. Incorrect treatment of the artificial boundaries of the model will cause spurious wave reflections. Three methods for dealing with these boundaries: application of constraints, use of the Smith condition and longshore dampers, are proposed. Numerical results show the dampers to be the best method.
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  • 27
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 239-251 
    ISSN: 0271-2091
    Keywords: Regular ; Discontinuous Boundary Elements ; Fluid Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Boundary Element Method is now well established as a valid numerical technique for the solution of field problems, equal to the Finite Element Method in generality and surpassing it in computational efficiency in some cases.1 In this paper is presented a 'Regular Boundary Element Method' as applied to inviscid laminar fluid flow problems. It involves the formation of a system of regular integral equations obtained by moving the singularity outside the domain of the given problem. It is also shown that non-conforming elements may be used whereby freedoms are not defined at the geometric nodes under the boundary element discretization. A linear element is developed here; higher order variants could easily be defined. Satisfactory numerical results have been obtained using the proposed regular method with both conventional (continuous across the boundary) and non-conforming boundary elements for two-dimensional inviscid laminar fluid flow problems having regular and singular solutions.
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  • 28
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 253-261 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; Sloping Shelf ; Moving Shoreline ; Finite-difference Integration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite-difference method is described for the numerical integration of the one-dimensional shallow water equations over a sloping shelf that allows for a continuously moving shoreline. An application of the technique is made to the propagation of non-breaking waves towards the shoreline. The results of the computation are compared with an evaluation based upon an exact analytical treatment of the non-linear equations. Excellent agreement is found for both tsunami and tidal scale oscillations.
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  • 29
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    International Journal for Numerical Methods in Fluids 2 (1982) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 313-315 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 277-297 
    ISSN: 0271-2091
    Keywords: Advection ; Convection ; Estuary ; Finite ; Element ; Hermite ; Polynomials ; Diffusion ; Dispersion ; Transport ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Space-time finite element solutions of the convection-dispersion equation using higher-order nodal continuity and Hermitian polynomial shape functions are described. Five separate elements ranging from a complete linear element with C0,0 nodal continuity to a complete first-order Hermitian element with C1,1 nodal continuity are subjected to detailed analysis. Wave deformation analyses identify the source of leading or trailing edge oscillations, trailing edge oscillations being the major source of difficulty. These observations are confirmed by numerical experiments which further demonstrate the potential of higher-order nodal continuity. The performance of the complete first-order Hermitian element is quite satisfactory and measurably superior to the linear element.
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 299-311 
    ISSN: 0271-2091
    Keywords: Turbines ; Compressors ; Optimal Design ; Blade Design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Hamilton's variational principle is applied to derive a system of conditions which expresses the balance of momentum and energy of an ideal gas across the selvadgesThe reviewer of this paper confesses to be unfamiliar with the term 'selvadge(s)' which appears frequently herein. Clearly, however, it (variously) means 'boundary', 'edge', 'projection of edge line' (meridional or axial), 'locus of leading edges', etc. of bladed zones within the flow tracts of turbines. This system provides the background for a correct formulation of optimal design problems for turbines and compressors. The exposition follows the model of a large number of blades when the basic equations can be averaged over the azimuthal co-ordinate.An analysis is given of the obtained conditions and a computational algorithm described.
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  • 33
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 317-330 
    ISSN: 0271-2091
    Keywords: Transonic flow ; Turbomachines ; Finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this work a study of the application of the finite element method to transonic flows in axial turbomachines is undertaken.Solution techniques capable of accurately predicting flows from the incompressible regime up to the establishment of shocks in the transonic regime are presented. In the subsonic and shockless transonic regimes a local linearization method capable of very rapid convergence is used. In the full transonic regime the artificial compressibility method is employed to exclude downstream influences in the supersonic regions. The two approaches can be combined in a unified package and appropriate switches introduced to select the relevant method in any flow regime.
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 331-347 
    ISSN: 0271-2091
    Keywords: Fluid Flow ; Turbulent ; Non-circular Passages ; Secondary Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite difference method has been developed to predict the overall features of the local mean flow in fully developed turbulent non-circular passage flows. The main transport effects of secondary flow have been identified and simulated with diffusion transport in a simple way which eliminates solution of the cross-plane momentum and continuity equations and produces a compact calculation method. Predictions are presented for four different passage shapes and are discussed in relation to experimental measurements and predictions from other more complex methods. Although some minor details were not predicted, the main effects of secondary flow on the mean flow were found to have been quite well simulated, yielding predictions that are in reasonable overall agreement with experiment.
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  • 35
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 349-366 
    ISSN: 0271-2091
    Keywords: Viscous Flow Modelling ; Convection Modelling ; Flow Boundary Treatment ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Stream function-vorticity finite element solution of two-dimensional incompressible viscous flow and natural convection is considered. Steady state solutions of the natural convection problem have been obtained for a wide range of the two independent parameters. Use of boundary vorticity formulae or iterative satisfaction of the no-slip boundary condition is avoided by application of the finite element discretization and a displacement of the appropriate discrete equations. Solution is obtained by Newton-Raphson iteration of all equations simultaneously. The method then appears to give a steady solution whenever the flow is physically steady, but it does not give a steady solution when the flow is physically unsteady. In particular, no form of asymmetric differencing is required. The method offers a degree of economy over primitive variable formulations. Physical results are given for the square cavity convection problem. The paper also reports on earlier work in which the most commonly used boundary vorticity formula was found not to satisfy the no-slip condition, and in which segregated solution procedures were attempted with very minimal success.
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  • 36
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 407-409 
    ISSN: 0271-2091
    Keywords: Incompressible Fluid Flows ; Cavity ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 367-386 
    ISSN: 0271-2091
    Keywords: Free Surface ; Thermocapillary ; Convective Flows ; Curvilinear Co-ordinates ; Interface Equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The importance of convective flows generated by surface tension gradients, in comparison with the ones generated by other driving forces, has been investigated in connection with space technological applications involving fluid processes. A theoretical model of the boundary conditions at the interface, considered free and diffusive, has been derived in general tensor form to allow for the use of non orthogonal curvilinear co-ordinates. For the study of flow fields contained in enclosures, these co-ordinates are more suitable to fit all teh boundaries, in particular near the contact angle between the interface and the solid walls, thus giving more accurate numerical solutions.A computational procedure to solve the complete set of bulk and surface equations is proposed and applied to a simplified two dimensional flow in a rectangular enclosure with a temperature gradient between the lateral walls. The numerical results show the importance of considering the interface to be deformable and diffusive for an accurate evaluation of the convective flow in the fluid bulk.
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 410-410 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 39
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 387-405 
    ISSN: 0271-2091
    Keywords: Hyperbolic ; Non-standard Finite Elements ; High Order ; Domain of Dependence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The method of non-standard finite elements was used to develop multilevel difference schemes for linear and quasilinear hyperbolic equations with Dirichlet boundary conditions. A closed form equation of kth-order accuracy in space and time (O(Δtk, Δxk)) was developed for one-dimensional systems of linear hyperbolic equations with Dirichlet boundary conditions. This same equation is also applied to quasilinear systems. For the quasilinear systems a simple iteration technique was used to maintain the kth-order accuracy.Numerical results are presented for the linear and non-linear inviscid Burger's equation and a system of shallow water equations with Dirichlet boundary conditions.
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    International Journal for Numerical Methods in Fluids 2 (1982), S. 410-412 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 42
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    International Journal for Numerical Methods in Fluids 3 (1983), S. i 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 1-21 
    ISSN: 0271-2091
    Keywords: Turbomachines ; Finite Elements ; Transonic Flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical approximation is taken to the solution of the complex flows existing in gas turbine engines with transonic blading. The quasi-3D approach decouples the problem into through-flow and blade-to-blade solutions. An industrially practical finite element through-flow solution is developed and for blade-to-blade solutions a transonic finite areas method is utilized. The finite element code developed is capable of operating in an analysis or a design mode. In both modes a dynamic relaxation factor is employed and considerable reduction in solution time can be achieved. Comparisons to streamline curvature methods are carried out for simple analytical and complex industrial problems.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 23-31 
    ISSN: 0271-2091
    Keywords: Finite Element ; Navier-Stokes ; Incompressible Flows ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A variational formulation for the solution of two dimensional, incompressible viscous flows has been developed by one of the authors.1 The main objective of the present paper is to demonstrate the applicability of this approach for the solution of practical problems and in particular to investigate the introduction of boundary conditions to the Navier-Stokes equations through a variational formulation. The application of boundary conditions for typical internal and external flow problems is presented. Sample cases include flow around a cylinder and flow through a stepped channel.Quadrilateral, bilinear isoparametric elements are utilized in the formulation. A single-step, implicit, and fully coupled numerical integration scheme based on the variational principle is employed. Presented results include sample cases with different Reynolds numbers for laminar and turbulent flows. Turbulence is modelled using a simple mixing length model. Numerical results show good agreement with existing solutions.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 61-70 
    ISSN: 0271-2091
    Keywords: Tides ; Residual Currents ; Finite Elements ; Modal Separation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: From the linearized, time-independent, constant depth, shallow water tidal equations in an f-plane for a two-layer estuary, two independent modal Helmholtz equations are derived. These modal equations are solved using a fifth-degree finite element technique. The first and second space derivatives of the complex modal tidal elevations, and thus the modal currents and their first derivatives, are evaluated directly from the solution at each node of the finite element mesh.The Stokes drift, which is the major part of the residual tidal flow, is evaluated from these nodal values of the currents and their derivatives. Good agreement is obtained with the exact analytical solution for a wedge-shaped estuary with a wedge angle of π/3, using a mesh of 64 equilateral triangles with sides approximately 1/10 of the wavelength 2πC2/σ of a Kelvin wave solution for the short-wavelength mode.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 71-92 
    ISSN: 0271-2091
    Keywords: Boundary Elements ; Hamel Flow ; Free Surface ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A formulation of the boundary element method for the solution of non-zero Reynolds number incompressible flows in which the non-linear terms are lumped together to form a forcing function is presented. Solutions can be obtained at low to moderate Reynolds numbers. The method was tested using the flow of a fluid in a two-dimensional converging channel (Hamel flow) for which an exact solution is available. An axisymmetric formulation is demonstrated by examining the drag experienced by a sphere held stationary in uniform flow. Performance of the method was satisfactory. New results for an axisymmetric free jet at zero Reynolds number obtained using the boundary element method are also included. The method is ideal for this type of free-surface problem.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 93-98 
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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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  • 48
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 33-60 
    ISSN: 0271-2091
    Keywords: Vertical ; Eddy ; Viscosity ; Galerkin ; Method ; Hydrodynamic ; Model ; Eigenfunction ; Currents ; Roughness length ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The three dimensional linear hydrodynamic equations which describe wind induced flow in a sea are solved using the Galerkin method. A basis set of eigenfunctions is used in the calculation. These eigenfunctions are determined numerically using an expansion of B-splines.Using the Galerkin method the problem of wind induced flow in a rectangular basin is examined in detail. A no-slip bottom boundary condition with a vertically varying eddy viscosity distribution is employed in the calculation. With a low (of order 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s) value of viscosity at the sea bed there is high current shear in this region. Viscosities of the order of 1 cm2/s near the sea bed together with high current shear in this region are physically realistic and have been observed in the sea.In order to accurately compute the eigenfunctions associated with large (of order 2000 cm2/s at the sea surface to 1 cm2/s at the sea bed) vertical variation of viscosity, an expansion of the order of thirty-five B-splines has to be used. The spline functions are distributed through the vertical so as to give the maximum resolution in the high shear region near the sea bed.Calculations show that in the case of a no-slip bottom boundary condition, with an associated region of high current shear near the sea bed, the Galerkin method with a basis set of the order of ten eigenfunctions (a Galerkin-eigenfunction method) yields an accurate solution of the hydrodynamic equations. However, solving the same problem using the Galerkin method with a basis set of B-splines, requires an expansion of the order of thirty-five spline functions in order to obtain the same accuracy.Comparisons of current profiles and time series of sea surface elevation computed using a model with a slip bottom boundary condition and a model with a no-slip boundary condition have been made. These comparisions show that consistent solutions are obtained from the two models when a physically relistic coefficient of bottom friction is used in the slip model, and a physically realistic bottom roughness length and thickness of the bottom boundary layer are employed in the no-slip model.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 99-101 
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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 3 (1983) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983), S. i 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 125-135 
    ISSN: 0271-2091
    Keywords: Gas Networks ; Computational Methods ; Simulation ; Optimization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Finite difference methods for solving the linear model describing unsteady state flow in pipelines are considered in the present paper. These methods are compared with each other in order to determine the best one, which meets the criteria of accuracy and relatively small computation time.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 103-123 
    ISSN: 0271-2091
    Keywords: Aquifers ; Convection ; Dispersion ; Finite Difference ; Finite Element ; Mass Transport ; Numerical Solutions ; Unconfined Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Two numerical methods for solving the problem of solute transport in unsteady flow in unconfined aquifers are studied. They are the method of characteristics (MOC) based on the finite difference method (FDM), and the finite element method (FEM). The FEM is further subdivided into four schemes: moving mesh, pseudo-Lagrangian (FEM1); stationary mesh, pseudo-Lagrangian (FEM2); pseudo saturated-unsaturated, Eulerian (FEM3); and non-stationary element, Eulerian (FEM4).Experiments on a one-dimensional flow case are performed to illustrate the schemes and to determine the effect of discretization on accuracy. In two-dimensional flow the above methods are compared with experimental results from a sand box model. Results indicate that for a similar degree of accuracy, the FEM requires less computational effort than the MOC. Among the four FEM schemes, FEM4 appears to be most attractive as it is the most efficient and most convenient to apply.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 137-163 
    ISSN: 0271-2091
    Keywords: Selective Lumping Scheme ; High Reynolds Number ; Vortex Shedding ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents the finite element method for the analysis of unsteady viscous flow of fluid at high Reynolds numbers. The method is based on the explicit numerical integration scheme in time and uses three node triangular finite elements. For the convenience of the formulation, slight compressibility is considered. For the explicit scheme, the selective lumping two step scheme has been successfully employed. Vortex shedding behind a cylinder has been computed and compared with the conventional experimental results. The results agree favourably when both schemes are compared.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 165-177 
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    Keywords: Viscoelastic Flow ; Non-Newtonian Flow ; Memory Fluids ; Memory Integral Fluids ; Maxwell Fluids ; Generalized Maxwell Fluids ; Convective Integration ; Metal Rolling ; Residence Time ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 3 (1983) 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 209-212 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 179-200 
    ISSN: 0271-2091
    Keywords: Wave ; Run-up ; Hydrodynamics ; Moving-boundary ; Finite-element Model ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element model to tackle the moving boundary problem of wave run-up on moderately steep slopes is developed. The special aspects considered in this study are (1) the modification of shallow water equations to accommodate the effect of vertical accelerations and (2) the use of Lagrangian acceleration coupled with an element that adapts itself to the moving boundary closely. The pressure term in the one-dimensional momentum equation is derived using the Eulerian equation in the vertical direction. This takes care of the vertical accelerations which are significant during the motion of a wave on moderately steep slopes. The element near the boundary is allowed to change its dimension so that the fluid boundary is closely followed. Such a flexible element precludes the need for approximation of the variables with regard to the indefinite position of the boundary. This element is split into two when its dimension becomes unduly large compared to the unchanging elements. The need for such a splitting is shown by an examination of the entries in the global matrix. Results of water profile as a wave runs up a structure are given. A brief history of the work on similar problems is outlined.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 201-208 
    ISSN: 0271-2091
    Keywords: Aquifer Model ; Leakage ; Noise ; Averaging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Previous papers12 have drawn attention to the sustained oscillations (‘noise’) in the solution by successive over-relaxation of the equations from the finite difference approximation of regional groundwater flow including ephemeral streams. This paper shows that the trouble can be avoided by introducing an averaging step in the algorithm; the trouble can also be avoided by ‘under-relaxation’ but this is far less efficient than averaging.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 213-216 
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    Keywords: Burgers' Equations ; Exact Solution ; Fluid Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 227-248 
    ISSN: 0271-2091
    Keywords: Comparison ; Natural Convection ; Numerical Methods ; Validation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A number of contributed solutions to the problem of laminar natural convection in a square cavity have been compared with what is regarded as a solution of high accuracy. The purposes of this exercise have been to confirm the accuracy of the bench mark solution and to provide a basis for the assessment of the various methods and computer codes used to obtain the contributed solutions.
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  • 62
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 217-225 
    ISSN: 0271-2091
    Keywords: Cathodic Reduction ; Convection-Diffusion-Reaction ; Characteristics ; Finite Differences ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper derives the convection-diffusion-reaction equation governing the reaction between the dissolved oxygen in sea-water and the steel walls of a pulsating crack. By the neglect of the diffusion term it is shown that an exact solution of the convection-reaction equation can be obtained. A numerical method for the solution of the complete convection-diffusion-reaction equation is derived by the use of finite differences. The numerical computation of the initial transient and the final periodic steady-state values is also discussed.
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  • 63
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 249-264 
    ISSN: 0271-2091
    Keywords: Natural Convection ; Numerical Methods ; Bench Mark Solution ; Square Cavity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Details are given of the computational method used to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls. Second-order, central difference approximations were used. Mesh refnement and extrapolation led to solutions for 103≤Ra≤10 6 which are believed to be accurate to better than 1 per cent at the highest Rayleigh number and down to one-tenth of that at the lowest value.
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  • 64
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 265-282 
    ISSN: 0271-2091
    Keywords: Optimization ; Finite Elements ; Partial Differential Equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Described in this paper is a methodology for solving a particular class of optimum design problems in Fluid Mechanics, namely optimum design problems for aerofoils when the corresponding fluid flow is potential. The methods described in this paper operate directly in the physical space, and take advantage of the variational formulation of the partial differential equation modelling the flow. The techniques of optimal control, optimization and the finite element method are used. Numerical examples are also given.
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  • 65
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 283-293 
    ISSN: 0271-2091
    Keywords: Random Vortex Method Model ; Multiple Jet Flow ; Two-Stroke Uniflow Diesel ; Intake Process ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical model is developed to study the interactions of multiple angled jet flows in the inlet port plane of the Detroit Diesel 6V-92 two-stroke engine cylinder. The random vortex method is used in two dimensions.Results show axisymmetric swirl initially. As flow develops, the centre of the swirl moves to the mid-radius region and begins to precess about the cylinder centre. The flow becomes progressively more chaotic as time progresses.
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  • 66
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 295-305 
    ISSN: 0271-2091
    Keywords: Primitive Variables ; Navier-Stokes ; Central Difference ; Upwind Difference ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The use of the velocity-pressure formulation of the Navier-Stokes equations for the numerical solution of fluid flow problems is favoured for free-surface problems, more involved flow configurations, and three-dimensional flows. Many engineering problems involve such features in addition to strong inertial effects. The computational instabilities arising from central-difference schemes for the convective terms of the governing equations impose serious limitations on the range of Reynolds numbers that can be investigated by the numerical method. Solutions for higher Reynolds numbers Re 〉 1000 could be reached using upwind-difference schemes. A comparative study of both schemes using a method based on the primitive variables is presented. The comparison is made for the model problem of the driven flow in a square cavity. Using a central scheme stable solutions of the pressure and velocity fields were obtained for Reynolds numbers up to 5000. The streamfunction and vorticity fields were calculated from the resulting velocity field and compared with previous solutions. It is concluded that total upwind differencing results in a considerable change in the flow pattern due to the false diffusion. For practical calculations, by a proper choice of a small amount of partial upwind differencing the vorticity diffusion near the walls and the global features of the solutions are not sigificantly altered.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 314-315 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 68
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 315-317 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 69
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 307-313 
    ISSN: 0271-2091
    Keywords: Collocation ; Finite Element Method ; Upwind Schemes ; 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: Upwind collocation on Hermite cubics is compared to orthogonal collocation with respect to effective diffusion. The one-dimensional constant coefficient advection-diffusion equation is employed to this end. The effective diffusion coefficient is determined exactly and is found to be dependent on the nodal solution values. The effective diffusion coefficients of three other upwinding schemes are also presented. Upwind collocation is found to have an effective diffusion coefficient like other upwinding schemes plus an extra term which may enhance or reduce the non-advective flux, depending on the problem solution and point location within the domain.
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  • 70
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    International Journal for Numerical Methods in Fluids 3 (1983) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 71
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    International Journal for Numerical Methods in Fluids 3 (1983), S. i 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 72
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 319-331 
    ISSN: 0271-2091
    Keywords: Convection Diffusion Equation ; Linearized Burger's Equation ; Finite Difference Schemes ; Accuracy Convection Dominated Flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a survey of several finite difference schemes for the steady-state convection-diffusion equation in one and two dimensions. Most difference schemes have O(h2) truncation error. The behaviour of these schemes on a one-dimensional model problem is analysed in detail, especially for the case when convection dominates diffusion. It is concluded that none of these schemes is universally second order. One recently proposed scheme is found to yield highly inaccurate solutions for the case of practical interest, i.e. when convection dominates diffusion. Extensions to two and threedimensions are also discussed.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 333-345 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; Liquid Column Collapse ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The shallow-water equations in radial symmetry are solved numerically to simulate the collapse of a cylindrical liquid column into an area surrounded by a concentric dike. The following three subcases of this problem are considered: a liquid column collapsing onto a layer of the same liquid, a liquid column collapsing onto a solid surface, and a column of lighter liquid collapsing onto a heavier liquid (i.e. liquefied natural gas (LNG) spilled onto water). The results for the three categories are compared and the differences and similarities between them are analysed.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 363-375 
    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: Heat transfer associated with forced convection between bundles of cylindrical fuel rods is analysed using the finite element method. A subchannel technique is employed and the numerical results are compared with previous experimental and numerical values. The solid and fluid zones are analysed, for temperature distribution, as a single domain.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 347-361 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; LNG Pool Spreading ; Continuous and Instantaneous Spills ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A simple numerical model based on the shallow water equations in radial symmetry is used to simulate both instantaneous and continuous spills of liquefied natural gas (LNG) onto a water surface. Using the computed results, a study is made of the similarities and differences in the pool structure resulting from the two types of spills. For instantaneous spills a relation linear on a logarithmic plot is suggested between the maximum pool size and the spill volume. The effects of shear forces and surface cohesivity on the evolution of the spill are also examined.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 425-427 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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    International Journal for Numerical Methods in Fluids 3 (1983) 
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    Keywords: Engineering ; Engineering General
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  • 78
    ISSN: 0271-2091
    Keywords: Mixed Method ; Assumed Deviatoric Stress ; Galerkin Formulation ; Engineering ; Engineering General
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A formulation of a mixed finite element method for the analysis of unsteady, convective, incompressible viscous flow is presented in which: (i) the deviatoric-stress, pressure, and velocity are discretized in each element, (ii) the deviatoric stress and pressure are subject to the constraint of the homogeneous momentum balance condition in each element, a priori, (iii) the convective acceleration is treated by the conventional Galerkin approach, (iv) the finite element system of equations involves only the constant term of the pressure field (which can otherwise be an arbitrary polynomial) in each element, in addition to the nodal velocities, and (v) all integrations are performed by the necessary order quadrature rules. A fundamental analysis of the stability of the numerical scheme is presented. The method is easily applicable to 3-dimensional problems. However, solutions to several problems of 2-dimensional Navier-Stokes' flow, and their comparisons with available solutions in terms of accuracy and efficiency, are discussed in detail in Part II of this paper.
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  • 79
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 399-424 
    ISSN: 0271-2091
    Keywords: Free Surface ; Waves ; Wave ; Motions ; Fluid-Structure ; Interactions ; Finite ; Difference ; Methods ; Lagrangian Formulation ; Triangular Grids ; Numerical Methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper investigates the problems involved in the numerical simulation of free surface wave motions and surface wave effects on marine structures. Various approaches that might be taken in meeting these problems are discussed, and their relative advantages and disadvantages are considered. One particular approach combines a Lagrangian formulation of the governing equations, a triangular grid and a finite-difference solution procedure. Since this approach has some distinct advantages in the numerical calculation of fluid flows which include a free surface, it formed the basis for the development of one particular computer code, SPLISH. Sufficient progress has been made with the SPLISH code to demonstrate the attractiveness of numerical calculations for wave flow problems. Recent computational results demonstrate that realistic time-varying local flow fields, pressures and forces on and near structures such as a half-cyclinder on the ocean floor can be determined from numerical calculations for certain conditions. Good agreement is found in comparison of the numerical results from SPLISH, recent linear wave Green's function and fifth-order asymptotic solutions for wave motion over a bottom seated half-cylinder, and an experimental simulation in a wave channel.
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  • 80
    ISSN: 0271-2091
    Keywords: Finite Elements ; Infinite Elements ; Acoustics ; Wave Propagation ; Radiation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Finite element models are presented for the calculation of near and far field acoustical radiation. These models are applied to the specific problem of fan noise radiation from axisymmetric turbofan inlets. In all cases conventional acoustic finite elements are used within an inner region close to the inlet. The far field is represented by infinite elements or wave envelope elements. Theory and results are presented for the case with zero mean flow. Comparisons of computed data with analytic solutions and measured values establish the utility of both the infinite element and wave envelope element schemes in determining the near field values of acoustical pressure. The wave envelope scheme is shown to be effective also in the far field. Both schemes use meshes an order of magnitude more sparse that would be required in conventional numerical discretizations, and may consequently be applied at modest computational cost.
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    International Journal for Numerical Methods in Fluids 3 (1983), S. 543-565 
    ISSN: 0271-2091
    Keywords: Low-aspect Ratio Wings ; Leading-edge Separation ; Vortex Shedding ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A multi-vortex model of the vortex sheets shed from the sharp leading edges of slender wings is considered. The method, which is developed within the framework of slender-body theory, is designed to deal with those situations in which more than one centre of rotation is formed on the wing, for example on a slender wing with lengthwise camber or with a strake. Numerical results are presented, firstly for situations where comparison can be made with a vortex sheet model and secondly for cases, such as those described above, where a vortex sheet model is unable to describe the flow. Where comparison is available, agreement is good and in the cases where more than one vortex system is present interesting interactions are obtained.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. i 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 21-46 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: An analysis is presented of the non-linear creep effects around a deep circular tunnel driven in ‘squeezing’ ground. The time-dependent behaviour of the geotechnical medium is described by means of a simple viscoplastic rheological model capable of approximating primary, secondary and tertiary creep behaviours. It is shown that tertiary creep can be allowed for by providing a suitable law governing the variation of some material parameters (such as viscosity) with stresses and strains. The basic operations of the ‘evolutive’ procedure adopted for time integration are outlined. Along each time integration step, quadratic variations of the stress and strain fields and linear variations of the material parameters are assumed. The results of various finite element analyses are presented concerning both lined and unlined cases. For the lined cases, the influence of the liner stiffness and of the time elapsed between the end of excavation and the liner installation is considered.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 47-76 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: In this paper, the ability of a displacement-type finite element analysis to predict collapse loads accurately is investigated. For the usual assumptions of ideal plasticity and infinitesimal deformations, attention is focused on undrained geotechnical problems. The theoretical criterion originally developed by Nagtegaal et al.1 is applied to each member of the serendipidity quadrilateral and triangular family of elements, up to and including those with a quartic displacement expansion. This method of assessing the suitability of a particular type of element is shown to be valid for any constitutive law which attempts to enforce the constant volume condition at failure, such as critical state type soil models. The method is also generalized to permit an assessment, a priori, of the suitability of any given mesh which is composed of a finite number of elements of the same type. It is postulated that the 15-noded, cubic strain triangle is theoretically capable of accurate computations in the fully plastic range for undrained geotechnical situations which involve axial symmetry or plane strain. This prediction is verified by a series of numerical experiments on footing problems. Extending the work of Nagtegaal et al., 1 it is established theretically that if lower order finite elements are employed rigorously for non-trivial undrained problems with axial symmetry, then it is impossible to predict the exact limit load accurately, regardless of how refined the mesh may be.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 77-94 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: It is commonly accepted that the mechanical behaviour of granular masses is strongly affected by their microstructure, namely the relative arrangement of voids and particles, i.e. the granular fabric. Therefore, parameters which characterize the granular fabric are of paramount importance in a fundamental description of the overall macroscopic stresses and deformation measures. In this paper several measures of granular fabric are introduced for a random assembly of spherical granules, using a statistical approach. In particular, a second-order symmetric tensor, Fij, emerges from this consideration, which seems to be of fundamental importance for the description of fabric, and which is closely related to the distribution of the contact normals in the assembly. The relation between fabric measures presented here and those discussed by other investigators is also discussed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 141-145 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A mapping finite element method is proposed for the solution of elastic problems in two-dimensions. This method, based on the logarithmic condensation of physical space, is found to give significantly greater accuracy than when the problem is solved in the physical plane using the standard FEM. Logarithmic condensation of space also permits the solution of large aspect-ratio problems of this type, accurately and economically.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 129-139 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Collapse loads are overestimated by finite-element or finite-difference procedures when the material discretization does not allow locally incompressible plastic flow: for example, constant-strain triangles or tetrahedra give unacceptable results. The use of different discretizations for the isotropic and deviatoric parts of the strain tensor is advocated for preventing this problem. The technique can be easily implemented in existing two- and three-dimensional computer programs. Its effectiveness is demonstrated by several examples.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 148-148 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 148-149 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Keywords: Engineering ; Engineering General
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. i 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. ii 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 173-194 
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    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The theory developed in Part I of this paper is extended to apply to the consolidation of horizontally layered soils under both axially symmetric and general surface loading. The method again leads to a considerable reduction in the amount of core storage necessary for computer solution and can be implimented on a mini-computer.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 151-171 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A method for the analysis of the consolidation of a horizontally layered soil under plane conditions is developed. The method depends upon the transformation of the governing equations by a Fourier trasform. This transformation has the effect of reducing the partial differential equations of consolidation to ordinary differential equations. The ordinary differential equations are then solved using a finite layer or finite difference approach. Once the solution in the transformed plane has been found, the actual solution is synthesized by Fourier inversion. The method leads to a considerable reduction in the amount of core storage necessary for solution and enables the solution of quite significant problems to be obtained on a mini-computer.
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  • 96
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. i 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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  • 97
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 392-392 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Type of Medium: Electronic Resource
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  • 99
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. i 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 441-459 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The present study is a continuation of the numerical modelling of geologic structures by the authors (see J. N. Reddy et al., Finite-element modelling of folding and faulting, this journal). The present paper is concerned with the computation of the stress and fracture density distributions in single layer folds by the finite-element method. It was found that variations in fracture patterns are related to several variables: (i) the viscosity of the competent layer, (ii) the ratio of the viscosity of the competent layer to the viscosity of the matrix, (iii) the cohesive strength of the material, and (iv) the boundary velocities during deformation. The fracture prediction is based on the Mohr-Coulomb criterion, which is a function of the stresses only. Prediction of fracture density is based on a function of the strain energy. It is found that there is a good correlation between the computer predicted fractures and the fracture pattern produced by the expermental buckiing of rock-beams. Itis, concluded that the viscosity ratio controls the location of fractures in single layer folds.
    Additional Material: 17 Ill.
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