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  • Articles  (44)
  • Articles: DFG German National Licenses  (44)
  • Finite elements  (44)
  • 2015-2019
  • 1990-1994  (44)
  • 1945-1949
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (43)
  • Computer Science  (1)
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  • Articles  (44)
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  • Articles: DFG German National Licenses  (44)
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  • 1
    Electronic Resource
    Electronic Resource
    Basic features of the time finite element approach for dynamics (1992)
    Springer
    Meccanica 27 (1992), S. 119-130 
    Details
    ISSN: 1572-9648
    Keywords: Finite elements ; Time integration ; Dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Due differenti formulazioni agli elementi finiti nel tempo sono presentate in questo lavoro quali casi particolari di una formulazione generale a tre campi: la prima è una formulazione agli spostamenti, mentre la seconda è una formulazione mista dove i campi indipendenti sono costituiti da spostamenti e momenti cinetici. Dopo aver sviluppato la linearizzazione e l'approssimazione agli elementi finiti delle forme, viene discussa una tecnica per il trattamento di vincoli di olonomia ed anolonomia. Le principali caratteristiche numeriche dei due metodi vengono infine evidenziate facendo anche ricorso ad esempli semplici ma significativi.
    Notes: Abstract Very general weak forms may be developed for dynamic systems, the most general being analogous to a Hu-Washizu three-field formulation, thus paralleling well-established weak methods of solid mechanics. In this work two different formulations are developed: a pure displacement formulation and a two-field mixed formulation. With the objective of developing a thorough understanding of the peculiar features of finite elements in time, the relevant methodologies associated with this approach for dynamics are extensively discussed. After having laid the theoretical bases, the finite element approximation and the linearization of the resulting forms are developed, together with a method for the treatment of holonomic and nonholonomic constraints, thus widening the horizons of applicability over the vast world of multibody system dynamics. With the purpose of enlightening on the peculiar numerical behavior of the different approaches, simple but meaningful examples are illustrated. To this aim, significant parallels with elastostatics are emphasized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00420590
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  • 2
    Electronic Resource
    Electronic Resource
    A new viewpoint on mixed elements (1992)
    Springer
    Meccanica 27 (1992), S. 3-11 
    Details
    ISSN: 1572-9648
    Keywords: Elliptic PDEs ; Finite elements ; Mixed elements ; Differential geometry ; Whitney forms ; Tonti diagrams ; Complementarity ; Duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Gli elementi misti sono elementi finiti speciali per campi vettoriali le cui funzioni di interpolazione non sono necessariamente continue in tutte le componenti; tali elementi vengono usati nell'ambito delle formulazioni ‘a due campi’, per esempio quando si calcolano simultaneamente spostamento e tensione in elasticità. In questo articolo viene presentata una famiglia di elementi finiti che traggono origine da un costrutto di geometria differenziale che in apparenza non ha alcun nesso con l'analisi numerica (le forme di Whitney): vengono illustrate le proprietà strutturali complessive di tale famiglia. Questa presentazione getta una nuova luce sugli elementi misti, sotto la quale essi acquistano un carattere più naturale.
    Notes: Abstract Mixed elements are special finite elements for vector fields, whose shape functions are not necessarily continuous in all their components. They are used in connection with ‘two-field’ formulations, for instance when one tries simultaneously to compute displacement and stress in elasticity. We present here a family of finite elements which originate from a chapter of differential geometry apparently unconnected with numerical analysis (Whitney forms) and insist on the structural properties of this family considered as a whole. This sheds a new light on mixed elements, under which they acquire a more natural character than in previous presentations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00452998
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  • 3
    Electronic Resource
    Electronic Resource
    Calculation of non-Newtonian flow of colloidal dispersions: Finite elements and Brownian dynamics (1993)
    Springer
    Journal of computer-aided materials design 1 (1993), S. 85-96 
    Details
    ISSN: 1573-4900
    Keywords: Finite elements ; Brownian dynamics ; Colloidal dispersion ; Plane Couette flow ; Simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary We present a novel method for the numerical calculation of the flow of particulate fluid systems and apply it to the flow of a colloidal dispersion. This method is based on the CONNFFESSIT (Calculation Of Non-Newtonian Flow: Finite Element and Stochastic Simulation Technique) [Laso and Öttinger, J. Non-Newtonian Fluid Mech., 47 (1993) 1]. It couples microscopic dynamic simulations (Brownian Dynamics, BD) with macroscopic Finite Element (FE) methods as traditionally used in the calculation of viscoelastic flow. The standard continuum-mechanical form of the momentum transport equation is closed by microscopic BD simulations. The coupling between the macroscopic FE formulation for the velocity field and the microscopic simulation is effected through the stress tensor, which is obtained as an ensemble average over BD trajectories. This combination of microscopic simulations with macroscopic FE methods obviates the need for a rheological constitutive equation (strain history-stress relationship) to describe the fluid system. It is therefore possible to solve flow problems for very general fluid systems, for which no exact constitutive equation can be derived. The method is applied to the start-up of plane Couette flow of an electrostatically stabilized colloidal dispersion. The calculation of the inhomogeneous start-up of Couette flow for a colloidal dispersion undergoing a disorder-order transition has remained intractable up to now, due to the difficulty of deriving a constitutive equation for the interacting colloidal dispersion in order to close the equation of motion. Besides giving the evolution of the velocity field, the combination of BD and FE techniques provides a fully detailed, time-dependent, dynamic and structural description of the colloidal dispersion. During inhomogeneous start-up, the colloidal dispersion undergoes a disorder-order phase transition as in the homogeneous case. However, depending on the ratio of the characteristic time for the phase transition and the transit time for a velocity disturbance, either the transition can occur simultaneously throughout the fluid or a moving front separating ordered and disordered regions can appear.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00712819
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  • 4
    Electronic Resource
    Electronic Resource
    Fast solutions to physical equilibrium and interpolation problems (1992)
    Springer
    The visual computer 8 (1992), S. 303-314 
    Details
    ISSN: 1432-2315
    Keywords: Finite elements ; Regularization ; Lofting ; Wavelets ; Preconditioning
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Efficient solutions to physical equilibrium and interpolation problems can be obtained by using wavelet basis vectors for problem discretization or for use as a preconditioning transform. Good approximations to these solutions can be obtained in onlyO(n) operations andO(n) storage locations, a property that can be extremely useful in visualization applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01897117
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  • 5
    Electronic Resource
    Electronic Resource
    A Taylor-Galerkin-based algorithm for viscous incompressible flow (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 327-351 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Taylor-Galerkin algorithm ; Fractional step method ; Cavity 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: In this paper the development and behaviour of a new finite element algorithm for viscous incompressible flow is presented. The stability and background theory are discussed and the numerical performance is considered for some benchmark problems. The Taylor-Galerkin approach naturally leads to a time-stepping algorithm which is shown to perform well for a wide range of Reynolds numbers (1 ≤ Re ≤ 400).A conventional definition for Re is assumed. Various modifications to the algorithm are investigated, particularly with respect to their effects on stability and accuracy.
    Additional Material: 23 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100307
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  • 6
    Electronic Resource
    Electronic Resource
    Implicit finite element methods for two-phase flow in oil reservoirs (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 651-681 
    Details
    ISSN: 0271-2091
    Keywords: Porous media ; Two-phase flow ; Oil recovery ; Finite elements ; Preconditioning ; Conjugate gradients ; 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 equations governing immiscible, incompressible, two-phase, porous media flow are discretized by generalized streamline diffusion Petrov-Galerkin methods in space and by implicit differences in time. Systems of non-linear algebraic equations are solved by Newton-Raphson iteration employing ILU-preconditioned conjugate-gradient-like methods to the non-symmetric matrix system in each iteration. The resulting solution methods are robust, enable complex grids with irregular nodal orderings and allow capillary effects.Several numerical formulations are tested and compared for one-, two- and three-dimensional flow cases, with emphasis on problems involving saturation shocks, heterogeneous media and curved boundaries. For reservoirs consisting of multiple rock types with differing capillary pressure properties, it is shown that traditional Bubnov-Galerkin methods give poor results and the new Petrov-Galerkin formulations are required. Investigations regarding the behaviour of several preconditioned conjugate-gradient-like methods in these type of problems are also reported.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100605
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  • 7
    Electronic Resource
    Electronic Resource
    Finite element solution of flow between eccentric cylinders with viscous dissipation (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 849-865 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Navier-stokes ; Rotating cylinders ; Viscous dissipation ; 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 study of viscous flow between two eccentrically rotating cylinders is presented in which the effect of viscous dissipation is taken into account. The space discretization is based on piecewise linear finite elements with velocity stabilization, while the method of characteristics is used for time integration. Numerical results illustrate the efficiency of the adopted approach.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110610
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  • 8
    Electronic Resource
    Electronic Resource
    Finite element solution of the Navier-Stokes equations by a velocity-vorticity method (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 661-675 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Navier-Stokes ; Velocity-vorticity ; 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 velocity-vorticity formulation of the Navier-Stokes equations is presented as an alternative to the primitive variables approach. The velocity components and the vorticity are solved for in a fully coupled manner using a Newton method. No artificial viscosity is required in this formulation. The pressure is updated by a method allowing natural imposition of boundary conditions. Incompressible and subsonic results are presented for two-dimensional laminar internal flows up to high Reynolds numbers.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110511
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  • 9
    Electronic Resource
    Electronic Resource
    Radiation boundary conditions for finite element solutions of generalized wave equations (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 765-783 
    Details
    ISSN: 0271-2091
    Keywords: Radiation boundary conditions ; Open boundary conditions ; Wave equation ; Finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: On the basis of the dispersion relation of the generalized linear wave equation we derive a radiation boundary condition (RBC) that explicitly incorporates the physical parameters of the governing equation into the form of the boundary condition. Using finite element techniques we investigate the properties of the generalized RBC by examining forced and unforced solutions to the telegraph and Klein-Gordon equations in one dimension. The results show that within the limits of the physical parameters of the problem the generalized RBC is an improvement over the Sommerfeld RBC when the governing equation contains additional terms that influence the propagation. These gains are achieved without introducing any computational overhead. A two-dimensional example suggests that the 1D findings can generalize to higher dimensions.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120806
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  • 10
    Electronic Resource
    Electronic Resource
    A one-dimensional moving grid solution for the coupled non-linear equations governing multiphase flow in porous media. 2: Example simulations and sensitivity analysis (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 47-69 
    Details
    ISSN: 0271-2091
    Keywords: Partial differential equations ; Non-linear equations ; Coupled system ; Numerical methods ; Finite elements ; Adaptive grid ; Flow in porous media ; Groundwater contamination ; Multiphase flow ; Immiscible 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: This paper presents numerical examples for the moving grid finite element algorithm derived in Part Ito solve the non-linear coupled set of PDEs governing immiscible multiphase flow in porous media in one dimension. Examples include single- and double-front simulations for two- and three-phase flow regimes and incorporating a mass sink. The modelling approach is shown to achieve significant savings in computation time and memory allocation when compared with fixed grid solutions of equivalent accuracy. This work includes sensitivity analyses for the parameters which are incorporated in the grid adaptation method, including the curvature weights, artificial viscosity and artificial repulsive force. It is found that the curvature weights are exponential functions of the negative ratio of the square root of the domain length to the number of discrete nodes. These weighting parameters are also shown to depend upon the shape of the front. On the basis of the examined simulations, it is recommended that artificial viscosity be neglected in the solution of the coupled non-linear set of PDEs governing multiphase flow in porous media. Similarly, use of a repulsive force is found to be unnecessary in simulations involving the migration of two liquid phases. For multiphase flows incorporating a gas phase it is recommended to use a non-zero value for the repulslive force to avoid development of an ill-conditioned nodal distribution matrix. An equation to evaluate the repulsive force under these circumstances is suggested.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140105
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  • 11
    Electronic Resource
    Electronic Resource
    Prediction of three-dimensional general shape extrudates by an implicit iterative scheme (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 609-625 
    Details
    ISSN: 0271-2091
    Keywords: 3D extrusion ; Moving boundaries ; Kinematic condition ; Remeshing ; Finite elements ; Free surfaces ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents a numerical technique for solving three-dimensional free surface problems in extrusion applications. The method is fully implicit in the sense that a Newton-Raphson scheme is applied on all variables, and geometrically general. In particular, the die section shape may be complex and contains multiple corners: very few restrictions apply on the mesh generation because the method does not require the nodes to be located on straight lines (spines). A clear distinction is introduced between the directions associated with the kinematic condition and the remeshing rules. As a difference with respect to earlier publications, these concepts are handled separately. Only Stokes problems are solved in this paper and we have not introduced surface tension. Therefore corners in the die section propagate discontinuities in the extrudate shape, an a method for relocating corners without losing the quadratic convergence of the scheme is presented. Data structures used for the implementation are briefly discussed.We present results on the extrusion of various profiles, including a rectangular die (a benchmark problem) and various complex sections containing multiple corners.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140507
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  • 12
    Electronic Resource
    Electronic Resource
    A finite element study of incompressible flows past oscillating cylinders and aerofoils (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 1073-1118 
    Details
    ISSN: 0271-2091
    Keywords: Space-time ; Finite elements ; Incompressible flows ; Galerkin/least-squares ; Deforming spatial domain ; Oscillating cylinder ; Pitching aerofoil ; Clustered element-by-element ; GMRES ; Vortex shedding ; Vortex-induced oscillations ; Lock-in ; Hysteresis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present our numerical results for certain unsteady flows past oscillating cylinders and aerofoils. The computations are based on the stabilized space-time finite element formulation. The implicit equation systems resulting from the space-time finite element discretizations are solved using iterative solution techniques.One of the problems studied is flow past a cylinder which is forced to oscillate in the horizontal direction. In this case we observe a change from an unsymmetric mode of vortex shedding to a symmetric one. An extensive study was carried out for the case in which a cylinder is mounted on lightly damped springs and allowed to oscillate in the vertical direction. In this case the motion of the cylinder needs to be determined as part of the solution, and under certain conditions this motion changes the vortex-shedding pattern of the flow field significantly. This non-linear fluid-structure interaction exhibits certain interesting behaviour such as ‘lock-in’ and ‘hysteresis’, which are in good agreement with the laboratory experiments carried out by other researchers in the past. Preliminary results for flow past a pitching aerofoil are also presented.
    Additional Material: 39 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650150911
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  • 13
    Electronic Resource
    Electronic Resource
    Simple test calculations concerning finite element applications to numerical weather prediction (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 209-226 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Atmospheric flow ; Petrov-Galerkin ; Staggered grids ; Hybrid scheme ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Different finite element schemes are investigated with respect to their application in numerical weather prediction. Different methods of staggering of variables are considered. The tests concern the accuracy of a Rossby wave prediction and the generation of noise in a geostrophic adjustment process. Theoretical results concerning the noise level of different schemes are confirmed by computations with a one-dimensional model. Favourable results were obtained by hybrid schemes, using different Galerkin treatments for different terms of the dynamic equations.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110207
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  • 14
    Electronic Resource
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    Global convergence of inexact Newton methods for transonic flow (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 1075-1095 
    Details
    ISSN: 0271-2091
    Keywords: Inexact Newton methods ; Global convergence ; Finite elements ; Full potential equation ; Damping strategies ; 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 computational fluid dynamics, non-linear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these non-linear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modelled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110803
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  • 15
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    Three-dimensional hydrodynamics on finite elements. Part II: Non-linear time-stepping model (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 507-533 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Hydrodynamics ; Three-dimensional hydrodynamics ; Non-linear hydrodynamics ; Tidal hydrodynamics ; 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 development and application of a non-linear 3D hydrodynamic model are described. The model is based on the wave equation rearrangement of the primitive 3D shallow water equations with a general eddy viscosity formulation for the vertical shear. A Galerkin procedure is used to discretize these on simple sixnode elements: linear triangles in the horizontal with linear variations in the vertical. Resolution of surface, bottom and interfacial boundary layers is facilitated and total flexibility is preserved for specifying spatial and temporal variations in the vertical viscosity and density fields. A semi-implicit time-stepping algorithm allows the solutions for elevation and velocity to be uncoupled during each time step. The elevation solution is essentially a 2D wave equation calculation with a stationary sparse matrix representing the gravity waves. With nodal quadrature the subsequent velocity calculation is achieved by factoring only a tridiagonal diffusion matrix representing the vertical viscous terms. As a result the overall calculation scales computationally as only a 2D problem but provides the full 3D solution. Application to field-scale problems is illustrated for the English Channel/Southern Bight system and the Lake Maracaibo system.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120602
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  • 16
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    Time-dependent solution of the incompressible Navier-Stokes equations to simulate air-conditioning (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 967-974 
    Details
    ISSN: 0271-2091
    Keywords: Permeable walls ; Bulk friction ; Time-dependent ; Incompressible Navier-Stokes ; Pressure correction ; Projection ; Semi-implicit ; 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: Computer simulations may contribute significantly to the optimal design of air-conditioning systems. To capture the effects of partially permeable walls such as bookshelves on the movement of air and heat, it is necessary to extend the density-dependent Navier-Stokes equations by an additional friction term. The finite element technique is convenient to approximate the extended equations in spatial co-ordinates. For the time co-ordinate a recently proposed semi-implicit finite difference method is very efficient in terms of accuracy and computational complexity. A pressure correction approach is most appropriate to decouple the primitive variables in the extended Navier-Stokes equations. The resulting algorithm has the interesting feature that small symmetric positive definite systems of equations can be solved sequentially for each of the primitive variables. Iterative solution of the systems of equations with preconditioned conjugate gradients combined with a compressed storage scheme allows fine grid computations at affordable costs. As an example a two-dimensional version of the code was applied to an enclosure which was heated from the side and contained a porous wall. The time-dependent computational results are compared with measurement data.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650150903
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  • 17
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    Die design: An implicit formulation for the inverse problem (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 29-42 
    Details
    ISSN: 0271-2091
    Keywords: 3D extrusion ; Moving boundaries ; Die design ; Remeshing ; Finite elements ; Free surfaces ; 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: Let us call a direct extrusion problem (DEP) the problem of finding the shape of the extrudate coming out of a die of prescribed shape. An implicit finite element formulation of the DEP which is geometrically general and for which a Newton-Raphson technique can be implemented has recently been proposed by Legat and Marchal. However, the problem posed to the die designer is frequently the inverse extrusion problem (IEP), i.e. finding the die shape which produces an extrudate of prescribed shape. This paper presents an extension of our original method for solving the IEP which avoids the ‘trial-and-error’ iteration on the die geometry itself.The advantage of the formulation lies in its capability to handle complex geometrics and in its low cost, because the CPU time and memory required to solve the IEP are almost identical to those of the DEP. We present benchmark results for squares and rectangles and new results obtained for geometries involving multiple corners. For an octagonal shape we also consider the case of a power-law fluid.For all results presented in this paper, surface tension has not been included.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650160103
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  • 18
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    Unsymmetric conjugate gradient methods and sparse direct methods in finite element flow simulation (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 925-945 
    Details
    ISSN: 0271-2091
    Keywords: Bi-conjugate gradient ; Conjugate gradient ; Conjugate gradient squared ; Finite elements ; Flow simulation ; Preconditioning ; Vector processor ; Frontal solver ; Navier-Stokes ; Boussinesq approximation Newton method ; Picard iteration ; Galerkin method ; Petrov-Galerkin ; 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 series of numerical experiments on the Cray XMP/48 and on the Cray 2 investigate the robustness and economy of direct and unsymmetric conjugate gradient (CG) type methods for the solution of matrix systems arising from a 3D FEM discretization of fluid flow problems. Computations on a Boussinesq flow model problem with either ILU preconditioned or unpreconditioned unsymmetric CG methods are presented. Such experiments seem to indicate that the unpreconditioned BICG method is robust for moderately non-linear incompressible Navier-Stokes FEM discretizations and that the ILU preconditioned BICG method is very robust and more economic than an unsymmetric frontal solver when the generous memory of the Cray 2 is exploited to store both the matrix and its preconditioner. We cover some of the programming aspects of direct and iterative methods on a supercomputer and find that direct methods have advantages: the crucial CPU-consuming area of code is compact but overwhelming, and its percentage of total CPU usage is independent of the spectral properties of the matrix involved. An optimal implementation of the unsymmetric CG method is more difficult because its work is related to the spectral distribution of the matrix considered and because there is no single portion of the code that overwhelmingly dominates the CPU usuage.
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    URL: http://dx.doi.org/10.1002/fld.1650100806
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    Periodic viscous flow: A bench-mark problem (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 87-97 
    Details
    ISSN: 0271-2091
    Keywords: Periodic ; Unsteady ; Viscous flow ; 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: A double-transform technique provides a semi-analytic solution in the form of a series expansion for unsteady axisymmetric Stokes flow in the entrance region of a semi-infinite rigid cylindrical tube. This in turn offers an appropriate bench-mark problem for evaluating the quality of numerical approximations. To illustrate this, periodic axial flow in a circular cylinder is considered. Some aspects of the bench-mark problem that are of interest include the reverse flow in the wall layers, the accuracy of the approximate method in different flow regimes and the mesh grading. This bench-mark problem and the numerical study provide some insight into practical issues pertinent to the approximate solution of unsteady and periodic flows.
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    URL: http://dx.doi.org/10.1002/fld.1650110106
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    A one-dimensional moving grid solution for the coupled non-linear equations governing multiphase flow in porous media. 1: Model development (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 25-45 
    Details
    ISSN: 0271-2091
    Keywords: Partial differential equations ; Non-linear equations ; Coupled system ; Numerical methods ; Finite elements ; Adaptive grid ; Flow in porous media ; Groundwater contamination ; Multiphase flow ; Immiscible 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 straightforward moving grid finite element method is developed to solve the one-dimensional coupled system of non-linear partial differential equations (PDEs) governing two- and three-phase flow in porous media. The method combines features from a number of self-adaptive grid techniques. These techniques are the equidistribution, the moving grid finite element and the local grid refinement/coarsening methods. Two equidistribution criteria, based on solution gradient and curvature, are employed and nodal distributions are computed iterativcly. Using the developed approach, an intermingle-free nodal distribution is guaranteed. The method involves examination of a single representative gradient to facilitate the application of moving grid algorithms to solve a non-linear coupled set of PDEs and includes a feature to limit mass balance error during nodal redistribution. The finite element part of the developed algorithm is verified against an existing finite difference model. A numerical simulation example involving a single-front two-phase flow problem is presented to illustrate model performance. Additional simulation examples are given in Part 2 of this paper. These examples include single and double moving fronts in two- and three-phase flow systems incorporating source/sink terms. Simulation sensitivity to the moving grid parameters is also explored in Part 2.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/fld.1650140104
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    A finite element solutionof three-dimensional mixed convection gas flows in horizontal chnnels using preconditioned iterative metrix methods (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 817-841 
    Details
    ISSN: 0271-2091
    Keywords: Mixed convection ; Finite elements ; CVD ; Iterative methods ; Preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An algorithm is presented for the finite element solution of three-dimensional mixed convection gas flows in channels heated from below. The algorithm uses Newton's method and iterative matrix methods. Two iterative solution algorithms, conjugate gradient squared (CGS) and generalized minimal residual (GMERS), are used in conjunction with a preconditioning technique that is simple to implement. The preconditioner is a subset of the full Jacobian matrix centered around the main diagonal but retaining the most fundamental axial coupling of the residual equations. A domain-renumbering scheme that enhances the overall algorithm performance is proposed on the basis of and analysis of the preconditioner. Comparison with the frontal elimination method demonstrates that the iterative method will be faster when the front width exceeds approximately 500. Techniques for the direct assembly f the problem into a compressed sparse row storage format are demonstrated. Elimination of fixed boundary conditions is shown to decrease the size of the matrix problem by up to 30%. Finally, fluid flow solutions obtained with the numerical technique are presented. These solutions reveal complex three-dimensional mixed convection fluid flow phenomena at low Reynolds numbers, including the reversal of the direction of longitudinal rolls in the presence of a strong recirculation in the entrance region of the channel.
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    URL: http://dx.doi.org/10.1002/fld.1650140705
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    A design method for turbomachinery blading in three-dimensional flow (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 179-197 
    Details
    ISSN: 0271-2091
    Keywords: Inverse problem ; Blade design ; Turbomachines ; Finite elements ; Aerodynamic design ; Subsonic 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 mixed spectral finite element scheme for the implementation of a design method for turbomachinery blading in three-dimensional subcritical compressible flow is presented. The method gives the detailed blade shape that would produce a prescribed tangential mean swirl schedule, given the hub and shroud profiles, the number of blades and their stacking position. After a presentation of the mathematical formulation of the design theory, the current numerical approach is described. It is then applied to the design of blading for radial inflow turbine impellers in three-dimensional flow.
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    URL: http://dx.doi.org/10.1002/fld.1650100205
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    Finite element solution of the Navier-Stokes equations by a velocity-vorticity method (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 461-475 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Navier-Stokes ; Velocity-vorticity ; 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 velocity-vorticity formulation of the Navier-Stokes equations is presented as an alternative to the primitive variables approach. The velocity components and the vorticity are solved for in a fully coupled manner using a Newton method. No artificial viscosity is required in this formulation. The pressure is updated by a method allowing natural imposition of boundary conditions. Incompressible and subsonic results are presented for two-dimensional laminar internal flows up to high Reynolds numbers.
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    URL: http://dx.doi.org/10.1002/fld.1650100408
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    A fractional-step Taylor-Galerkin method for unsteady incompressible flows (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 501-513 
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    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Time-dependent advection-dominated flows ; Taylor-Galerkin method ; 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: This paper describes the application of the Taylor-Galerkin method to the calculation of incompressible viscous flows. A finite element fractional-step method for the Navier-Stokes equations is combined with the Taylor-Galerkin method to achieve an accurate treatment of the convection part of the problem. A scheme of second-order accuracy in time for the non-linear convection written in non-conservative form is presented. Numerical results are provided to illustrate the quality of the computed transient solutions in two dimensions.
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    URL: http://dx.doi.org/10.1002/fld.1650110504
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    The application of finite element analysis to the solution of Stokes wave diffraction problems (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 343-367 
    Details
    ISSN: 0271-2091
    Keywords: Stokes waves ; Non-linear waves ; Second order waves ; Wave diffraction ; Finite elements ; Wave loading ; 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 based method of calculating non-linear wave loads on offshore structures in extreme seas is presented in this paper. The diffraction wave field is modelled using Stokes wave theory developed to second order. Wave loads and free surface elevations are obtained for fixed surface-piercing structures by solving a boundary value problem for the second-order velocity potential. Special attention has been given to the radiation condition for the second-order diffraction field. Results are presented for three test examples, the vertical cylinders of Kim and Yue and of Chakrabarti, and an elliptic cylinder. These results demonstrate that early problems with the application of second-order theory arising from inadequate radiation conditions have been overcome.
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    URL: http://dx.doi.org/10.1002/fld.1650120404
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    Finite element modelling of quasi-three-dimensional nearly horizontal flow (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 559-576 
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    ISSN: 0271-2091
    Keywords: Finite elements ; Quasi-three-dimensional ; Numerical oceanography ; 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 quasi-three-dimensional numerical model is presented and applied to some test problems with constant density. The numerical technique is based on a finite element formulation and the three-dimensional problem is factorized into one- and two-dimensional subproblems. The non-linear advection is treated by use of a weak formulation of the characteristics method and the equations are transformed to ‘sigma’ coordinates.
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    URL: http://dx.doi.org/10.1002/fld.1650120604
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    Laminar mixed convection in the entrance region of horizontal rectangular ducts (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 33-48 
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    ISSN: 0271-2091
    Keywords: Laminar mixed convection ; Parabolic flow ; 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: A generally applicable finite element procedure for the prediction of laminar mixed convection in horizontal straight ducts of arbitrary cross-section is presented. The procedure, based on the parabolized simplification of the complete Navier-Stokes equations and on the Boussinesq approximation of the buoyancy terms, is validated through comparisons of computed results with the available literature data for mixed convection in the entrance region of a rectangular duct of aspect ratio a=2. Uniform heating at different sides is considered as the thermal boundary condition, although the proposed formulation allows specification of most thermal boundary conditions of practical interest.
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    Three-dimensional adaptive finite element computations and applications to non-Newtonian fluids (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 145-165 
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    ISSN: 0271-2091
    Keywords: Finite elements ; Meshing ; Adaptivity ; Navier-Stokes ; Power law ; Error estimation ; 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 adaptive strategy for the finite element solution of three-dimensional viscous flow problems is defined and implemented. The solution strategy is based on an advancing front mesh generator making use of binary data structures for fast geometrical data handling. The error is estimated a posteriori with a residual-type bound. The error estimate is shown to exhibit proper convergence for tetrahedral elements. Its combination with the mesh generator and an interpolation scheme for unstructured meshes is shown to generate adaptive meshes and to reduce the solution cost for a given error level, as illustrated by the isothermal flow of a shear-thinning fluid.
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    URL: http://dx.doi.org/10.1002/fld.1650130203
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    A new decoupled finite element algorithm for viscoelastic flow. Part 1: Numerical algorithm and sample results (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 1367-1376 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Viscoelastic flow ; Convergence failure ; 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 an algorithm for two-dimensional Steady viscoelastic flow Simulation in which the Solution of the momentum and continuity equations is decoupled from that of the constitutive equations. The governing equations are discretized by the finite element method, with 3 × 3 element subdivision for the stress field approximation. Non-consistent Streamline upwinding is also used. Results are given for flow through a converging channel and through an abrupt planar 4:1 contraction.
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    URL: http://dx.doi.org/10.1002/fld.1650141107
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    A new decoupled finite element algorithm for viscoelastic flow. Part 2: Convergence properties of the algorithm (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 1377-1382 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Viscoelastic flow ; Convergence failure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present the results of some numerical experiments which were carried out in order to investigate the general characteristics of the algorithm described in Part I of this paper.
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    URL: http://dx.doi.org/10.1002/fld.1650141108
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    Adaptive h-refinement on 3D unstructured grids for transient problems (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 1407-1419 
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    ISSN: 0271-2091
    Keywords: Adaptive mesh refinement ; Finite elements ; Compressible flow ; Transient problems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An adaptive finite element scheme for transient problems is presented. The classic h-enrichment/coarsening is employed in conjunction with a tetrahedral finite element discretization in three dimensions. A mesh change is performed every n time steps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved by pre-sorting the elements and then performing the refinement/coarsening groupwise according to the case at hand. Further reductions in CPU requirements arc realized by optimizing the identification and sorting of elements for refinement and deletion. The developed technology has been used extensively for shock-shock and shock-object interaction runs in a production mode. A typical example of this class of problems is given.
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    Computer simulation of moist atmospheric convection with finite elements (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 217-230 
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    ISSN: 0271-2091
    Keywords: Finite elements ; Moist atmosphere ; Convection ; Computation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A computer simulation is made of cellular convection in a moist atmosphere in an endeavour to obtain a computer model which more closely approximates the observed modes of convection. A finite element Galerkin technique, with Taylor approximation and Crank-Nicolson, is employed and comparisons are made with the author's earlier finite element models of convection in an absolutely unstable atmosphere and with finite difference models. It is found that the inclusion of the moisture effects alters the structure of a cell to that of a narrow ascending region and a wider descending region with the former of larger velocities than the latter, and also alters the preferred mode of convection by increasing the aspect ratio. This more closely resembles that which is observed in the atmosphere.
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    Finite element modelling of sheared flow effects on the radiation characteristics of acoustic sources in a circular duct (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 613-627 
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    ISSN: 0271-2091
    Keywords: Finite elements ; Aeroacoustics ; Propellers ; Sheared 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 recent interest in propeller noise generation, stimulated by development of new propeller types for commerical propjets, has generated a need for the ability of measure the noise characteristics of propellers. However, wind tunnel noise measurements are affected by reflections from the wind tunnel walls. Computer codes predicting the free-field noise of a propeller and its noise field in a circular wind tunnel allow validating the use of wind tunnel measurements to predict free-field noise characteristics. A wind tunnel contains flow which is uniform in the duct axial direction, but can vary in the radial direction. It can be shown that a third-order differential equation governs the acoustic pressure field for such a duct containing radially sheared subsonic flow. This third-order problem is then posed as a coupled pair of equations which are second-order in terms of acoustic density and first-order in terms of an artificial variable which represents the effects of the flow being sheared. It is shown that this form of the problem allows a natural extension of the existing numerical solution techniques for non-sheared flow. The sheared flow problem is presented, and a finite element method is developed to yield a solution for propeller-type acoustic forces. The finite element code and method are refined with numerical experiments, and results are presented for a specific propeller and duct geometry. Good agreement is shown between this method and an alternate approach to the sheared flow problem using a piecewise constant representation of the velocity in the boundary layer. This validates both the numerical methods.
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    Non-symmetric CG-like schemes and the finite element solution of the advection-dispersion equation (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 955-974 
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    ISSN: 0271-2091
    Keywords: Advection-dispersion equation ; Finite elements ; Iterative methods ; Non-symmetric linear systems ; Conjugate gradients ; 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: Seven leading iterative methods for non-symmetric linear systems (GMRES, BCG, QMR, CGS, Bi-CGSTAB, TFQMR and CGNR) are compared in the specific context of solving the advection-dispersion equation by a classic approach: The space derivatives are approximated by linear finite elements while an implicit scheme is used to integrate the time derivatives. Convergence formulas that predict the behaviour of the iterative methods as a function of the discretization parameters are developed and validated by experiments. It is shown that all methods converge nicely when the coefficent matrix of the linear system is close to normal and the finite element approximation of the advection-dispersion equation yields accurate results.
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    A least squares finite element method for viscoelastic fluid flow problems (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 943-953 
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    ISSN: 0271-2091
    Keywords: Viscoelastic ; Least squares ; 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: Viscoelastic flows remain a demanding class of problems for approximate analysis, particularly at increasing Weissenberg numbers. Part of the difficulty stems from the convective behavior and in the treatment of the stress field as a primary unknown. This latter aspect has led to the use of higher-order piecewise approximations for the stress approximation spaces in recent finite element research. The computational complexity of the discretized problem is increased significantly by this approach but at present it appears the most viable technique for solving these problems. Motivated by recent success in treating mixed systems and convective problems, we formulate here a least squares finite element method for the viscoelastic flow problem. Numerical experiments are conducted to test the method and examine its strengths and limitations. Some difficulties and open issues are identified through the numerical experiments. We consider the use of high degree elements (p refinement) to improve performance and accuracy.
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    Optimal design of spiral casing tongue and wicket gate angle by decomposition method (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 995-1002 
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    ISSN: 0271-2091
    Keywords: Finite elements ; Turbomachinery flow ; Optimal design ; Decomposition method ; Potential 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 method of optimal design of Francis turbine tongue and wicket gate angle for given spiral casing is proposed. The potential flow in the doubly connected domain is decomposed into basic and circulation flows. The intensity of circulation is then calculated by the least-squares method minimizing the error function equal to the sum of squares of differences between given and calculated circumferential velocities in the outflow boundary nodes. It is shown that the error function has a sharp minimum, which qualifies the proposed method as well defined. For given numerical example, the variations in the outflow velocity angles are much smaller for optimal than for already used non-optimal design. A finite element method is used, with originally developed pre- and post-processor and frontal solver suited for personal computers.
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    The influence of normal flow boundary conditions on spurious modes in finite element solutions to the shallow water equations (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 1021-1060 
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    ISSN: 0271-2091
    Keywords: Finite elements ; Shallow water equations ; Boundary conditions ; Dispersion analysis ; Spurious modes ; Wave equation ; Primitive 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: Finite element solutions of the primitive equation (PE) form of the shallow water equations are notorious for the severe spurious 2Δx modes which appear. Wave equation (WE) solutions do not exhibit these numerical modes. In this paper we show that the severe spurious modes in PE solutions are strongly influenced by essential normal flow boundary conditions in the coupled continuity-momentum system of equations. This is demonstrated through numerical examples that avoid the use of essential normal flow boundary conditions either by specifying elevation values over the entire boundary or by implementing natural flow boundary conditions in the weak weighted residual form of the continuity equation. Results from a series of convergence tests show that PE solutions are of nearly the same quality as WE solutions when spurious modes are suppressed by alternative specification of the boundary conditions. Network intercomparisons indicate that varying nodal support does not excite spurious modes in a solution, although it does enhance the spurious modes introduced when an essential normal flow boundary condition is used.Dispersion analysis of discrete equations for interior and boundary nodes offers an explanation of the observed solution behaviour. For certain PE algorithms a mixed situation can arise where the boundary nodes exhibit a monotonic (noise-free) dispersion relationship and the interior nodes exhibit a folded (noisy) dispersion relationship. We have found that the mixed situation occurs when all boundary nodes are specified elevation nodes (which are enforced as essential conditions in the continuity equation) or when specified flow boundary nodes are treated as natural boundary conditions in the continuity equation. In either case the effect is to generate a solution that is essentially free of noise. Apparently, the monotonic dispersion behaviour at the boundaries suppresses the otherwise noisy behaviour caused by the folded dispersion relation on the interior.
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    Finite element solution of the streamfunction-vorticity equations for incompressible two-dimensional flows (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 513-525 
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    ISSN: 0271-2091
    Keywords: Finite elements ; Incompressible viscous flow ; Streamfunction-vorticity ; Vorticity boundary conditions ; 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 streamfunction-vorticity equations for incompressible two-dimensional flows are uncoupled and solved in sequence by the finite element method. The vorticity at no-slip boundaries is evaluated in the framework of the streamfunction equation. The resulting scheme achieves convergence, even for very high values of the Reynolds number, without the traditional need for upwinding. The stability and accuracy of the approach are demonstrated by the solution of two well-known benchmark problems: flow in a lid-driven cavity at Re ≤ 10,000 and flow over a backward-facing step at Re = 800.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650190605
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    Finite element analysis of confined turbulent swirling flows (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 697-717 
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    ISSN: 0271-2091
    Keywords: Finite elements ; Turbulent swirling flows ; Algebraic stress model ; Particle motion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The finite element method is applied to incompressible and statistically steady confined turbulent swirling flows. A velocity-pressure formulation is employed. The momentum and continuity equations are solved using a segregated algorithm. Two turbulence models, namely the standard κ-ε model and the algebraic stress model, are considered. It is shown that the algebraic stress model leads to significantly more accurate results in swirling flows compared to the κ-ε model. A novel way of implementing the algebraic stress model is presented in which the stresses are coupled to the Navier-Stokes equations in such a way that they ‘correct’ the effective viscosity hypothesis. This formulation seems to provide a convenient approach for finite elements. In deriving the discretization equations, a streamline-upwind/Petrov-Galerkin method is employed. Comparisons performed between various upwind schemes show that the numerical solution may be substantially affected by the particular upwind procedure used. The analysis is extended to the prediction of particle motion in turbulent swirling flow fields. Here the fluid turbulence is modelled adopting a stochastic approach. The influence of turbulence modelling on particle movement is investigated.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110602
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  • 40
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    The integrated singular basis function method for the stick-slip and the die-swell problems (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 1251-1265 
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    ISSN: 0271-2091
    Keywords: Singular basis functions ; Finite elements ; Stick-slip problem ; Die-swell problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We further develop a new singular finite element method, the integrated singular basis function method (ISBFM), for the solution of Newtonian flow problems with stress singularities. The ISBFM is based on the direct subtraction of the leading local solution terms from the governing equations and boundary conditions of the original problem, followed by a double integration by parts applied to those integrals with singular contributions. The method is applied to the stick-slip and the die-swell problems and improves the accuracy of the numerical results in both cases. In the case of the die-swell problem it considerably accelerates the convergence of the free surface profile with mesh refinement. The advantages and disadvantages of the ISBFM when compared to other singular methods are also discussed.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650131005
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  • 41
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    Transient finite element method for calculating steady state three-dimensional free surfaces (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 343-360 
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    ISSN: 0271-2091
    Keywords: Free surfaces ; Extrusion ; Conjugate gradients ; Finite elements ; Three-dimensional free surfaces ; 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 order to reduce the cost of large three-dimensional calculations of steady state free surfaces, we have combined a time-dependent approach, a decoupling algorithm and a conjugate gradient solver along the lines introduced earlier by Gresho and Chan. The free surface is calculated separately by applying the kinematic condition to a number of faces defined on the undeformed surface. For the pseudo-time-marching technique we show that it is economical to adopt different time steps for the free surface calculation and the other fields. The accuracy of the method is tested on the well-known circular die problem; the method is then used to reveal the effects of inertia and shear thinning on square and rectangular dies.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650140307
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    Calculation of quasi-three-dimensional incompressible viscous flows by the finite element method (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 953-966 
    Details
    ISSN: 0271-2091
    Keywords: Curvilinear co-ordinate system ; Incompressible viscous flow ; Finite elements ; Penalization and reduced integration ; Streamline upwind artificial viscosity ; Algebraic model 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: This paper discusses the calculation of quasi-three-dimensional incompressible viscous flow by FEM. The Reynolds-averaged Navier-Stokes equations are solved in curvilinear co-ordinates by the reduced integration and penalty method (RIP). Streamline upwind artificial viscosity (SUAV) and the Baldwin-Lomax algebraic model of turbulence are used. Time discretization is by the general implicit θ-method.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650161102
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  • 43
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    A finite element solution of the time-dependent incompressible Navier-Stokes equations using a modified velocity correction method (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 349-364 
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    ISSN: 0271-2091
    Keywords: Finite elements ; Velocity correction method ; Flow past a cylinder ; Navier-Stokes 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: A finite element solution of the two-dimensional incompressible Navier-Stokes equations has been developed. The present method is a modified velocity correction approach. First an intermediate velocity is calculated, and then this is corrected by the pressure gradient which is the solution of a Poisson equation derived from the continuity equation. The novelty, in this paper, is that a second-order Runge-Kutta method for time integration has been used. Discretization in space is carried out by the Galerkin weighted residual method. The solution is in terms of primitive variables, which are approximated by polynomial basis functions defined on three-noded, isoparametric triangular elements. To demonstrate the present method, two examples are provided. Results from the first example, the driven cavity flow problem, are compared with previous works. Results from the second example, uniform flow past a cylinder, are compared with experimental data.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170502
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    A monotone streamline upwind method for quadratic finite elementsThis study was funded by the Turbomachinery Research Consortium, contract number 32519-15190 (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 463-475 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Streamline upwind ; Quadratic 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: A direct streamline upwind method has been developed for convection-dominated flow problems utilizing quadratic elements. The approach presented retains the curve-sidedness feature offered by these elements. This facilitates the use of boundary conforming elements in domains that possess extreme curvature such as turbomachinery bladed components, for which the method is particularly suited. Three test cases are solved to evaluate the stability and diffusive characteristics of the numerical solution. The results presented clearly demonstrate that the proposed method does not exhibit any non-physical spatial oscillations, nor does it suffer from the traditional problem of excessive numerical diffusion.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170603
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