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  • Articles  (61)
  • Finite elements  (61)
  • Wiley-Blackwell  (61)
  • Nature Publishing Group (NPG)
  • Springer Science + Business Media
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (56)
  • Technology  (4)
  • Geosciences  (1)
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  • Articles  (61)
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  • Wiley-Blackwell  (61)
  • Nature Publishing Group (NPG)
  • Springer Science + Business Media
  • Springer  (15)
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  • 1
    Electronic Resource
    Electronic Resource
    Preconditioned conjugate gradients for solving the transient Boussinesq equations in three-dimensional geometries (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 283-303 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Transient flow ; Three-dimensional flow ; Natural convection ; Incomplete ; Choleski conjugate gradients ; Iterative solver ; Vectorization ; Crystal growth ; Gallium arsenide ; 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 we present a new version of the ‘modified finite element method’ (MFEM) presented by Gresho, Chan, Lee and Upson.1 The main modification of the original algorithm is the introduction of a cost-effective and memory-saving iterative solver for the discretized Poisson equation for the pressure. The vectorization of the preconditioner has been especially considered. For low Prandtl number problems we also split the advection-diffusion operator of the energy equation into explicit and implicit parts. In that sense the present approach is related to the recent implicitization of the diffusive terms introduced by Gresho and Chan2 and by Gresho.3 The algorithm is applied to the study of buoyancy-driven flow oscillations occuring in a horizontal crucible of molten metal under the action of a horizontal temperature gradient.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080303
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  • 2
    Electronic Resource
    Electronic Resource
    Conjugate gradient methods and ILU preconditioning of non-symmetric matrix systems with arbitrary sparsity patterns (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 213-233 
    Details
    ISSN: 0271-2091
    Keywords: Preconditioning ; Conjugate gradients ; Non-symmetric matrices ; Finite elements ; Convective 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: Preconditioning techniques based on incomplete Gaussian elimination for large, sparse, non-symmetric matrix systems are described. A certain level of fill-in may be specified in the incomplete factorizations. All methods considered may be applied to matrices with arbitrary sparsity patterns, for instance those associated with the general preprocessor algorithms or adaptive mesh techniques. The preconditioners have been combined with five conjugate gradient-like methods and tested on finite element discretized scalar convection-diffusion equations in 2D and 3D. It is found from numerical experiments that an amount of fill-in corresponding to about 50% of the number of original non-zero matrix entries is the optimal choice for this class of preconditioners. The preconditioners show almost no sensitivity to grid distortion. In problems with significantly variable coefficients or anisotropy the preconditioners stabilize the basic iterative schemes in addition to reducing the computational work substantially, mostly by more than 90%. The modified preconditioning technique, where fill-in is added on the main diagonal, performs in general better than the standard incomplete LU factorization, but is inferior to the latter in 3D problems and for matrix systems with complicated sparsity patterns.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090207
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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    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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  • 9
    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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  • 10
    Electronic Resource
    Electronic Resource
    A multiblock Navier-Stokes algorithm using equal-order quadratic finite elements (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 169-185 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Multiblock ; Quadratic elements ; Equal-order ; 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 multiblock pressure-based finite element algorithm has been developed. This methodology implements quadratic interpolation for both the elemental velocity and pressure fields. A direct streamline upwinding scheme previously developedby the authors is used to model the non-linear inertia effects. Details of the algorithm and its multiblock foundation are provided along with validating test cases. The results presented clearly demonstrate the accuracy of this new approach and the differences in the pressure field for an element using quadratic versus the traditional bi linear approximation of the pressure field.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650200206
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